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Quantum Thinking","How quantum makes a departure from classical mechanics.",3,[37,146,227],{"id":38,"data":39,"type":25,"version":25,"maxContentLevel":35,"summaryPage":41,"introPage":50,"pages":58},"f04c30a4-e1ed-48e5-957f-c2b1ac6e205a",{"type":25,"title":40},"The Foundations of Classical Physics",{"id":42,"data":43,"type":35,"maxContentLevel":35,"version":24},"a220c93f-a305-4cc3-8cce-e63072570445",{"type":35,"title":44,"summary":45},"The Foundations of Classical Physics summary",[46,47,48,49],"At the turn of the 20th century, scientists thought they had nature all figured out","Newton's prism experiments showed white light is made of seven colors","Newton's theory said light is tiny particles called corpuscles","Newton's theory was wrong; light actually moves slower in denser materials",{"id":51,"data":52,"type":53,"maxContentLevel":35,"version":24},"b6b4db18-80e4-481b-a5f1-57a9687d331f",{"type":53,"title":54,"intro":55},10,"The Foundations of Classical Physics intro",[56,57],"What did Newton's experiments with prisms reveal about sunlight?","Why did Newton's theory of light fail to explain refraction correctly?",[59,76,103,119],{"id":60,"data":61,"type":24,"maxContentLevel":35,"version":25,"reviews":65},"56c0f8a1-eaa3-471f-b059-739e8387718b",{"type":24,"title":62,"markdownContent":63,"audioMediaId":64},"The Foundations of Classical Physics page 1","At the turn of the twentieth century, scientists were pleased with themselves. After centuries of progress by the likes of Galileo and Isaac Newton, there was a strong belief that the most fundamental principles of nature were finally understood.\n\n![Graph](image://0924ccff-bb5c-4a90-b6ce-9ca72d6dd054 \"Sir Isaac Newton. Image: See page for author, CC BY 4.0 \u003Chttps://creativecommons.org/licenses/by/4.0>, via Wikimedia Commons\")\n\nFor example, the motion of all sorts of bodies from falling apples to the planets orbiting our Sun had been fairly accurately described by the laws of ‘classical physics’. Yet their confidence was short-lived, as it soon transpired that not all physical phenomena could be explained within this simplistic framework. Brand new physics and ways of thinking were the only way forward.\n\n![Graph](image://9c7307ab-7f46-4d5d-b2b8-b5083c307d4a \"Newton's laws were a framework for explaining almost everything. Image: Public domain, jarmoluk via Pixabay. \")","9d9c8100-6375-4686-9e9c-4ed7bf08291f",[66],{"id":67,"data":68,"type":69,"version":24,"maxContentLevel":35},"12941444-93a9-46a5-823e-46100158b473",{"type":69,"reviewType":25,"spacingBehaviour":24,"binaryQuestion":70,"binaryCorrect":72,"binaryIncorrect":74},11,[71],"Classical physics can describe the movement of all known bodies in the universe.",[73],"FALSE",[75],"TRUE",{"id":77,"data":78,"type":24,"maxContentLevel":35,"version":25,"reviews":82},"8bae3fc1-d6e9-4f12-9239-c9649b4fe61e",{"type":24,"title":79,"markdownContent":80,"audioMediaId":81},"The Foundations of Classical Physics page 2","In this introductory tile, we will cover the most problematic phenomenon, which ultimately sparked the ‘Quantum Revolution’ in thinking as the true nature of light was laid bare. But before getting there, let us set the scene by exploring how scientists viewed the world up until everything changed.\n\nIn the seventeenth century, there was widespread debate about the fundamental nature of light. In the 1660s, Isaac Newton obsessively studied it by conducting experiments with glass prisms and sunlight.\n\n![Graph](image://d65c59a3-e05c-467f-b282-d2b564272743 \"Light refracted through a prism. Image: Public domain.\")\n\nIn the process, he scientifically established the ‘visible spectrum’ of a rainbow, demonstrating that everyday white light from the Sun is composed of seven distinct colors. The light dispersed due to ‘refraction’, the redirection of a wave as it passes from one medium to another.","f5cec837-3f1d-4e2e-b3e5-870859b0228e",[83,94],{"id":84,"data":85,"type":69,"version":24,"maxContentLevel":35},"8936ec85-2860-43b9-a09f-69aa0e46c92a",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":86,"multiChoiceCorrect":88,"multiChoiceIncorrect":90,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[87],"What sparked the 'Quantum Revolution' in thinking?",[89],"Discoveries about the true nature of light",[91,92,93],"The motion of bodies","The laws of classical physics","The confidence of scientists",{"id":95,"data":96,"type":69,"version":24,"maxContentLevel":35},"e629c78c-23c9-49ab-a2d4-693dbc07ba70",{"type":69,"reviewType":25,"spacingBehaviour":24,"binaryQuestion":97,"binaryCorrect":99,"binaryIncorrect":101},[98],"What scientific process did Isaac Newton discover when studying light with glass prisms and sunlight?",[100],"Refraction",[102],"Reflection",{"id":104,"data":105,"type":24,"maxContentLevel":35,"version":25,"reviews":109},"552f0232-77b6-450e-a7f4-08d48317aa05",{"type":24,"title":106,"markdownContent":107,"audioMediaId":108},"The Foundations of Classical Physics page 3","Light travels more slowly in denser materials, so the part of the wave which first hits the glass is slowed before the rest of the wave, which is still travelling at ‘normal’ speed through the air. This caused Newton’s light to bend or ‘refract’. Not that Newton understood this at the time, but since different colors of light have differing wavelengths, they travel at different speeds in glass and are refracted at ever so slightly different angles. The result? A dazzling spectrum!\n\nIt’s everywhere and immeasurably important to life, so what exactly is light? Newton contemplated this and theorized in 1704 that light is a spray of tiny particles of negligible mass called ‘corpuscles’, each moving in a straight line.\n\n![Graph](image://c577f4d3-5955-4a5b-b412-a885872e0df5 \"Light reflects from a polished floor. Image: Public domain via pxhere\")\n\nHis corpuscular theory of light attempted to explain light’s well-established properties of reflection and refraction. So why does light reflect, according to this theory? Using his trusty corpuscles, Newton equated the reflection of light to an elastic ball bouncing off a hard surface.","533787b0-69f5-46be-9816-2fabb3e8030b",[110],{"id":111,"data":112,"type":69,"version":24,"maxContentLevel":35},"3847e829-a1f8-4029-a5f2-111c55892b45",{"type":69,"reviewType":25,"spacingBehaviour":24,"binaryQuestion":113,"binaryCorrect":115,"binaryIncorrect":117},[114],"According to Newton's corpuscular theory of light, why does light reflect?",[116],"Tiny particles bounce off a surface",[118],"Light is attracted to refracting surfaces",{"id":120,"data":121,"type":24,"maxContentLevel":35,"version":25,"reviews":125},"383722b0-4082-4d2f-8a37-2fcaf3e20efb",{"type":24,"title":122,"markdownContent":123,"audioMediaId":124},"The Foundations of Classical Physics page 4","What about refraction? In Newton’s view, as corpuscles approach a refracting surface they become increasingly attracted to it and change direction, gaining speed as they enter the denser medium. Crucially, Newton’s theory was very wrong.\n\nFor starters, light actually moves slower in a denser medium. But that didn’t stop it from eclipsing the – slightly more correct – wave theory of light as the prevailing view of his time, in no small part due to his staggering reputation.","adc6a74a-c09d-4d69-93eb-aa62669a1b20",[126],{"id":127,"data":128,"type":69,"version":24,"maxContentLevel":35},"8236e354-e645-4544-9365-d73af2ae5cb2",{"type":69,"reviewType":35,"spacingBehaviour":24,"collapsingSiblings":129,"multiChoiceQuestion":133,"multiChoiceCorrect":135,"multiChoiceIncorrect":137,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6,"matchPairsQuestion":141,"matchPairsPairs":143},[130,131,132],"70ddacd9-7c0c-4fa6-898f-98b08da52fe6","79e94f33-1a24-4486-8c38-9203b02bc7d4","1355011f-22bf-4c0e-95be-36626ce1e082",[134],"Which of the following best describes the corpuscular theory?",[136],"Theory that light is a particle with mass",[138,139,140],"Fundamental to wave theory of light","Demonstrated by James Clerk Maxwell","Theory proposed by Max Planck",[142],"Match the pairs below:",[144],{"left":145,"right":136,"direction":35},"Corpuscular theory",{"id":147,"data":148,"type":25,"version":25,"maxContentLevel":35,"summaryPage":150,"introPage":159,"pages":166},"d7686a75-3b94-46a2-8965-c0162203b794",{"type":25,"title":149},"The Wave Theory and its Limitations",{"id":151,"data":152,"type":35,"maxContentLevel":35,"version":24},"94af0e93-1166-4858-a988-e74a7bf5def2",{"type":35,"title":153,"summary":154},"The Wave Theory and its Limitations summary",[155,156,157,158],"Huygens thought light was a wave in a mysterious substance called 'aether'","Huygens' Principle says each point on a wavefront creates new wavelets that interfere","Young's double-slit experiment showed light's wave nature with an interference pattern","Light's diffraction and interference proved it wasn't just particles",{"id":160,"data":161,"type":53,"maxContentLevel":35,"version":24},"01420613-1467-4a8f-9bd5-0c362a8fa4d3",{"type":53,"title":162,"intro":163},"The Wave Theory and its Limitations intro",[164,165],"What did Huygens' Principle explain about light?","How did Young's double-slit experiment prove light is a wave?",[167,181,211],{"id":168,"data":169,"type":24,"maxContentLevel":35,"version":25,"reviews":173},"88f8ec48-9881-4790-ad43-f25f232ff243",{"type":24,"title":170,"markdownContent":171,"audioMediaId":172},"The Wave Theory and its Limitations page 1","In the fierce debate over the fundamental nature of light, Newton was an ardent advocate for it being particle-like. But his Dutch contemporary, Christian Huygens, had put forward an entirely different idea in 1678. To Huygens, light was instead a wave-like disturbance in a mysterious, weightless, and all-encompassing substance known as the ‘aether'. It became very fashionable for scientists to believe that light propagated through and was mediated by this invisible aether.\n\n![Graph](image://bc30cb24-9e9a-4057-b075-0c6c997c85fb \"Christian Huygens. Image: Caspar Netscher, Public domain, via Wikimedia Commons\")\n\nIn fact, the concept of an aether lasted until at least the late 1800s and consumed a significant amount of resources along the way as every search for its existence proved fruitless. Huygens believed that this aether vibrated in the same direction as light waves, forming a wave itself as it carried the light onwards. He also incorrectly suggested that light was a ‘longitudinal wave’ just like sound waves. That is, a wave whose vibrations are back-and-forth along the direction of travel.","e3e0b991-dc90-4ece-9e05-090c887456a7",[174],{"id":175,"data":176,"type":69,"version":24,"maxContentLevel":35},"fec2f123-67d7-46d4-9a3f-7ef9a64e86d0",{"type":69,"reviewType":24,"spacingBehaviour":24,"activeRecallQuestion":177,"activeRecallAnswers":179},[178],"What did Christian Huygens propose as the medium through which light propagated?",[180],"Aether",{"id":182,"data":183,"type":24,"maxContentLevel":35,"version":25,"reviews":187},"f75a2283-2da2-4aad-bf4a-2042b38e2f35",{"type":24,"title":184,"markdownContent":185,"audioMediaId":186},"The Wave Theory and its Limitations page 2","In 1678, Huygens proposed a model of light where each point on a wavefront becomes a new source of spherical ‘wavelets’ expanding in every direction. These secondary wavelets then combine or ‘interfere’ with each other to determine the form of the overall wavefront at any later time. If the peak of one wavelet meets the lowest point or ‘trough’ of another, they cancel each other out in an example of ‘destructive interference’. Similarly, two peaks or troughs would sum up to form a larger wave via ‘constructive interference’.\n\n![Graph](image://b1ad629d-072f-46d5-837f-01c60653c33b \"Constructive interference (left), and destructive interference (right). Image: Haade, CC BY-SA 3.0, via Wikimedia Commons\")\n\nThis is ‘Huygens’ Principle’, and using it he was able to convincingly account for the laws of reflection and refraction, while also correctly predicting that light travels more slowly in a denser medium. Huygens’ model was critical in establishing a credible wave view of light rather than a particle one, but it still left a lot to be desired as a comprehensive theory…","c3b486ac-f58f-4921-8dc7-382d4ea38456",[188,200],{"id":130,"data":189,"type":69,"version":24,"maxContentLevel":35},{"type":69,"reviewType":35,"spacingBehaviour":24,"collapsingSiblings":190,"multiChoiceQuestion":191,"multiChoiceCorrect":193,"multiChoiceIncorrect":194,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6,"matchPairsQuestion":195,"matchPairsPairs":196},[127,131,132],[192],"Which of the following best describes interference (constructive and destructive)?",[138],[136,139,140],[142],[197],{"left":198,"right":199,"direction":35},"Interference (constructive and destructive)","Fundamental to wave theory of light.",{"id":201,"data":202,"type":69,"version":24,"maxContentLevel":35},"00943ce3-0e81-4e1f-813f-42cc90225076",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":203,"multiChoiceCorrect":205,"multiChoiceIncorrect":207,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[204],"What is the name of the model of light where light is made of tiny 'wavelets'?",[206],"Huygens’ Principle",[208,209,210],"The Wave Model","The Particle Model","The Reflection Model",{"id":212,"data":213,"type":24,"maxContentLevel":35,"version":25,"reviews":217},"ac3a014f-3ace-4cf6-8a8a-808cf8e683f1",{"type":24,"title":214,"markdownContent":215,"audioMediaId":216},"The Wave Theory and its Limitations page 3","Newton’s corpuscular theory triumphed despite the success of Huygens’ Principle in explaining observations in a far easier-to-visualise way. It wasn’t until 1801 that English physicist Thomas Young conducted his famous ‘double-slit experiment’, which ultimately led to the general acceptance of light as a wave. In his experiment, he shined light through two narrow, closely spaced vertical slits and observed the ‘interference pattern’ on the wall beyond.\n\n![Graph](image://7fad6267-219a-42f5-a92a-0b61a4d25f1a \"Waves defract through small openings in a wall. Image: Stannered, CC BY-SA 3.0 \u003Chttps://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons\")\n\nAll waves spread out and undergo ‘diffraction’ when they encounter an obstacle or opening. However, the opening must be comparable in size to the ‘wavelength’ in question for this effect to be observed. Since light has an extremely small wavelength, Young’s narrow slits worked like a charm in demonstrating the wave nature of light. Light coming through each slit diffracted and subsequently interfered to create a distinctive pattern of alternating bright and dark lines. Without the characteristic wave properties of diffraction and interference, the light would simply leave two lines on the screen.","c3f46ef4-2c25-4acf-80c1-a33874933401",[218],{"id":219,"data":220,"type":69,"version":24,"maxContentLevel":35},"c232ed88-d841-4e6f-8a6b-10ffa89d80da",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":221,"multiChoiceCorrect":223,"multiChoiceIncorrect":225,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[222],"What phenomenon did Thomas Young observe when he shone light through two narrow, closely spaced vertical slits?",[224],"Interference pattern",[226,100,102],"A single central peak",{"id":228,"data":229,"type":25,"version":25,"maxContentLevel":35,"summaryPage":231,"introPage":240,"pages":247},"93b63bdd-7880-4f49-a9ae-99857c7d9482",{"type":25,"title":230},"Electromagnetic Radiation and The Quantum Revolution",{"id":232,"data":233,"type":35,"maxContentLevel":35,"version":24},"cce28754-7773-4488-b309-747ab4dab006",{"type":35,"title":234,"summary":235},"Electromagnetic Radiation and The Quantum Revolution summary",[236,237,238,239],"Light is a type of electromagnetic radiation, part of a spectrum that includes X-rays, microwaves, and radio waves","James Clerk Maxwell showed that electric and magnetic fields are different forms of the same force, electromagnetism","Black bodies absorb all electromagnetic radiation and emit a distinctive black-body radiation curve","Max Planck introduced the idea that electromagnetic radiation is emitted in discrete packets called quanta",{"id":241,"data":242,"type":53,"maxContentLevel":35,"version":24},"cd9a4095-92d8-48f5-8a20-cc2607ef1fb8",{"type":53,"title":243,"intro":244},"Electromagnetic Radiation and The Quantum Revolution intro",[245,246],"What was the 'ultraviolet catastrophe'?","How did Max Planck's idea of 'quanta' change our understanding of black-body radiation?",[248,277,295,309,327],{"id":249,"data":250,"type":24,"maxContentLevel":35,"version":25,"reviews":254},"6302e468-4836-4264-8be3-1ded26f167eb",{"type":24,"title":251,"markdownContent":252,"audioMediaId":253},"Electromagnetic Radiation and The Quantum Revolution page 1","In the 1860s, light was understood as a form of ‘electromagnetic radiation’ occupying a small window of possible wavelengths in a far broader ‘electromagnetic spectrum’. Visible light sits between UV rays, which have a shorter wavelength, and infrared rays which have a longer wavelength. Other well-known examples of this radiation are X-rays, microwaves, and radio waves.\n\n![Graph](image://f546bbc0-d8d7-4c3e-b96a-fd5e75d6e790 \"Visible light. Image: Public domain via Pexels\")\n\nIn classical physics, electromagnetic waves are the result of coupled magnetic and electric fields oscillating perpendicularly to each other as well as the wave’s direction of travel. That is, they are ‘transverse’ waves, and not longitudinal as previously thought!\n\nIt was esteemed Scottish physicist James Clerk Maxwell who championed this ground-breaking work, which he used to demonstrate that electric and magnetic phenomena are merely different manifestations of the same fundamental force of the universe known as ‘electromagnetism’. He also proved in his famous ‘Maxwell’s Equations’, that all electromagnetic waves travel through a vacuum at the ‘speed of light’ – 3 × 10^8 metres per second.","2a248002-7659-4fe5-8c46-7ed751fa771e",[255,266],{"id":131,"data":256,"type":69,"version":24,"maxContentLevel":35},{"type":69,"reviewType":35,"spacingBehaviour":24,"collapsingSiblings":257,"multiChoiceQuestion":258,"multiChoiceCorrect":260,"multiChoiceIncorrect":261,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6,"matchPairsQuestion":262,"matchPairsPairs":263},[127,130,132],[259],"Which of the following best describes electromagnetism?",[139],[138,136,140],[142],[264],{"left":265,"right":139,"direction":35},"Electromagnetism",{"id":267,"data":268,"type":69,"version":24,"maxContentLevel":35},"6a5a3523-65ce-4624-8a51-06a7b22ecd9a",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":269,"multiChoiceCorrect":271,"multiChoiceIncorrect":273,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[270],"Who championed the ground-breaking work that demonstrated electric and magnetic phenomena are merely different manifestations of the same fundamental force of the universe?",[272],"James Clerk Maxwell",[274,275,276],"Albert Einstein","Isaac Newton","Stephen Hawking",{"id":278,"data":279,"type":24,"maxContentLevel":35,"version":25,"reviews":283},"97e3eaa3-52ab-442f-bf2a-3a961ec0ccf1",{"type":24,"title":280,"markdownContent":281,"audioMediaId":282},"Electromagnetic Radiation and The Quantum Revolution page 2","All objects or ‘bodies’ both emit and absorb infrared rays, an invisible form of electromagnetic radiation which we feel as heat. The hotter a body, the more infrared radiation it emits. Yet no known object in our universe can perfectly emit or absorb all radiation of every possible frequency across the electromagnetic spectrum. Some objects such as stars do, however, come approximately close to this definition and are therefore referred to as ‘black bodies’.\n\n![Graph](image://1c454037-b21c-496c-ab3b-d0adaef53ec6 \"A black body radiator. Image: Luminforum, CC BY 4.0, via Wikimedia Commons\")\n\nA black body is a hypothetical object which absorbs all electromagnetic radiation incident upon it, explaining why the name came about as every color of light is absorbed. A black body doesn’t just absorb, it emits too. This ‘black-body radiation’ – which has a very distinctive pattern when plotted as an ‘emission spectrum’ – is something we can experimentally detect from distant stars. Unfortunately, this pattern didn’t fit with and couldn’t be adequately described by the laws of classical physics…","a45e1196-4310-458d-8fb5-2cb711f1feb8",[284],{"id":285,"data":286,"type":69,"version":24,"maxContentLevel":35},"278d75ce-5238-4dff-9d1c-c781e9cf9c7a",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":287,"multiChoiceCorrect":289,"multiChoiceIncorrect":291,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[288],"What is the name given to objects that absorb and emit all radiation of every possible frequency across the electromagnetic spectrum?",[290],"Black body",[292,293,294],"White body","Grey body","Colored body",{"id":296,"data":297,"type":24,"maxContentLevel":35,"version":25,"reviews":301},"9c8dd68e-caf9-4902-b248-80de0be8c946",{"type":24,"title":298,"markdownContent":299,"audioMediaId":300},"Electromagnetic Radiation and The Quantum Revolution page 3","We can plot the approximate black-body radiation we observe from stars as a ‘black-body radiation curve’. These curves – which are temperature-dependent – tend to plot wavelength or frequency against a quantity called ‘spectral radiance’, which can be simply thought of as a measure of the amount or intensity of radiation emitted within each window of the electromagnetic spectrum. The hotter a black body is, the steeper and further to the left towards shorter wavelengths its peak, but the distinctive profile of the curve remains the same.\n\n![Graph](image://abff396a-632b-47cb-9924-9524ade13320 \"The black-body radiation curve. Image: Maxmath12, CC0, via Wikimedia Commons\")\n\nInterestingly, we can use these curves to deduce the temperature of a distant star using an equation known as ‘Wien’s Displacement Law’ which links the wavelength at the curve’s peak to the body’s temperature. What makes these curves so fiendish however is the fact that classical physics presented no way to explain them or derive them mathematically! It would require a completely novel set of ideas to set the record straight.","36bf4b10-26c4-4455-b681-19fa6580150d",[302],{"id":303,"data":304,"type":69,"version":24,"maxContentLevel":35},"0b1b131d-8cf6-4c68-83a8-6ab58844e693",{"type":69,"reviewType":28,"spacingBehaviour":24,"clozeQuestion":305,"clozeWords":307},[306],"We can use black-body radiation curves to deduce the temperature of a distant star using Wien's Displacement Law.",[308],"Wien",{"id":310,"data":311,"type":24,"maxContentLevel":35,"version":25,"reviews":315},"89a54cb9-4e2c-463a-8209-6cc3b57bd4a8",{"type":24,"title":312,"markdownContent":313,"audioMediaId":314},"Electromagnetic Radiation and The Quantum Revolution page 4","Still firmly in the classical era, the ‘Rayleigh-Jeans Law’ was conceived in the early twentieth century as an attempt to mathematically describe black-body radiation curves and match experimental findings.\n\n![Graph](image://75ee1dfa-b1fb-4ca2-abf6-0460152f4dc1 \"Rayleigh-Jeans Law. Geek3, CC BY-SA 4.0 \u003Chttps://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons\")\n\nTrouble is, this law agreed with experimental results at large wavelengths or low frequencies, but disagreed dramatically at short wavelengths or high frequencies. In fact, it was so hilariously wrong that it suggested that the energy output of an idealized black body would shoot up to infinity at wavelengths close to the ultraviolet region of the electromagnetic spectrum!\n\nThe ludicrous implications of this law are why the event was retrospectively dubbed the ‘ultraviolet catastrophe’. The reason for this huge error? The equation underpinning the law was derived through classical arguments and assumptions only. With this inescapable problem, the classical foundations began to crack and fall apart. If Newton and all the others were wrong, then what’s right? It was time for Max Planck to take a “quantum leap”.","326b5a23-fd69-4593-a9d3-cd19205e2d92",[316],{"id":317,"data":318,"type":69,"version":24,"maxContentLevel":35},"ae97d23b-decb-4eaa-a260-a3ceaad65049",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":319,"multiChoiceCorrect":321,"multiChoiceIncorrect":323,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[320],"Which law led to an error later dubbed the 'ultraviolet catastrophe'?",[322],"The Rayleigh-Jeans Law",[324,325,326],"The Planck Theory","The Wien Displacement Law","The Stefan-Boltzmann Law",{"id":328,"data":329,"type":24,"maxContentLevel":35,"version":25,"reviews":333},"84e22c70-dc1d-4d1c-97e0-adc19fbe507e",{"type":24,"title":330,"markdownContent":331,"audioMediaId":332},"Electromagnetic Radiation and The Quantum Revolution page 5","The “father of quantum physics”, German physicist Max Planck came to the rescue in 1900 by figuring out how to correctly describe the behavior of black bodies mathematically, across all wavelengths. His outlandish concept? He assumed that electromagnetic radiation could only be absorbed or emitted in discrete packets – or ‘quanta’ – of energy.\n\n![Graph](image://f0180b64-0f5a-4f7b-8df7-a38041557019 \"Max Planck. Image: Unknown author, credited to Transocean Berlin, Public domain, via Wikimedia Commons\")\n\nHe reasoned that the energy released by a black body originated from oscillations of its atoms, and that these oscillations – like those of a violin string – would have certain harmonic ‘modes’. Radiation is released when an atom switches between modes of oscillation, and so tends to have predictable wavelengths. At any given temperature, very small or large changes would be less common than those in the middle of the range, explaining why the distribution of emitted wavelengths forms the shape of the black-body radiation curve. Planck’s idea set the stage for the impending revolution, but it would require Albert Einstein to provide the next big step in ‘quantization’.","16215e0f-157c-473a-b900-2ea1dd553f47",[334,345],{"id":132,"data":335,"type":69,"version":24,"maxContentLevel":35},{"type":69,"reviewType":35,"spacingBehaviour":24,"collapsingSiblings":336,"multiChoiceQuestion":337,"multiChoiceCorrect":339,"multiChoiceIncorrect":340,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6,"matchPairsQuestion":341,"matchPairsPairs":342},[127,130,131],[338],"Which of the following best describes quantization?",[140],[138,136,139],[142],[343],{"left":344,"right":140,"direction":35},"Quantization",{"id":346,"data":347,"type":69,"version":24,"maxContentLevel":35},"88e95f33-a463-4cf0-9fcb-863a257e2fb9",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":348,"multiChoiceCorrect":350,"multiChoiceIncorrect":352,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[349],"Who is credited as the \"father of quantum physics\" for his work on the behavior of black bodies mathematically?",[351],"Max Planck",[274,353,354],"Werner Heisenberg","Niels Bohr",{"id":356,"data":357,"type":27,"maxContentLevel":35,"version":25,"orbs":360},"6a98234d-dc35-417a-b458-a7eff6475be9",{"type":27,"title":358,"tagline":359},"Einstein’s Quantum Theory of Light","How Einstein's theory of light shaped quantum theory.",[361,464,528],{"id":362,"data":363,"type":25,"version":25,"maxContentLevel":35,"summaryPage":365,"introPage":374,"pages":381},"3aacc511-3490-454d-be1e-6503b6f3e544",{"type":25,"title":364},"Electromagnetism and the Photoelectric Effect",{"id":366,"data":367,"type":35,"maxContentLevel":35,"version":24},"3835364e-42f9-42c5-87d1-8d7a3bd2658e",{"type":35,"title":368,"summary":369},"Electromagnetism and the Photoelectric Effect summary",[370,371,372,373],"Heinrich Hertz discovered the photoelectric effect when UV light made sparks jump across a gap","JJ Thomson found electrons using cathode ray tubes, leading to the 'plum pudding model' of the atom","Philipp Lenard showed that light can eject electrons from metal, but classical physics couldn't explain it","Albert Einstein proposed that light is made of photons, introducing wave-particle duality",{"id":375,"data":376,"type":53,"maxContentLevel":35,"version":24},"2bd76257-6162-43c6-b66e-89df8ccfe20e",{"type":53,"title":377,"intro":378},"Electromagnetism and the Photoelectric Effect intro",[379,380],"What did Heinrich Hertz accidentally discover while experimenting with a spark gap?","How did Einstein's theory of light challenge the classical wave theory?",[382,419,433,450],{"id":383,"data":384,"type":24,"maxContentLevel":35,"version":25,"reviews":388},"a4de6406-6fa9-4d33-afac-9fca42faa6db",{"type":24,"title":385,"markdownContent":386,"audioMediaId":387},"Electromagnetism and the Photoelectric Effect page 1","Maxwell’s theory predicted the existence of electromagnetic waves, stating that light itself was one such wave. This greatly excited fellow scientists, who sought to prove his assertions experimentally. In 1887, German physicist Heinrich Hertz was toying around with a ‘spark gap’ when he noticed something peculiar. Hertz’s set-up was a pair of conducting electrodes separated by a tiny gap across which a spark was generated upon detection of electromagnetic waves. After covering his apparatus in a dark box to see the sparks better, he noticed that a glass box decreased the spark length whereas a quartz box had no effect.\n\n![Graph](image://a5d09d39-8914-473f-baa0-af5259337994 \"The photoelectric effect. Image: Ponor, CC BY-SA 4.0, via Wikimedia Commons\")\n\nLittle did he know that it was ultraviolet radiation which was interacting with the electrons in the current and supplying them with energy to jump across the gap. Hertz couldn’t explain his findings, but it soon became clear that the phenomenon occurred because glass absorbs UV and quartz doesn’t. He had accidentally witnessed the first example of the ‘Photoelectric Effect’.","b0861eb0-386c-48e0-95d0-a4f9dbe96ba3",[389,408],{"id":390,"data":391,"type":69,"version":24,"maxContentLevel":35},"49892bdb-7b79-4e10-91a7-ebbea9edb126",{"type":69,"reviewType":35,"spacingBehaviour":24,"collapsingSiblings":392,"multiChoiceQuestion":396,"multiChoiceCorrect":398,"multiChoiceIncorrect":400,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6,"matchPairsQuestion":404,"matchPairsPairs":405},[393,394,395],"740c625a-2bd5-476f-8db7-92377b5a7136","41cecd66-f60f-4395-b867-524a6cbb273b","4642f563-2780-4715-8042-8835a24dadfe",[397],"Which of the following best describes the Photoelectric Effect?",[399],"The phenomenon of electrons being emitted from a material when light shines on it",[401,402,403],"A form of energy that is propagated as a wave","The energy needed to remove an electron away from a metal","Developed by John Dalton, further refined by other scientists",[142],[406],{"left":407,"right":399,"direction":35},"Photoelectric Effect",{"id":409,"data":410,"type":69,"version":24,"maxContentLevel":35},"ddae544f-bd00-4afb-a8c1-f958b0f29045",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":411,"multiChoiceCorrect":413,"multiChoiceIncorrect":415,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[412],"What phenomenon was decreased when using a glass box in Hertz's experiment?",[414],"Spark length",[416,417,418],"Quantum length","Nuclear length","Electron length",{"id":420,"data":421,"type":24,"maxContentLevel":35,"version":25,"reviews":425},"08c9c500-e096-4d3a-a5be-0e21ee326c60",{"type":24,"title":422,"markdownContent":423,"audioMediaId":424},"Electromagnetism and the Photoelectric Effect page 2","In 1897, British physicist J.J. Thomson made one of the most significant discoveries in scientific history, the electron. Using cathode ray tubes, he demonstrated that all atoms contain tiny, negatively charged particles. The electrons he identified inspired Thomson to conceive his ‘plum pudding model’ of the atom, in which negatively charged “plums” were embedded within a positively charged “pudding”.\n\n![Graph](image://32395b01-1dff-4e9d-9e69-0b893b5241f3 \"J.J. Thomson. Image: Bain News Service, publisher, Public domain, via Wikimedia Commons\")\n\nBefore moving on, it’s worth examining what constitutes a metal. At the atomic level, a metal is a closely packed lattice of metal ‘ions’, which are simply atoms with a net positive or negative charge.\n\nThe structure of a solid metal consists of charged ions because each atom has donated at least one of its outermost electrons to form a “sea” of ‘delocalised electrons’. The electrostatic force of attraction between the metal ions and delocalised electrons is what imparts metals with their rigidity and strength. In theory, if given enough energy, these delocalised electrons could become liberated from the metal’s surface.","4719a167-708a-47c6-9757-7754ea890f49",[426],{"id":427,"data":428,"type":69,"version":24,"maxContentLevel":35},"e768bfef-9443-4a05-b3fe-2ae5b2df2d8d",{"type":69,"reviewType":28,"spacingBehaviour":24,"clozeQuestion":429,"clozeWords":431},[430],"Metals are closely packed lattices of metal ions and delocalized electrons.",[432],"delocalized",{"id":434,"data":435,"type":24,"maxContentLevel":35,"version":25,"reviews":439},"c56a3ef4-b0b5-49ce-89d0-c294ae33151a",{"type":24,"title":436,"markdownContent":437,"audioMediaId":438},"Electromagnetism and the Photoelectric Effect page 3","In 1902, another German physicist Philipp Lenard demonstrated that illuminating a metal surface with light or another form of electromagnetic radiation could cause electrons in the material to be expelled or ‘liberated’.\n\nThe electrons absorbed incoming ‘radiant energy’, allowing them to break free from the electrostatic forces binding them to the metallic ions. Unfortunately, this ‘photoelectric effect’ represented an interaction between light and matter which couldn’t be explained by classical physics, or by viewing light as an electromagnetic wave.\n\n![Graph](image://ce7c6a71-8746-4f6c-98b8-368ff97e9bf1 \"Philip Lennard. Image: Public domain, via Wikimedia Commons\")\n\nIf light were only a wave, the energy of the released electrons would depend on the light source’s intensity. Except it didn’t! It was actually dependent on the light’s frequency, which according to wave theory should have zero effect. The intensity instead determined the number of electrons released from the metal’s surface. What was made clear is that classical ideas and the wave picture of light simply weren’t cutting it in explaining this puzzling effect.","03cf278d-91ff-474c-b5fd-e3d569988cd8",[440],{"id":441,"data":442,"type":69,"version":24,"maxContentLevel":35},"0d1c0748-ce6f-4983-b353-2f1833005d5a",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":443,"multiChoiceCorrect":445,"multiChoiceIncorrect":447,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[444],"What phenomenon could not be explained by classical physics or the wave picture of light?",[446],"The Photoelectric Effect",[358,448,449],"The Bohr Photoelectric Effect","The Heisenberg Principle",{"id":451,"data":452,"type":24,"maxContentLevel":35,"version":25,"reviews":456},"821ee30c-c74f-4ce8-984b-4b1f1605b00f",{"type":24,"title":453,"markdownContent":454,"audioMediaId":455},"Electromagnetism and the Photoelectric Effect page 4","Albert Einstein made his mark in 1905 by formulating a startling new theory of light. He did this by expanding upon Planck’s idea of quantization to conjecture that light itself is made up of discrete packets or ‘quanta’. Each of these quanta contained a fixed amount of energy directly related to the light’s frequency. Their name? Photons!\n\nThis is where things took a strange turn, as Einstein was not only suggesting that light is composed of what are essentially particles, but that it also possesses wave-like properties such as frequency and therefore also an effective ‘wavelength’.\n\n![Graph](image://778408f4-026a-4335-93f9-001c6b88c374 \"Albert Einstein. Image: Photograph by Oren Jack Turner, Princeton, N.J., Public domain, via Wikimedia Commons\")\n\nIt became apparent from that point onwards that light isn’t fully described by a wave or a particle. This was the first example of ‘wave-particle duality’, a prominent concept in quantum mechanics stating that every particle may be described as either a particle or a wave. Neither description alone nor their classical interpretations are sufficient to fully describe the behaviour of any quantum system.","99e49045-1e49-4d10-93e9-1846dcdd655c",[457],{"id":458,"data":459,"type":69,"version":24,"maxContentLevel":35},"0f36222f-82c0-42b8-9a46-0f2c5357e02c",{"type":69,"reviewType":24,"spacingBehaviour":24,"activeRecallQuestion":460,"activeRecallAnswers":462},[461],"What is the name of the discrete packets of energy that make up light?",[463],"Photons",{"id":465,"data":466,"type":25,"version":25,"maxContentLevel":35,"summaryPage":468,"introPage":477,"pages":484},"fa77ca64-5266-4c0a-b81f-3eafabb6f7f5",{"type":25,"title":467},"Understanding Photons",{"id":469,"data":470,"type":35,"maxContentLevel":35,"version":24},"80f55c85-e5b5-401e-83d0-685219c9b5ad",{"type":35,"title":471,"summary":472},"Understanding Photons summary",[473,474,475,476],"Light energy travels in discrete units called photons","Photons move at light speed, are neutral, and have zero mass","The energy of a photon is tied to its frequency: higher frequency means more energy","Planck's constant links photon energy to frequency: E = h × f",{"id":478,"data":479,"type":53,"maxContentLevel":35,"version":24},"b7ce4686-fa3f-4f47-ac09-f396ce5f4f3f",{"type":53,"title":480,"intro":481},"Understanding Photons intro",[482,483],"How does the energy of a photon relate to its frequency?","What happens to photons when they encounter matter?",[485,514],{"id":486,"data":487,"type":24,"maxContentLevel":35,"version":24,"reviews":491},"ccd9cb42-3d9e-45f7-b6ac-604cee8c23b7",{"type":24,"title":488,"markdownContent":489,"audioMediaId":490},"Understanding Photons page 1","Like all forms of electromagnetic radiation, light transports energy across space. Einstein was able to convincingly show that the energy transmitted by light arrives at a receiver not continuously but in discrete units called ‘photons’. Instead of the energy being continuously distributed over a wavefront, it was now carried in neat, quantized packages. Therefore, we can view photons as effective “particles” of light! So what do we know about them?\n\nFollowing on from Maxwell’s work, we know that photons always move at the speed of light. We also know that they are electrically neutral and have zero mass, but still carry an energy proportional to the light’s frequency. The higher the frequency or shorter the wavelength, the more energetic the photon. Lastly, photons can be created or destroyed. When a source emits electromagnetic waves, photons are created. When photons encounter matter, they can be absorbed and transfer their energy to the atoms and molecules.","6ed240bd-3bdb-490e-badc-d5f127384908",[492,503],{"id":393,"data":493,"type":69,"version":24,"maxContentLevel":35},{"type":69,"reviewType":35,"spacingBehaviour":24,"collapsingSiblings":494,"multiChoiceQuestion":495,"multiChoiceCorrect":497,"multiChoiceIncorrect":498,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6,"matchPairsQuestion":499,"matchPairsPairs":500},[390,394,395],[496],"Which of the following best describes electromagnetic radiation?",[401],[399,402,403],[142],[501],{"left":502,"right":401,"direction":35},"Electromagnetic radiation",{"id":504,"data":505,"type":69,"version":24,"maxContentLevel":35},"af326fb0-5abc-4bd0-859f-b06ba128f151",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":506,"multiChoiceCorrect":508,"multiChoiceIncorrect":510,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[507],"What is the speed that photons always move at?",[509],"The speed of light",[511,512,513],"The speed of sound","The speed of electricity","The speed of terminal velocity",{"id":515,"data":516,"type":24,"maxContentLevel":35,"version":25,"reviews":520},"f1d4e7ce-69e3-4c87-9ee7-1580964b3914",{"type":24,"title":517,"markdownContent":518,"audioMediaId":519},"Understanding Photons page 2","When Planck derived an equation that described black body radiation curves with tremendous accuracy and resolved the ultraviolet catastrophe, he defined a universal constant ‘h’ in his calculations. This ‘Planck constant’ is incredibly small – approximately 6.63 × 10^-34 joules/second – and just like the speed of light or the charge of an electron, it is a fundamental, unchanging quantity that has profound importance in quantum mechanics. In fact, this constant appears in any equation in which the phenomenon under consideration exhibits quantum mechanical behavior.\n\nIn Einstein’s quantum theory of light, he carried the Planck constant forward, capturing the relationship between the energy of a photon and its frequency via the straightforward equation E = h × f or E = hc / λ where ‘c’ is the speed of light and ‘λ’ is its wavelength. Therefore, according to Einstein’s work, red light photons possess lower energy than blue light photons due to the former having a relatively longer wavelength or lower frequency.","ab26a64f-6f9f-4bbb-b9b1-93fcb2ee5dd4",[521],{"id":522,"data":523,"type":69,"version":24,"maxContentLevel":35},"8af963ae-2929-4497-b01b-2474f81ae2c5",{"type":69,"reviewType":28,"spacingBehaviour":24,"clozeQuestion":524,"clozeWords":526},[525],"According to Einstein’s work, red photons possess lower energy than blue photons.",[527],"lower",{"id":529,"data":530,"type":25,"version":25,"maxContentLevel":35,"summaryPage":532,"introPage":541,"pages":548},"612e6930-fcb1-4fe0-93c7-cc875fd92e3d",{"type":25,"title":531},"Photoelectric Effect and its Implications",{"id":533,"data":534,"type":35,"maxContentLevel":35,"version":24},"6795ec56-52c8-4b40-9445-ef60b5389842",{"type":35,"title":535,"summary":536},"Photoelectric Effect and its Implications summary",[537,538,539,540],"Light's frequency, not intensity, determines if electrons are emitted from a metal","Each material has a unique cut-off frequency below which no electrons are released","The work function is the minimum energy needed to free an electron from a metal","Photoelectric emission is instant when a photon with enough energy hits an electron",{"id":542,"data":543,"type":53,"maxContentLevel":35,"version":24},"85360d17-8c48-4480-a848-0a422fac1f25",{"type":53,"title":544,"intro":545},"Photoelectric Effect and its Implications intro",[546,547],"Why does increasing light intensity not always cause electron emission from a metal?","What determines the maximum kinetic energy of electrons in the photoelectric effect?",[549,565,583],{"id":550,"data":551,"type":24,"maxContentLevel":35,"version":25,"reviews":555},"3b05ceb3-6a10-4718-8cbf-ed6123d4db51",{"type":24,"title":552,"markdownContent":553,"audioMediaId":554},"Photoelectric Effect and its Implications page 1","When light is shone on a metal surface, sometimes no electrons are emitted regardless of the light’s intensity. But if light were a wave, even a low intensity light source should continually transfer energy to the electrons until they absorb enough to escape from their metallic bonds.\n\nIn quantum physics, it’s the light source’s frequency which matters. It turns out that every material has a unique ‘cut-off frequency’ below which no electrons are released and above which photoelectric effects are witnessed.\n\n![Graph](image://2199eb20-0f25-4aac-bec9-0e0e98119a40 \"Particles being reflected from waves\")","ef300803-9569-4ab8-99db-cb316ec9fdd8",[556],{"id":557,"data":558,"type":69,"version":24,"maxContentLevel":35},"83c868c2-0683-4c4f-a33c-b46711b4e020",{"type":69,"reviewType":25,"spacingBehaviour":24,"binaryQuestion":559,"binaryCorrect":561,"binaryIncorrect":563},[560],"What determines whether electrons are emitted from a metal surface undergoing the photoelectric effect?",[562],"The frequency of the light source",[564],"The intensity of the light source",{"id":566,"data":567,"type":24,"maxContentLevel":35,"version":25,"reviews":571},"5768f60c-15e0-4083-8f96-b5703a38bf94",{"type":24,"title":568,"markdownContent":569,"audioMediaId":570},"Photoelectric Effect and its Implications page 2","The quantum view of light states that intensity only affects the rate of electron emission, not whether they will be emitted. In other words, a greater number of photons transmitted per unit area and time means more opportunities for electrons to be liberated, assuming each photon has sufficient energy! When a photon with sufficient energy impacts an electron, it causes it to be liberated. Nothing happens if the photon lacks sufficient energy, regardless of how many there are!\n\nTo liberate an electron from a metal surface the incoming radiation needs to have energy surpassing Φ, which is related to the cut-off frequency fc by Φ = h × fc and known as the ‘work function’ of the metal. This work function is the minimum energy required to induce ‘photoemission’ of electrons, and it depends on the specific metal being illuminated.","098612a5-d804-45f2-b46d-6512f6fbbb3a",[572],{"id":394,"data":573,"type":69,"version":24,"maxContentLevel":35},{"type":69,"reviewType":35,"spacingBehaviour":24,"collapsingSiblings":574,"multiChoiceQuestion":575,"multiChoiceCorrect":577,"multiChoiceIncorrect":578,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6,"matchPairsQuestion":579,"matchPairsPairs":580},[390,393,395],[576],"Which of the following best describes the work function?",[402],[399,401,403],[142],[581],{"left":582,"right":402,"direction":35},"Work Function",{"id":584,"data":585,"type":24,"maxContentLevel":35,"version":25,"reviews":589},"73c7e509-e835-4508-a52d-6ff200766520",{"type":24,"title":586,"markdownContent":587,"audioMediaId":588},"Photoelectric Effect and its Implications page 3","If an incoming photon’s energy exceeds the work function of the material, an electron can be freed, and any excess energy appears as kinetic energy of the electron. It was established that the maximum kinetic energy of liberated electrons was independent of the light’s intensity, which only makes sense when light is quantized into photons. Each photon has a fixed energy based on frequency only, meaning that electrons will have a maximum kinetic energy – calculated as the difference between the energy of the photon and the work function of the metal – that doesn’t vary with intensity.\n\nAccording to classical wave theory, a measurable time lag should exist between the time when light first starts to illuminate a surface and the subsequent ejection of electrons. However, no detectable time lag has ever been measured in the photoelectric experiment. In other words, when a single photon with sufficient energy interacts with a single electron the photoelectric emission process is instantaneous.\n\nClassically, the time scale of the interaction should be measurable as the incoming wave continuously supplies energy until the electron has enough to escape, but this is not what was observed. The lack of a time lag in the photoelectric effect was another finding in favor of the quantum view.","c6655d2a-aea7-45f2-b66d-7d5f5bdf677a",[590,597],{"id":591,"data":592,"type":69,"version":24,"maxContentLevel":35},"a16b8c27-3e72-485b-834b-8261c2e8a734",{"type":69,"reviewType":28,"spacingBehaviour":24,"clozeQuestion":593,"clozeWords":595},[594],"The maximum kinetic energy of liberated electrons is independent of the light’s intensity.",[596],"independent",{"id":598,"data":599,"type":69,"version":24,"maxContentLevel":35},"40985fa0-cc4a-4182-a2fd-e9457257ac1e",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":600,"multiChoiceCorrect":602,"multiChoiceIncorrect":604,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[601],"What was the unexpected finding in the photoelectric experiment that favored the quantum view?",[603],"No time lag",[605,606,607],"Measurable time lag","Gamma radiation","Covalent bonding",{"id":609,"data":610,"type":27,"maxContentLevel":35,"version":25,"orbs":613},"6176951f-38d4-4480-a231-cacd028b094f",{"type":27,"title":611,"tagline":612},"Bohr’s Quantum Theory of the Atom","How the Bohr model modified our understanding of electrons and the atom.",[614,698,788],{"id":615,"data":616,"type":25,"version":25,"maxContentLevel":35,"summaryPage":618,"introPage":627,"pages":634},"89251487-b187-4f5e-81b2-0b7925e9fe32",{"type":25,"title":617},"The Evolution of Atomic Theory",{"id":619,"data":620,"type":35,"maxContentLevel":35,"version":24},"282f1f82-8d5b-43ec-9ada-afd689e92ea9",{"type":35,"title":621,"summary":622},"The Evolution of Atomic Theory summary",[623,624,625,626],"John Dalton's atomic theory in 1803 introduced atoms as indivisible particles","JJ Thomson discovered the electron in 1897, leading to his Plum Pudding Model","Thomson's model depicted atoms as electrons in a positively charged \"pudding\"","Dalton's theory missed subatomic particles like protons, neutrons, and electrons",{"id":628,"data":629,"type":53,"maxContentLevel":35,"version":24},"854b3728-57a5-470e-925c-820c6e0b1249",{"type":53,"title":630,"intro":631},"The Evolution of Atomic Theory intro",[632,633],"What did John Dalton's atomic theory fail to predict?","How did J.J. Thomson's 'Plum Pudding Model' describe the structure of an atom?",[635,649],{"id":636,"data":637,"type":24,"maxContentLevel":35,"version":25,"reviews":641},"3abf822f-82b9-4861-9d53-2ae24c6795a1",{"type":24,"title":638,"markdownContent":639,"audioMediaId":640},"The Evolution of Atomic Theory page 1","In the same way we have refined our understanding of light over the years, scientists have embarked on a similar journey with the nature of matter and the atoms that comprise it. In this tile we will embark on a whistle-stop tour of the most influential atomic models which have been developed, and the experimental evidence that inspired them.\n\nOnce we have explored the dramatic shifts in how atoms and subatomic particles have been envisaged over time, we will discover what the building blocks of our universe look like when examined under a quantum lens.","d9266726-e376-4120-8288-0a0260fe94d6",[642],{"id":643,"data":644,"type":69,"version":24,"maxContentLevel":35},"62fa3bee-3659-407e-b0bc-ddabf8dc445b",{"type":69,"reviewType":25,"spacingBehaviour":24,"binaryQuestion":645,"binaryCorrect":647,"binaryIncorrect":648},[646],"Scientists have had the same understanding of atoms and subatomic particles for several millennia now",[73],[75],{"id":650,"data":651,"type":24,"maxContentLevel":35,"version":25,"reviews":655},"980c0548-a75d-4f31-99b3-89e9ac0d0169",{"type":24,"title":652,"markdownContent":653,"audioMediaId":654},"The Evolution of Atomic Theory page 2","![Graph](image://9d92090b-7228-4f3a-8a8e-9ed16367d135 \"John Dalton. Image: See page for author, CC BY 4.0 \u003Chttps://creativecommons.org/licenses/by/4.0>, via Wikimedia Commons\")\n\nIn 1803, English chemist John Dalton published his atomic theory which revolutionized the field of chemistry. He hypothesized that matter is made up of tiny, indivisible particles called ‘atoms’ which could form molecules and be rearranged, combined, or separated during chemical reactions. A giant leap forward, but his theory failed to predict the existence of subatomic particles such as protons, neutrons, and electrons.\n\nEnglish Physicist J.J. Thomson outlined his ‘Plum Pudding Model’ of the atom in 1904 a few years after discovering the electron in 1897. Since his work predated the ‘atomic nucleus’, he represented the atom as negatively charged “plums” embedded in a positively charged “pudding”.\n\n![Graph](image://3e42239b-3a6e-4eac-9342-fa9a07f3b883 \"The Plum Pudding Model. Image: Tjlafave, CC BY-SA 4.0 \u003Chttps://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons\")\n\nHis model attempted to explain the two known properties of atoms at the time: 1) the negative charge of electrons and 2) that atoms have zero net charge, meaning the positive and negative components must balance out somehow. His work stands out as the very first attempt to represent the atomic structure of matter. He visualized materials and substances as being made up of countless small spheres, each sphere having a positive charge spread uniformly around its volume and being distributed with electrons. It wasn’t long however until a new ‘nuclear’ model was announced a few years late.","9d3d5c27-562c-4206-9098-442fc1cd7070",[656,667,676,687],{"id":395,"data":657,"type":69,"version":24,"maxContentLevel":35},{"type":69,"reviewType":35,"spacingBehaviour":24,"collapsingSiblings":658,"multiChoiceQuestion":659,"multiChoiceCorrect":661,"multiChoiceIncorrect":662,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6,"matchPairsQuestion":663,"matchPairsPairs":664},[390,393,394],[660],"Which of the following best describes Atomic Theory?",[403],[399,401,402],[142],[665],{"left":666,"right":403,"direction":35},"Atomic Theory",{"id":668,"data":669,"type":69,"version":24,"maxContentLevel":35},"27ce5272-1c6e-47e3-bcfc-2e406fd64a04",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":670,"multiChoiceCorrect":672,"multiChoiceIncorrect":674,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[671],"Who proposed the first atomic theory in 1803?",[673],"John Dalton",[274,354,675],"Ernest Rutherford",{"id":677,"data":678,"type":69,"version":24,"maxContentLevel":35},"7300a4fc-29c6-4902-ac46-0a621e1dcc81",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":679,"multiChoiceCorrect":681,"multiChoiceIncorrect":683,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[680],"What was the name of the atomic model proposed by J.J. Thomson in 1904?",[682],"The Plum Pudding Atomic Model",[684,685,686],"The Solar System Atomic Model","The Nuclear Atomic Model","The Bohr's Quantum Theory of the Atom",{"id":688,"data":689,"type":69,"version":24,"maxContentLevel":35},"f73b10da-82f6-4bcd-b368-98fd67cc6c73",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":690,"multiChoiceCorrect":692,"multiChoiceIncorrect":694,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[691],"Which of the following best describes the 'Plum Pudding Model'?",[693],"Early model of atomic structure proposed by J.J. Thomson",[695,696,697],"The lowest energy state of an atom","Atomic model proposed by Ernest Rutherfod","Can be used to describe the position of electrons through probable 'atomic orbitals'",{"id":699,"data":700,"type":25,"version":25,"maxContentLevel":35,"summaryPage":701,"introPage":710,"pages":717},"c5579a85-35a2-4233-926e-9da52da432e8",{"type":25,"title":685},{"id":702,"data":703,"type":35,"maxContentLevel":35,"version":24},"62003a57-41ad-4f29-b50c-0ecd485e534c",{"type":35,"title":704,"summary":705},"The Nuclear Atomic Model summary",[706,707,708,709],"Rutherford's experiment showed atoms are mostly empty space","Alpha particles deflected by a tiny, dense nucleus","Electrons emit light when they return to lower energy levels","Atomic emission spectra proved energy levels are quantized",{"id":711,"data":712,"type":53,"maxContentLevel":35,"version":24},"0f7180f6-87ab-482c-9431-1343659acd78",{"type":53,"title":713,"intro":714},"The Nuclear Atomic Model intro",[715,716],"What surprising result did Rutherford observe in the Geiger-Marsden experiments?","Why did Rutherford conclude that atoms have a tiny, dense nucleus?",[718,732,755],{"id":719,"data":720,"type":24,"maxContentLevel":35,"version":25,"reviews":724},"a51757d9-bd97-436e-adfb-7b5bf15b8dc9",{"type":24,"title":721,"markdownContent":722,"audioMediaId":723},"The Nuclear Atomic Model page 1","In 1909, Ernest Rutherford oversaw the ‘Geiger-Marsden experiments’. The experiments involved firing a narrow beam of ‘alpha particles’ emitted from a decaying radioactive source at a very thin sheet of gold foil.\n\nIf Thomson’s plum pudding model were correct, the alpha particles would have whizzed through the sheet undeflected.\n\nAlpha particles, as used in Rutherford's experiment, are helium nuclei, meaning they consist of two protons and two neutrons. They carry a positive charge because of the protons. If Thomson's 'plum pudding' model was correct — where an atom is a uniform positive soup with negative electrons embedded within — the positively charged alpha particles should have passed through the thin gold foil without deviation.","87cd9692-4356-43cf-bacf-860b6856daa4",[725],{"id":726,"data":727,"type":69,"version":24,"maxContentLevel":35},"b99ce493-a629-40ab-ac40-1c6702a6ea90",{"type":69,"reviewType":24,"spacingBehaviour":24,"activeRecallQuestion":728,"activeRecallAnswers":730},[729],"How did the Geiger-Marsden experiments, overseen by Ernest Rutherford, aim to prove the plum pudding model of the atom?",[731],"By firing alpha particles at gold foil, to see if they were deflected",{"id":733,"data":734,"type":24,"maxContentLevel":35,"version":25,"reviews":738},"019ec1ee-52c9-4000-adfd-115a77f812c4",{"type":24,"title":735,"markdownContent":736,"audioMediaId":737},"The Nuclear Atomic Model page 2","While most of the alpha particles did pass through the foil, a surprising number were significantly deflected, or even bounced back. Rutherford used these unexpected results to conclude that atoms must be primarily empty space, which allowed most alpha particles to pass straight through.\n\n![Graph](image://d5ce5095-5df3-4786-a870-23b285ff81cb \"A diagram showing the deflections in the Geiger Marsden experiments. Kurzon, CC BY 3.0 \u003Chttps://creativecommons.org/licenses/by/3.0>, via Wikimedia Commons\")\n\nThe large angle deflections were explained by the presence of a concentrated positive charge within the atom, which repelled the also positively charged alpha particles.\n\nThe small fraction of alpha particles that bounced straight back, around 1 in 10,000, led Rutherford to further infer that the positive charge and most of the atom's mass are concentrated in a tiny volume at the center of the atom, known as the nucleus. This deviated significantly from the plum pudding model, leading to our modern understanding of atomic structure.","2d7bd337-bfb8-45b6-be72-5d6ef4d2c9ea",[739,746],{"id":740,"data":741,"type":69,"version":24,"maxContentLevel":35},"21de2733-4a78-4b4c-b975-6bf9fde91009",{"type":69,"reviewType":24,"spacingBehaviour":24,"activeRecallQuestion":742,"activeRecallAnswers":744},[743],"Why did the fact that alpha particles passed through the gold foil undeflected disprove the plum pudding model?",[745],"Because it meant there must be densely concentrated, positively charged centers within the atoms",{"id":747,"data":748,"type":69,"version":24,"maxContentLevel":35},"1060d3b9-422b-4d50-abb5-16f8820e0b35",{"type":69,"reviewType":749,"spacingBehaviour":24,"imageRecallQuestion":750,"imageRecallMediaId":752,"imageRecallAnswers":753},5,[751],"What led Rutherford to conclude that there must be an atomic nucleus, as shown in this image?","2abb3a13-f86f-4153-9d17-a2c769826612",[754],"Alpha particles were sometimes being deflected, rather than passing straight through the atoms.",{"id":756,"data":757,"type":24,"maxContentLevel":35,"version":25,"reviews":761},"d83eff78-1431-4942-a15a-4e02ab275cd1",{"type":24,"title":758,"markdownContent":759,"audioMediaId":760},"The Nuclear Atomic Model page 3","The electrons in an atom are usually arranged such that its overall energy is kept as low as possible i.e., the ‘ground state’. When an atom is supplied with energy which its electrons absorb to move into higher ‘energy levels’, the atom is said to enter an ‘excited state’.\n\n![Graph](image://5256d253-b06f-49ac-a5fc-f01ddea90a70 \"An atomic emission spectra. Image: McZusatz, CC0, via Wikimedia Commons\")\n\nThese states aren’t stable, meaning the atom can’t remain in this configuration for long. Upon returning to the ground state, the electrons return to their original energy levels, emitting energy in the form of electromagnetic radiation which we can detect. Different elements emit different frequencies of light which can be plotted as ‘atomic emission spectra’.\n\nClassical physics had no explanation for these spectra, as instead of being ‘continuous’ and containing all frequencies, they were characterized by discrete ‘spectral lines’. This indicated that the energy released by electrons in excited atoms was quantized, providing further proof of the quantization of light and leading to atomic models based on quantum theory.","f876f4b9-9228-4fda-9126-c310fc2e7bfb",[762,777],{"id":763,"data":764,"type":69,"version":24,"maxContentLevel":35},"aa1d1c1b-f11b-4881-80fb-90c12df37ed7",{"type":69,"reviewType":35,"spacingBehaviour":24,"collapsingSiblings":765,"multiChoiceQuestion":769,"multiChoiceCorrect":771,"multiChoiceIncorrect":772,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6,"matchPairsQuestion":773,"matchPairsPairs":774},[766,767,768],"41fed7bc-9ed4-4a18-aba0-666a53c175f9","22fa524e-21e7-4b02-89a1-f3e078ef9fa7","05d9d88c-56fc-477b-a2e9-68d11c0c1280",[770],"Which of these best describes the Plum Pudding Model?",[693],[695,696,697],[142],[775],{"left":776,"right":693,"direction":35},"Plum Pudding Model'",{"id":766,"data":778,"type":69,"version":24,"maxContentLevel":35},{"type":69,"reviewType":35,"spacingBehaviour":24,"collapsingSiblings":779,"multiChoiceQuestion":780,"multiChoiceCorrect":782,"multiChoiceIncorrect":783,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6,"matchPairsQuestion":784,"matchPairsPairs":785},[763,767,768],[781],"Which of the following best describes the ground state?",[695],[693,696,697],[142],[786],{"left":787,"right":695,"direction":35},"Ground state",{"id":789,"data":790,"type":25,"version":25,"maxContentLevel":35,"summaryPage":792,"introPage":801,"pages":808},"b032e005-f060-4999-8ffc-b63ab7daa078",{"type":25,"title":791},"The Quantum Atomic Model",{"id":793,"data":794,"type":35,"maxContentLevel":35,"version":24},"993bf717-e7d9-4de5-8b07-a68bd5347837",{"type":35,"title":795,"summary":796},"The Quantum Atomic Model summary",[797,798,799,800],"Rutherford's model introduced a dense, positively charged nucleus with electrons orbiting like planets","Bohr explained why electrons don't crash into the nucleus by comparing electrical force to gravity","Bohr's quantum model introduced specific, quantized energy levels for electrons","Electrons are best described as 'clouds' of possible locations, forming atomic orbitals",{"id":802,"data":803,"type":53,"maxContentLevel":35,"version":24},"be797c1e-2f02-4255-a62b-3782d0ff75e7",{"type":53,"title":804,"intro":805},"The Quantum Atomic Model intro",[806,807],"How do atomic orbitals differ from Bohr's electron orbits?","What concept explains the wave-like properties of electrons?",[809,835,849,865],{"id":810,"data":811,"type":24,"maxContentLevel":35,"version":25,"reviews":815},"9d87f684-a690-421d-98c4-563166134e10",{"type":24,"title":812,"markdownContent":813,"audioMediaId":814},"The Quantum Atomic Model page 1","Once the existence of a positively charged nucleus was established by Rutherford’s experiments, he put forward a nuclear model which eclipsed Thomson’s plum pudding model as it was far better able to explain observations.\n\nThe atom now consisted of a tiny, dense, positively charged ‘nucleus’ surrounded by a cloud of – comparatively much lighter – negatively charged electrons which orbited the nucleus like planets revolving around the sun. Nearly all the mass of an atom was concentrated in its nucleus!\n\n![Graph](image://d652e975-74b7-4710-839d-5f32074d5d8a \"Rutherford's atomic model. Bensteele1995, CC BY-SA 3.0 \u003Chttps://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons\")","299c11c6-9df8-4a36-b2e4-66b04f2e992d",[816,827],{"id":767,"data":817,"type":69,"version":24,"maxContentLevel":35},{"type":69,"reviewType":35,"spacingBehaviour":24,"collapsingSiblings":818,"multiChoiceQuestion":819,"multiChoiceCorrect":821,"multiChoiceIncorrect":822,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6,"matchPairsQuestion":823,"matchPairsPairs":824},[763,766,768],[820],"Which of the following best describes the nuclear model?",[696],[693,695,697],[142],[825],{"left":826,"right":696,"direction":35},"Nuclear model",{"id":828,"data":829,"type":69,"version":24,"maxContentLevel":35},"86398ec2-61dd-45d7-8b34-55aab115bf67",{"type":69,"reviewType":25,"spacingBehaviour":24,"binaryQuestion":830,"binaryCorrect":832,"binaryIncorrect":833},[831],"What model of the atom did Rutherford put forward?",[826],[834],"Plum pudding model",{"id":836,"data":837,"type":24,"maxContentLevel":35,"version":25,"reviews":841},"f992355b-dc7d-4a47-abbc-9fbae4dd38dd",{"type":24,"title":838,"markdownContent":839,"audioMediaId":840},"The Quantum Atomic Model page 2","Unfortunately, the model wasn’t without its issues. The most prominent flaw was the fact that this planetary model of the atom failed to explain why the atoms of a given element produce discrete – and not continuous – ‘line spectra’ as there was not yet a concept of quantized electron energy levels. His model also couldn’t explain why the cloud of negatively charged electrons surrounding the nucleus remained in orbit instead of tumbling into the positively charged nucleus that they are attracted to.\n\nBohr modified Rutherford’s model by stating that the electrical force between the nucleus and orbiting electrons was mathematically identical to the gravitational force responsible for keeping the planets in orbit around the Sun, explaining why electrons don’t simply “fly into” the nucleus.\n\n![Graph](image://6ecdff13-df75-4a6d-b39b-03ac072229dd \"Niels Bohr. Image: https://pixel17.com, CC BY-SA 2.0 \u003Chttps://creativecommons.org/licenses/by-sa/2.0>, via Wikimedia Commons\")","50e24427-1ab6-4a1b-8bfc-bcc1f442bf7f",[842],{"id":843,"data":844,"type":69,"version":24,"maxContentLevel":35},"36c8a92d-d7ab-46ba-b0d9-7249608d8351",{"type":69,"reviewType":28,"spacingBehaviour":24,"clozeQuestion":845,"clozeWords":847},[846],"Bohr's model used comparisons to gravitational force between planets to explain why electrons don't fly into the nucleus and quantization to explain atomic emission spectra.",[848],"gravitational",{"id":850,"data":851,"type":24,"maxContentLevel":35,"version":25,"reviews":855},"c261bd67-99eb-4854-9452-3d8a163e72d6",{"type":24,"title":852,"markdownContent":853,"audioMediaId":854},"The Quantum Atomic Model page 3","He also used quantum thinking to posit that only certain electron orbits are permitted in an atom. Since electromagnetic energy is absorbed or emitted if the electrons within an atom move from one orbit – or energy level – to another, Bohr reasoned that the discrete lines seen in atomic emission spectra were due to electrons having specific, quantized energy levels to move between.\n\n![Graph](image://88851949-3b6a-49dc-b095-88d8cf03caf9 \"Bohr's quantum model. JabberWok, CC BY-SA 3.0 \u003Chttp://creativecommons.org/licenses/by-sa/3.0/>, via Wikimedia Commons\")\n\nAlthough Bohr’s model could only make poor predictions of the atomic emission spectra of atoms heavier than hydrogen and would need later refinement to better explain some of the more sophisticated phenomena seen in atoms, its use of quantization set the stage for a wealth of exciting developments in physics.\n\nThe major issue with Bohr’s model was that it treated electrons as particles moving in precisely defined orbits. Since light demonstrated both particle-like and wave-like properties, who’s to say particles too don’t possess a similar “fuzziness”? What if we could be justified in some situations to treat particles as ‘matter waves’?\n\n![Graph](image://364b83e6-17d4-472c-993e-8c6777298882 \"Atomic orbitals. Image: Public domain via Wikimedia\")","cf98b424-ff0a-4ced-9e64-2541749261d6",[856],{"id":857,"data":858,"type":69,"version":24,"maxContentLevel":35},"7801becd-f1d6-4bd3-87c0-e4fdaeeb260f",{"type":69,"reviewType":25,"spacingBehaviour":24,"binaryQuestion":859,"binaryCorrect":861,"binaryIncorrect":863},[860],"Which of these is an accurate description of Bohr's model of electron orbits?",[862],"Electrons can only hold specific, discrete energy levels, giving them a limited number of possible orbit paths",[864],"Electrons can hold any amount of energy, meaning they can orbit the nucles along an infinite number of possible paths",{"id":866,"data":867,"type":24,"maxContentLevel":35,"version":25,"reviews":871},"6dc66034-9951-45a3-b474-f5924b89feaa",{"type":24,"title":868,"markdownContent":869,"audioMediaId":870},"The Quantum Atomic Model page 4","Instead of electrons existing in clean orbits, it turns out that each electron is far better described as a ‘cloud’ of possible locations in space. So how do chemists and physicists approximate the location of an electron, if they can no longer tell exactly where it is or how it moves?\n\nThe ‘wave function’ which we discuss in the fourth tile can be solved for electrons to give rise to distinctively shaped – depending on the energy level the electron is in – regions within an atom which enclose where the electron is likely to be around ninety percent of the time! These are known as ‘atomic orbitals’.","8ba20b80-64e7-4ce7-a5ef-0bed19e53e94",[872,883,894],{"id":768,"data":873,"type":69,"version":24,"maxContentLevel":35},{"type":69,"reviewType":35,"spacingBehaviour":24,"collapsingSiblings":874,"multiChoiceQuestion":875,"multiChoiceCorrect":877,"multiChoiceIncorrect":878,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6,"matchPairsQuestion":879,"matchPairsPairs":880},[763,766,767],[876],"Which of the following best describes a wave function?",[697],[693,695,696],[142],[881],{"left":882,"right":697,"direction":35},"Wave function",{"id":884,"data":885,"type":69,"version":24,"maxContentLevel":35},"ac2384f4-1cd7-4be7-a7bb-161d0e6299b0",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":886,"multiChoiceCorrect":888,"multiChoiceIncorrect":890,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[887],"What are the regions within an atom which enclose where the electron is likely to be around ninety percent of the time called?",[889],"Atomic orbitals",[891,892,893],"Electron clouds","Wave functions","Matter waves",{"id":895,"data":896,"type":69,"version":24,"maxContentLevel":35},"6a642636-b420-452b-bcfc-73532f9570aa",{"type":69,"reviewType":24,"spacingBehaviour":24,"activeRecallQuestion":897,"activeRecallAnswers":899},[898],"How do chemists and physicists approximate the location of an electron?",[900],"By solving the wave function to calculate a probability of that electron's location",{"id":902,"data":903,"type":27,"maxContentLevel":35,"version":25,"orbs":906},"32262c0d-a0fc-4b28-9737-590c86c3c188",{"type":27,"title":904,"tagline":905},"Schrodinger’s Equation and Wave Functions","Erwin Schrodinger's fundamental impact on the development of quantum theory.",[907,974,1074,1157],{"id":908,"data":909,"type":25,"version":25,"maxContentLevel":35,"summaryPage":911,"introPage":920,"pages":927},"3cc17c39-77c0-4368-b44c-aa073c826999",{"type":25,"title":910},"Introduction to Quantum Mechanics",{"id":912,"data":913,"type":35,"maxContentLevel":35,"version":24},"739ee084-40ee-424f-920d-a504ae0f0770",{"type":35,"title":914,"summary":915},"Introduction to Quantum Mechanics summary",[916,917,918,919],"Newton’s laws fall apart at tiny scales; quantum mechanics steps in","Schrödinger’s equation is the quantum version of Newton’s second law","Quantum systems aren’t like tiny billiard balls; think waves","Wave functions from Schrödinger’s equation give us quantum probabilities",{"id":921,"data":922,"type":53,"maxContentLevel":35,"version":24},"6155542f-d5ad-430e-9e13-6243db96d689",{"type":53,"title":923,"intro":924},"Introduction to Quantum Mechanics intro",[925,926],"Why can't we use position and momentum to describe quantum systems?","What does Schrödinger’s equation help us calculate in quantum mechanics?",[928,942,960],{"id":929,"data":930,"type":24,"maxContentLevel":35,"version":25,"reviews":934},"465952e0-5fc4-419d-9019-5628ceeb9f47",{"type":24,"title":931,"markdownContent":932,"audioMediaId":933},"Introduction to Quantum Mechanics page 1","Before quantum mechanics, things were a whole lot simpler. For example, Newton’s laws of motion were naively thought to be all we needed to – at least in theory – describe motion of any kind.\n\nAll physicists had to do was apply his second law of motion F = m × a linking the force on a body with its mass and acceleration, and they could answer pretty much any question one could think to ask about the world! Except, they couldn’t.","adcdf0ed-4f52-4853-8c1f-992c33831a6b",[935],{"id":936,"data":937,"type":69,"version":24,"maxContentLevel":35},"963be49e-b5f9-4fdd-8e3a-bd984784e81a",{"type":69,"reviewType":25,"spacingBehaviour":24,"binaryQuestion":938,"binaryCorrect":940,"binaryIncorrect":941},[939],"Newton's mechanics can explain the entire universe",[73],[75],{"id":943,"data":944,"type":24,"maxContentLevel":35,"version":25,"reviews":948},"5bec0291-6409-4620-8ad5-805f8580ebfa",{"type":24,"title":945,"markdownContent":946,"audioMediaId":947},"Introduction to Quantum Mechanics page 2","As soon as scientists zoomed in to view reality at the smallest possible scales, Newton’s laws fell apart and things became very weird indeed. In fact, things only started to make sense again when the theory and equations of quantum mechanics were employed. The core equation of this new theory, and the analogue of Newton’s second law, is known as ‘Schrödinger’s equation’.\n\nIt’s usual in classical mechanics to describe the state of a physical system using the quantities of position and momentum. If we know the initial conditions of such a system, we can in theory use Newton’s laws to work out the ‘dynamical evolution’ of said system at any later time. In other words, it’s ‘deterministic’.","37aa804c-37bf-4809-b310-374a9e9355ac",[949],{"id":950,"data":951,"type":69,"version":24,"maxContentLevel":35},"6ba25c82-dd3d-4a91-ad3e-0eb97e5142d1",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":952,"multiChoiceCorrect":954,"multiChoiceIncorrect":956,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[953],"What is the core equation of quantum mechanics, which is the analogue of Newton's second law?",[955],"Schrödinger's equation",[957,958,959],"Bohr's equation","Heisenberg's equation","Einstein's equation",{"id":961,"data":962,"type":24,"maxContentLevel":35,"version":25,"reviews":966},"f3d78449-252d-4a71-abd8-1a3c8fdc1823",{"type":24,"title":963,"markdownContent":964,"audioMediaId":965},"Introduction to Quantum Mechanics page 3","It turns out that it’s nowhere near as easy to predict or understand the future evolution of quantum systems, and concepts of position and momentum are no longer the correct variables to use to describe them. Unfortunately, quantum objects don’t behave like tiny billiard balls, and sometimes it’s better to think of them as waves!\n\n![Graph](image://39cbaecd-e876-4ad9-bc6d-1017fd86d31a \"Billiard balls. Image: MichaelMaggs, CC BY-SA 3.0 \u003Chttps://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons\")\n\nTo fully embrace the quantum way of thinking, we need to become comfortable with uncertainty and a fuzzy ‘probabilistic’ way of talking about the behavior of systems. How can such probabilities be calculated? All we need to know about quantum systems is contained in the solution to Schrödinger’s equation, known as a ’wave function’.","dc7a805d-f785-4b30-869e-38d815e651db",[967],{"id":968,"data":969,"type":69,"version":24,"maxContentLevel":35},"d6cf2ab3-9d94-42cb-b6c3-aaf9d8336839",{"type":69,"reviewType":24,"spacingBehaviour":24,"activeRecallQuestion":970,"activeRecallAnswers":972},[971],"How can probabilities be calculated for quantum systems?",[973],"By solving Schrödinger's equation to find the wave function",{"id":975,"data":976,"type":25,"version":25,"maxContentLevel":35,"summaryPage":978,"introPage":987,"pages":994},"4ba64089-a05d-4ef0-86e0-b27be2d21d0d",{"type":25,"title":977},"Wave-Particle Duality",{"id":979,"data":980,"type":35,"maxContentLevel":35,"version":24},"535163c5-9e8c-4d5f-bd25-0a8d7e61569e",{"type":35,"title":981,"summary":982},"Wave-Particle Duality summary",[983,984,985,986],"Louis de Broglie proposed that all matter has a wavelength, called the de Broglie wavelength","The de Broglie wavelength is calculated using λ = h / p, where h is Planck’s constant and p is momentum","The double-slit experiment with electrons showed they create an interference pattern, proving wave-particle duality","Electrons fired one by one still create an interference pattern, acting like waves passing through both slits",{"id":988,"data":989,"type":53,"maxContentLevel":35,"version":24},"039ee302-92f4-4aeb-905c-618be1d82ffc",{"type":53,"title":990,"intro":991},"Wave-Particle Duality intro",[992,993],"What pattern appears on the detector screen in the double-slit experiment with electrons?","How does the double-slit experiment prove wave-particle duality?",[995,1012,1045],{"id":996,"data":997,"type":24,"maxContentLevel":35,"version":25,"reviews":1001},"fa252f40-71b9-4003-97fd-bda18826bf3e",{"type":24,"title":998,"markdownContent":999,"audioMediaId":1000},"Wave-Particle Duality page 1","In 1923, French physicist Louis de Broglie defined his ‘de Broglie wavelength’, a wavelength which all objects in quantum mechanics manifest. It’s related to Planck’s constant and the momentum ‘p’ of a particle through λ = h / p. Since in quantum theory, all matter exhibits wave-like behavior, such waves are also described as ‘matter waves’.\n\n![Graph](image://53d233b5-29a7-4d4a-83f2-bc3b4c6d1fa3 \"Louis de Broglie. Image: Public domain via Wikimedia\")\n\nThe de Broglie wavelength indicates the length scale at which wave-like properties are important. For example, if a particle is interacting with something significantly larger than its “wavelength”, then its wave-like properties won’t be noticeable!","5b4fc660-4a38-4e1c-9d99-cd077074cc19",[1002],{"id":1003,"data":1004,"type":69,"version":24,"maxContentLevel":35},"50394db5-5660-4392-ab1a-1c5b0c3c5929",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":1005,"multiChoiceCorrect":1007,"multiChoiceIncorrect":1008,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[1006],"What term is sometimes given to de Broglie's waves, to describe the fact that particles can exhibit wave-like qualities?",[893],[1009,1010,1011],"Converse waves","Quantum waves","Bohr's waves",{"id":1013,"data":1014,"type":24,"maxContentLevel":35,"version":25,"reviews":1018},"2fb3820e-9fb3-4c85-b3c7-e6e788de19e1",{"type":24,"title":1015,"markdownContent":1016,"audioMediaId":1017},"Wave-Particle Duality page 2","His ideas were later proven correct, most notably by experiments demonstrating the diffraction – historically, a wave property! – of electrons and therefore their ‘wave-particle duality’. de Broglie arrived at his equation by combining Einstein’s famous energy equation E = mc^2 with the energy of a photon E = h × f, making the first theoretical hypothesis that matter too may demonstrate this incredibly strange wave-particle duality.\n\nEvidence of de Broglie’s idea came with an updated version of the double-slit experiment, in which a beam of electrons was fired at the slits instead. If electrons only behaved like particles, you’d expect them to pile up in two straight lines behind both slits.","e4b6b984-fc89-4562-902e-1ed377adf192",[1019,1038],{"id":1020,"data":1021,"type":69,"version":24,"maxContentLevel":35},"fa39cf86-226f-4124-8007-18bb8196582f",{"type":69,"reviewType":35,"spacingBehaviour":24,"collapsingSiblings":1022,"multiChoiceQuestion":1026,"multiChoiceCorrect":1028,"multiChoiceIncorrect":1030,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6,"matchPairsQuestion":1034,"matchPairsPairs":1035},[1023,1024,1025],"6ec34542-1300-4480-8419-4ec202ecd388","3a11dfd9-4dce-4cd5-a740-7862c25fd15e","2b8b19f0-c0d5-4a1a-8eb5-4536b6fcdebc",[1027],"Which of the following best describes the double-slit experiment?",[1029],"Experiment used to illustrate wave-particle duality",[1031,1032,1033],"Allows a particle to be in several places at once","Calculates the probability that a particle exists at a given location","States how it is impossible to measure both position and momentum of quantum object",[142],[1036],{"left":1037,"right":1029,"direction":35},"Double-slit experiment",{"id":1039,"data":1040,"type":69,"version":24,"maxContentLevel":35},"fc78b4fc-fd55-4851-aee8-0d8e53e831b5",{"type":69,"reviewType":28,"spacingBehaviour":24,"clozeQuestion":1041,"clozeWords":1043},[1042],"Louis de Broglie proposed that matter could demonstrate a wave-particle duality.",[1044],"wave-particle",{"id":1046,"data":1047,"type":24,"maxContentLevel":35,"version":25,"reviews":1051},"9cadb382-13fa-44cf-97a2-969e4fb7b7ec",{"type":24,"title":1048,"markdownContent":1049,"audioMediaId":1050},"Wave-Particle Duality page 3","But what you actually see on the detector screen is an interference pattern! Diffraction and interference are two properties only possible with waves, so the presence of an interference pattern was direct proof that electrons must be behaving as waves!\n\n![Graph](image://ad07eafc-b65e-44db-80ae-f686501c3f42 \"The double-slit experiment. Image: Nekojanekoja, CC BY-SA 4.0, via Wikimedia Commons\")\n\nBizarrely, this experiment even worked when electrons were fired one by one! It was as if each electron passed through both slits simultaneously as a matter wave and interfered with itself as the constituent waves spread out again on the other side.\n\nThis experiment’s result is identical to what was seen all historically with a light source: a pattern of ‘bright’ – where electrons hit the detector screen most often – and ‘dark’ patches arranged horizontally.","b9b05add-d574-4824-a4f1-8009af78ab45",[1052,1063],{"id":1053,"data":1054,"type":69,"version":24,"maxContentLevel":35},"a9e6530e-fbf8-4634-8dce-fe0149b6404b",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":1055,"multiChoiceCorrect":1057,"multiChoiceIncorrect":1059,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[1056],"What was the result of the updated version of the double-slit experiment, when a beam of electrons was fired at the slits?",[1058],"An interference pattern",[1060,1061,1062],"A pile up in two straight lines","A pattern of bright and dark patches","Diffraction and interference",{"id":1064,"data":1065,"type":69,"version":24,"maxContentLevel":35},"cce9e8b6-fad1-4018-a3f6-69551c39655f",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":1066,"multiChoiceCorrect":1068,"multiChoiceIncorrect":1070,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[1067],"What did the interference pattern observed from electrons in the double-slit experiment prove?",[1069],"Electrons could behave like waves",[1071,1072,1073],"Electrons obeyed Newtonian mechanics","Electrons weren't particles at all","Electrons were in fact positively charged",{"id":1075,"data":1076,"type":25,"version":25,"maxContentLevel":35,"summaryPage":1078,"introPage":1087,"pages":1094},"43e1b612-640b-4fd2-a0e9-ab2b32733a11",{"type":25,"title":1077},"Schrödinger's Equation",{"id":1079,"data":1080,"type":35,"maxContentLevel":35,"version":24},"e5e67363-7355-4806-961c-61437bef199f",{"type":35,"title":1081,"summary":1082},"Schrödinger's Equation summary",[1083,1084,1085,1086],"Schrödinger's Equation predicts how matter waves behave over time and space","The wave function from Schrödinger's Equation gives a probability of finding a particle at a specific location","Max Born's interpretation of the wave function revolutionized our understanding of quantum mechanics","Schrödinger's Equation accurately predicted the energy levels of hydrogen, confirming its validity",{"id":1088,"data":1089,"type":53,"maxContentLevel":35,"version":24},"eaa53265-bbf2-47ae-9053-abf02d57a4a6",{"type":53,"title":1090,"intro":1091},"Schrödinger's Equation intro",[1092,1093],"What does the wave function tell us about a particle's location?","How did Schrödinger's Equation validate Bohr's model of the hydrogen atom?",[1095,1113,1139],{"id":1096,"data":1097,"type":24,"maxContentLevel":35,"version":25,"reviews":1101},"6b4a8fee-3e54-426a-8397-27319d2076af",{"type":24,"title":1098,"markdownContent":1099,"audioMediaId":1100},"Schrödinger's Equation page 1","Inspired by de Broglie, Austrian physicist Erwin Schrödinger reasoned in 1925 that since classical wave systems like sound waves or waves on an oscillating string have well-established equations governing their motion over time and space, so too must matter waves have their own equation. The solution to such an equation is a ‘wave function’, which in theory would tell you everything important about your quantum system.\n\n![Graph](image://1c9aef0f-c50c-4347-beb6-5d2298e55270 \"Erwin Schrödinger. Image:  Public domain, via Wikimedia Commons\")\n\nFor simple systems, like one particle moving in three dimensions, the equation can be written in its more complex time-dependent form where ‘V’ is the particle’s ‘potential energy’. If the potential energy of the system is constant, we can simplify things further and use the time-independent form. Schrödinger’s Equation is an example of a ‘differential equation’ in mathematics, and the methods used to solve it can be quite sophisticated. When a suitable solution is found (the wave function for a particular system, whether one particle or multiple), that’s where the real fun begins…","9e28d37b-5773-489b-bef0-03f0df3674d5",[1102],{"id":1103,"data":1104,"type":69,"version":24,"maxContentLevel":35},"edd52770-aa99-4187-97b6-100f21f5ff57",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":1105,"multiChoiceCorrect":1107,"multiChoiceIncorrect":1109,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[1106],"What type of equation is Schrödinger's Equation?",[1108],"Differential equation",[1110,1111,1112],"Integral equation","Algebraic equation","Trigonometric equation",{"id":1114,"data":1115,"type":24,"maxContentLevel":35,"version":25,"reviews":1119},"c8052cb5-2af0-4551-96c3-383085e07ddc",{"type":24,"title":1116,"markdownContent":1117,"audioMediaId":1118},"Schrödinger's Equation page 2","The solution to Schrödinger’s Equation for a system is called its ‘wave function’, due to its similarity to classical equations describing waves. However, a quantum wave function doesn’t provide a precise location for your particle(s) at any time ‘t’ as in classical physics.\n\n![Graph](image://eb6b1835-77f7-407e-bada-ee0234451ef1 \"Max Born. Image: Public domain via Wikimedia\")\n\nInstead, the wave function outputs an abstract value for every point in three-dimensional space. Schrödinger’s Equation contains four variables: time ‘t’, and three spatial coordinates ‘x’, ‘y’ and ‘z’.\n\nNobody knew how to interpret these values, until in 1926, Max Born conceived a profound ‘probabilistic interpretation’. He postulated that the squared absolute value of the wave function tells you the ‘probability density’ associated with finding a particle at a given position (x, y, z).\n\nIn quantum theory, we must surrender any notion of certainty and instead embrace a probability-based view of reality. We no longer know where a particle will be, but with Schrödinger's Equation, we can be reasonably sure of where it’s most likely to be.","722dbc92-7df6-4d2c-9fb7-128922d10146",[1120,1132],{"id":1121,"data":1122,"type":69,"version":24,"maxContentLevel":35},"124e92fa-7c11-4c8b-9706-c45bb27fe20b",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":1123,"multiChoiceCorrect":1125,"multiChoiceIncorrect":1128,"multiChoiceMultiSelect":21,"multiChoiceRevealAnswerOption":6},[1124],"Which of these variables would affect the wave function value outputted for a given particle in Schrödinger’s Equation?",[1126,1127],"Time","Position",[1129,1130,1131],"Energy","Speed","Spin",{"id":1133,"data":1134,"type":69,"version":24,"maxContentLevel":35},"299803f4-3445-493c-b915-1cbe7dd82710",{"type":69,"reviewType":24,"spacingBehaviour":24,"activeRecallQuestion":1135,"activeRecallAnswers":1137},[1136],"What is the squared absolute value of the wave function said to tell us?",[1138],"The probability density associated with finding a particle at a given position",{"id":1140,"data":1141,"type":24,"maxContentLevel":35,"version":25,"reviews":1145},"8cc78b55-9f35-489b-ade5-59848251d6c0",{"type":24,"title":1142,"markdownContent":1143,"audioMediaId":1144},"Schrödinger's Equation page 3","Why is Schrödinger's Equation worth trusting as the correct view of reality? After all, Richard Feynman once said that the equation – which wasn’t derived from anything previously known – “came out of the mind of Schrödinger only”.\n\n![Graph](image://9712a6a8-d374-4560-8241-1bdb0aa7a55e \"The discrete energy emission spectra of the hydrogen atom. Image: OrangeDog, CC BY-SA 3.0, via Wikimedia Commons\")\n\nWell, the equation has held its own in every single experiment carried out so far to test it. In fact, it’s one of the most successful equations in history, with predictions that have been verified countless times. Therefore, it has earned its place as the fundamental equation in quantum mechanics and the starting point for every quantum system we seek to describe.\n\nOne of the equation's earliest successes was in helping to elucidate one of the phenomena that gave rise to quantum theory in the first place: the discrete energy emission spectra of the hydrogen atom. Amazingly, the solution to Schrödinger's Equation when applied to a hydrogen atom exactly reproduced the same quantized energy levels theorized by Bohr in his quantum atomic model!","0baea7f3-c9e2-4fc0-891f-6f268df6f516",[1146],{"id":1147,"data":1148,"type":69,"version":24,"maxContentLevel":35},"19c51b4d-2e96-4c40-8c2a-0b3ced9e6ec1",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":1149,"multiChoiceCorrect":1151,"multiChoiceIncorrect":1153,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[1150],"What did Schrödinger's Equation help elucidate regarding the hydrogen atom?",[1152],"The discrete energy emission spectra",[1154,1155,1156],"The quantized energy levels","The atomic model","The quantum theory",{"id":1158,"data":1159,"type":25,"version":25,"maxContentLevel":35,"summaryPage":1161,"introPage":1170,"pages":1177},"56d8cf46-efd8-45c4-9f31-dd233096f51a",{"type":25,"title":1160},"Quantum Superposition and Schrödinger's Cat",{"id":1162,"data":1163,"type":35,"maxContentLevel":35,"version":24},"1cd0304a-0c03-4dcb-9065-d89646d5d2de",{"type":35,"title":1164,"summary":1165},"Quantum Superposition and Schrödinger's Cat summary",[1166,1167,1168,1169],"Quantum particles don't have a clear path; we only know probabilities","Without looking, a particle exists in all possible places at once","Schrödinger's Cat is a thought experiment showing a cat can be dead and alive","Superposition means particles can be in multiple states until observed",{"id":1171,"data":1172,"type":53,"maxContentLevel":35,"version":24},"417d0be6-cce2-439d-91cd-352580d60467",{"type":53,"title":1173,"intro":1174},"Quantum Superposition and Schrödinger's Cat intro",[1175,1176],"What does quantum superposition mean for a particle in a box?","Why is Schrödinger's cat both dead and alive?",[1178,1216],{"id":1179,"data":1180,"type":24,"maxContentLevel":35,"version":25,"reviews":1184},"26ae250c-c6c0-4369-a9f5-865908e1538b",{"type":24,"title":1181,"markdownContent":1182,"audioMediaId":1183},"Quantum Superposition and Schrödinger's Cat page 1","Imagine a particle in a box. Unlike a billiard ball, which exists at a scale large enough that it obeys the classical laws of physics very well, a quantum particle doesn’t have a clearly defined trajectory. Upon opening the box and looking inside, we will find the particle at a particular point, but as per Schrödinger's Equation, we have no way of predicting in advance where this point will be. All we have are probabilities!\n\nAnother consideration: if we decide not to open the box and spot the particle in a particular location, then where is it? According to the maths and theory of Schrödinger's Equation, the answer to that is that the particle exists in all the places we could have potentially seen it, simultaneously. This wacky idea that a particle can be said to be in several places at once is known as ‘quantum superposition’, and it was the inspiration for Schrödinger's famous thought experiment involving a cat.","a74c11d7-72e8-46ca-a291-e71019552553",[1185,1196,1206],{"id":1023,"data":1186,"type":69,"version":24,"maxContentLevel":35},{"type":69,"reviewType":35,"spacingBehaviour":24,"collapsingSiblings":1187,"multiChoiceQuestion":1188,"multiChoiceCorrect":1190,"multiChoiceIncorrect":1191,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6,"matchPairsQuestion":1192,"matchPairsPairs":1193},[1020,1024,1025],[1189],"Which of the following most closely applies to quantum superposition?",[1031],[1029,1032,1033],[142],[1194],{"left":1195,"right":1031,"direction":35},"Quantum superposition",{"id":1024,"data":1197,"type":69,"version":24,"maxContentLevel":35},{"type":69,"reviewType":35,"spacingBehaviour":24,"collapsingSiblings":1198,"multiChoiceQuestion":1199,"multiChoiceCorrect":1201,"multiChoiceIncorrect":1202,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6,"matchPairsQuestion":1203,"matchPairsPairs":1204},[1020,1023,1025],[1200],"Which of the following most closely applies to Schrödinger's Equation?",[1032],[1029,1031,1033],[142],[1205],{"left":1077,"right":1032,"direction":35},{"id":1207,"data":1208,"type":69,"version":24,"maxContentLevel":35},"c073154c-1320-43bf-95ed-e5ff24d1f72e",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":1209,"multiChoiceCorrect":1211,"multiChoiceIncorrect":1212,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[1210],"What is the term used to describe the idea that a particle can exist in multiple places at once?",[1195],[1213,1214,1215],"Quantum entanglement","Quantum mechanics","Quantum physics",{"id":1217,"data":1218,"type":24,"maxContentLevel":35,"version":25,"reviews":1222},"b3ddd201-9334-4b34-b418-eb3e3cf6d947",{"type":24,"title":1219,"markdownContent":1220,"audioMediaId":1221},"Quantum Superposition and Schrödinger's Cat page 2","Beyond his equation, ‘Schrödinger's Cat’ is the esteemed scientist’s second-best known claim to fame! He conceived this now household-name thought experiment as a critique of sorts, to demonstrate just how absurd and counterintuitive the idea of superposition as implied by quantum physics is. It goes as follows: imagine a cat in a steel chamber, next to a ‘Geiger counter’ containing a tiny amount of radioactive substance so small that perhaps it decays over the next second, and perhaps it doesn’t…\n\nIn this probabilistic arrangement, if the substance does decay, poison is released from the flask and the unfortunate cat is killed. So, according to quantum superposition, as long as we don’t look inside the chamber, the system evolves into a superposition state of radioactive atoms that have simultaneously decayed and not decayed. It follows from this logic that Schrödinger's cat will be simultaneously dead and alive. Weird.\n\n![Graph](image://f305e5e9-8c15-4d6a-a572-c18fe69767c9 \"Schrödinger's cat diagram. Image: Master of the Universe 322, CC BY-SA 4.0 \u003Chttps://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons\")","c214eff2-e644-44e8-b73b-eca5205d7491",[1223],{"id":1224,"data":1225,"type":69,"version":24,"maxContentLevel":35},"c53318c7-82e2-451b-923e-6d51fc08ff03",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":1226,"multiChoiceCorrect":1228,"multiChoiceIncorrect":1230,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[1227],"What thought experiment did Schrödinger conceive of to demonstrate the counterintuitive idea of quantum superposition?",[1229],"Schrödinger's Cat",[1231,1232,1233],"Schrödinger's Dog","Schrödinger's Monkey","Schrödinger's Alpaca",{"id":1235,"data":1236,"type":27,"maxContentLevel":35,"version":25,"orbs":1239},"7d576b88-6f45-450f-85ad-4a08b02f545a",{"type":27,"title":1237,"tagline":1238},"Heisenberg’s Uncertainty Principle and Other Quantum Weirdness","Werner Heisenberg and the importance of the uncertainty principle.",[1240,1310,1376],{"id":1241,"data":1242,"type":25,"version":25,"maxContentLevel":35,"summaryPage":1244,"introPage":1253,"pages":1260},"a43eda85-b866-4f70-a835-c14ca3d868f3",{"type":25,"title":1243},"Understanding Quantum Uncertainty",{"id":1245,"data":1246,"type":35,"maxContentLevel":35,"version":24},"92aa4895-ddcb-4553-a235-6d65d570183b",{"type":35,"title":1247,"summary":1248},"Understanding Quantum Uncertainty summary",[1249,1250,1251,1252],"Heisenberg's Uncertainty Principle says you can't precisely measure both position and momentum of a quantum particle","Schrödinger's Equation shows that we can only get probabilities, not exact answers, about a particle's location","Quantum superposition vanishes when we measure a particle, making it impossible to see a particle in multiple places at once","Measurement causes the wave function to collapse, snapping the particle into a specific state",{"id":1254,"data":1255,"type":53,"maxContentLevel":35,"version":24},"31e27818-5d30-4427-81a1-2934e03f52f5",{"type":53,"title":1256,"intro":1257},"Understanding Quantum Uncertainty intro",[1258,1259],"What does Heisenberg's Uncertainty Principle say about measuring a particle's position?","What happens to the wave function of a particle when it is observed?",[1261,1279,1293],{"id":1262,"data":1263,"type":24,"maxContentLevel":35,"version":25,"reviews":1267},"70048343-822e-4882-954d-70e264d95526",{"type":24,"title":1264,"markdownContent":1265,"audioMediaId":1266},"Understanding Quantum Uncertainty page 1","In 1927, German physicist Werner Heisenberg was able to show that a ‘fundamental limit’ exists for the precision with which you can measure the position and momentum of a quantum particle. The more precise you want to be about one, the less you can say about the other. This isn’t down to the quality of your measuring equipment either; it instead speaks to the inherent uncertainty encoded in nature!\n\n![Graph](image://a59dc132-52f8-41d0-abfa-b0cffbd78043 \"Werner Heisenberg. Image: Bundesarchiv, Bild 183-R57262 CC-BY-SA 3.0\")\n\nThis counterintuitive result is popularly known as ‘Heisenberg’s Uncertainty Principle’. It once again reminds us that in quantum mechanics we simply can no longer talk about the location or the trajectory of a particle with any certainty.","e199b778-306b-4793-ba2c-b9c674fb8dd1",[1268],{"id":1269,"data":1270,"type":69,"version":24,"maxContentLevel":35},"4931a9f3-5386-4052-b460-4dbe74e9142a",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":1271,"multiChoiceCorrect":1273,"multiChoiceIncorrect":1275,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[1272],"What is the popular name for the counterintuitive result of Werner Heisenberg's 1927 experiment?",[1274],"Heisenberg's Uncertainty Principle",[1276,1277,1278],"The Unlikeliness Principle","The Improbability Principle","The Wave Function Principle",{"id":1280,"data":1281,"type":24,"maxContentLevel":35,"version":25,"reviews":1285},"b950e11b-05ca-4efe-b9f1-0b5edc8bef48",{"type":24,"title":1282,"markdownContent":1283,"audioMediaId":1284},"Understanding Quantum Uncertainty page 2","Accepting the results of Schrödinger's Equation means accepting a probabilistic view of nature as we no longer can have exact answers to previously straightforward sounding questions like ‘Where is the electron at time ‘t’?’ The absolute best we can get from the mathematical representation of a quantum state – the wave function – is a probability.\n\nIt’s been made clear by experimental observations that the phenomenon of quantum superposition disappears when we look at a particle. After all, nobody has ever explicitly seen a single particle in several places at once! So why then does superposition disappear upon measurement? And how?","7b38410d-5bae-43bf-b086-4a5ad5a53cfe",[1286],{"id":1287,"data":1288,"type":69,"version":24,"maxContentLevel":35},"05bbb61a-d567-4eb0-a20f-c777629ee225",{"type":69,"reviewType":25,"spacingBehaviour":24,"binaryQuestion":1289,"binaryCorrect":1291,"binaryIncorrect":1292},[1290],"The wave function can give a definite statement of an electron's position",[73],[75],{"id":1294,"data":1295,"type":24,"maxContentLevel":35,"version":24,"reviews":1299},"e436e50a-f779-4edb-8b4f-d2910a7c6cd9",{"type":24,"title":1296,"markdownContent":1297,"audioMediaId":1298},"Understanding Quantum Uncertainty page 3","These are still unanswered questions in the field, but somehow in this strange new world the act of measurement causes reality to ‘snap’ into just one of the countless possible outcomes.\n\nPut in a slightly different way, it is said that the wave function – which previously told us that the particle was effectively ‘everywhere’ with an assortment of probabilities of actually being in any one place at each time – ‘collapses’ by some unknown quantum mechanism upon observation to have a specific location or momentum.","10235310-a31f-4db5-879c-35065a621e85",[1300],{"id":1301,"data":1302,"type":69,"version":24,"maxContentLevel":35},"88c12b1e-ac0f-489b-83ef-ac2d4c8c1412",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":1303,"multiChoiceCorrect":1305,"multiChoiceIncorrect":1307,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[1304],"What is the phenomenon that occurs when a particle is observed, causing the wave function to ‘collapse’ and reality to ‘snap’ into one of the possible outcomes?",[1306],"Wave Function Collapse",[1237,1308,1309],"Quantum Entanglement","Quantum Tunneling",{"id":1311,"data":1312,"type":25,"version":25,"maxContentLevel":35,"summaryPage":1314,"introPage":1323,"pages":1330},"be4cc9fb-cd57-4d41-8c4b-9b6628e8ba9c",{"type":25,"title":1313},"Exploring Quantum Phenomena",{"id":1315,"data":1316,"type":35,"maxContentLevel":35,"version":24},"8a7d16e5-d2e5-48b1-a5ce-ed5f173275c2",{"type":35,"title":1317,"summary":1318},"Exploring Quantum Phenomena summary",[1319,1320,1321,1322],"Heisenberg’s Uncertainty Principle means you can't measure both position and momentum of a quantum object perfectly","Time and energy in a quantum system can't be measured precisely at the same time","Quantum tunnelling lets particles pass through barriers by borrowing energy briefly","Subatomic particles can sometimes act like waves and tunnel through thin barriers",{"id":1324,"data":1325,"type":53,"maxContentLevel":35,"version":24},"ce7f635e-7d51-4abb-a8fe-2ba01d9a8c3a",{"type":53,"title":1326,"intro":1327},"Exploring Quantum Phenomena intro",[1328,1329],"What does Heisenberg’s Uncertainty Principle say about measuring position and momentum?","How does quantum tunnelling let particles pass through barriers?",[1331,1356,1370],{"id":1332,"data":1333,"type":24,"maxContentLevel":35,"version":24,"reviews":1337},"45d5f3aa-c9a3-4f65-9acd-ecac75e22bbe",{"type":24,"title":1334,"markdownContent":1335,"audioMediaId":1336},"Exploring Quantum Phenomena page 1","Heisenberg’s Uncertainty Principle states that you can never measure both the position and momentum of a quantum object with perfect precision. The more precise you are about one, the less precise you are about the other. However, position and momentum aren’t the only ‘observables’ – as they are often called in quantum physics – that can’t be measured simultaneously with arbitrary accuracy.\n\nThe time elapsed and energy of a quantum system are in fact another such pair. In other words, the more precise you are about the time span an event in your quantum system happens over, the less precise you can be about the energy associated with the event!","e9890a6f-3c00-4342-b01b-a9f6ac26abf4",[1338,1349],{"id":1025,"data":1339,"type":69,"version":24,"maxContentLevel":35},{"type":69,"reviewType":35,"spacingBehaviour":24,"collapsingSiblings":1340,"multiChoiceQuestion":1341,"multiChoiceCorrect":1343,"multiChoiceIncorrect":1344,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6,"matchPairsQuestion":1345,"matchPairsPairs":1346},[1020,1023,1024],[1342],"Which of the following most closely applies to Heisenberg's Uncertainty Principle?",[1033],[1029,1031,1032],[142],[1347],{"left":1348,"right":1033,"direction":35},"Heisenberg’s Uncertainty Principle",{"id":1350,"data":1351,"type":69,"version":24,"maxContentLevel":35},"7415455c-6aef-4479-9eac-5ea24ec85d65",{"type":69,"reviewType":24,"spacingBehaviour":24,"activeRecallQuestion":1352,"activeRecallAnswers":1354},[1353],"What is Heisenberg's Uncertainty Principle?",[1355],"You can never measure both the position and momentum of a quantum object with perfect precision",{"id":1357,"data":1358,"type":24,"maxContentLevel":35,"version":25,"reviews":1362},"60fa0e31-91de-4e89-b945-f8515fc6126b",{"type":24,"title":1359,"markdownContent":1360,"audioMediaId":1361},"Exploring Quantum Phenomena page 2","This is why particles can sometimes defy the rules of everyday life and acquire energy seemingly “out of nowhere” for a very brief moment of time, allowing for the bizarre phenomenon known as ‘quantum tunnelling’ in which a particle is said to ‘tunnel through’ what would normally be an unsurmountable energy barrier.\n\nOne of the quirkiest repercussions of quantum theory and its insistence on wave-particle duality, an electron – or any other subatomic particle for that matter – can potentially cancel the effects of an energy barrier if the barrier is thin enough. We can interpret this more practically as a particle being able to traverse through walls and doors if the barrier is thin enough. This is due to the quantum reliance on probability.","fa6c8c09-aef1-4a92-a69d-59806dc51634",[1363],{"id":1364,"data":1365,"type":69,"version":24,"maxContentLevel":35},"1294b568-c989-4ff8-aed3-7467c4e0252a",{"type":69,"reviewType":24,"spacingBehaviour":24,"activeRecallQuestion":1366,"activeRecallAnswers":1368},[1367],"How is it possible for a particle to traverse through thin layers?",[1369],"Quantum tunnelling",{"id":1371,"data":1372,"type":24,"maxContentLevel":35,"version":25},"69846045-b09c-40ae-8f27-860b5b1db706",{"type":24,"title":1373,"markdownContent":1374,"audioMediaId":1375},"Exploring Quantum Phenomena page 3","![Graph](image://93cd4fbc-22b6-4239-91f4-7838a4e41069 \"An illustration of quantum tunnelling. Image: MikeRun, CC BY-SA 4.0, via Wikimedia Commons\")\n\nQuantum tunnelling like this is possible because when a particle behaves as a ‘matter wave’, it can focus a great deal of energy on the barrier, ultimately negating it.\n\nClearly, the chance of macroscopic, everyday objects doing this is unthinkably small, but for subatomic particles or quarks – the even smaller ‘elementary’ particles which make up protons and neutrons – it is a very real and unsettling possibility.","b57915af-2955-4e73-8d16-35c61385f234",{"id":1377,"data":1378,"type":25,"version":25,"maxContentLevel":35,"summaryPage":1380,"introPage":1389,"pages":1396},"4543768a-29f2-4551-85b2-880733396698",{"type":25,"title":1379},"Unravelling Quantum Entanglement",{"id":1381,"data":1382,"type":35,"maxContentLevel":35,"version":24},"581f6a57-bef1-4bf8-bc49-270ac720b232",{"type":35,"title":1383,"summary":1384},"Unravelling Quantum Entanglement summary",[1385,1386,1387,1388],"Quantum entanglement links particles even if they are far apart","Entangled particles affect each other instantly, no matter the distance","Spin is a quantum property that gives particles angular momentum","Lasers can create entangled photons with opposite spin states",{"id":1390,"data":1391,"type":53,"maxContentLevel":35,"version":24},"59df3a8d-6f2a-442e-9fc2-a7be9a53030a",{"type":53,"title":1392,"intro":1393},"Unravelling Quantum Entanglement intro",[1394,1395],"What is the role of 'spin' in quantum entanglement?","How does observing the spin state of one entangled photon affect its partner?",[1397,1413,1436],{"id":1398,"data":1399,"type":24,"maxContentLevel":35,"version":25,"reviews":1403},"6ad02757-d3df-44db-ac5d-42e456863786",{"type":24,"title":1400,"markdownContent":1401,"audioMediaId":1402},"Unravelling Quantum Entanglement page 1","Yet another popular example of quantum weirdness that often captures the public imagination is that of ‘quantum entanglement’, which arises as an implication of the wave function derived from Schrödinger's Equation. It’s all down to the fact that a wave function – a solution to Schrödinger's Equation for a given quantum system that gives you information about it – can be used to describe a system of many particles and not just one.\n\n![Graph](image://0a8a04a1-cd23-4791-9581-392f2192336a \"Two particles experience quantum entanglement. Image: Kanijoman, CC BY 2.0 via Flickr, https://creativecommons.org/licenses/by/2.0/\")\n\nOften, it’s simply not possible to decompose an overall wave function for a multi-particle system into components that correspond to the individual particles. When that happens, the interpretation is that the particles involved have become inextricably linked, even if they were to move far, far away from each other.","3eaddb1c-11b5-4616-8e57-43f449ebcc13",[1404],{"id":1405,"data":1406,"type":69,"version":24,"maxContentLevel":35},"89f0a1e5-f4f4-4edf-bc81-de0261ca75d2",{"type":69,"reviewType":25,"spacingBehaviour":24,"binaryQuestion":1407,"binaryCorrect":1409,"binaryIncorrect":1411},[1408],"Select the definition of quantum entanglement:",[1410],"Particles share a single wave function, making them interconnected, even when far apart",[1412],"The negative charge of an electron is disrupted by quantum mechanics, causing a tangled position",{"id":1414,"data":1415,"type":24,"maxContentLevel":35,"version":25,"reviews":1419},"9ad8bacf-2437-4f65-8fe8-5e89c58a296c",{"type":24,"title":1416,"markdownContent":1417,"audioMediaId":1418},"Unravelling Quantum Entanglement page 2","The particles are said to be ‘entangled’, and when something happens to one of the particles, a corresponding thing happens to its distant partner. Einstein famously described this phenomenon as “spooky action at a distance”.\n\nThere’s a uniquely quantum property that all particles possess known as ‘spin’ which can either be in the ‘up-spin state’ or ‘down-spin state’. It has nothing to do with any physical rotation and is instead a property that results in a particle having ‘angular momentum’, without it rotating. For this reason, it’s usually called ‘intrinsic angular momentum’.\n\n![Graph](image://b8c1f92b-9746-4d7c-820c-bb55858b0a1d \"A laser beam fired through crystal. Image: Neath g, CC BY-SA 4.0 \u003Chttps://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons\")","7f3b68af-a8a2-4d15-b6c0-8c5154434efc",[1420,1428],{"id":1421,"data":1422,"type":69,"version":24,"maxContentLevel":35},"afb296cb-182f-4fb5-a135-1919709dfde2",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":1423,"multiChoiceCorrect":1425,"multiChoiceIncorrect":1426,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[1424],"What did Einstein famously describe as “spooky action at a distance”?",[1213],[1348,1427,882],"Schrödinger’s Equation",{"id":1429,"data":1430,"type":69,"version":24,"maxContentLevel":35},"2b57bebf-9206-4c01-998e-c260d159cda2",{"type":69,"reviewType":25,"spacingBehaviour":24,"binaryQuestion":1431,"binaryCorrect":1433,"binaryIncorrect":1434},[1432],"What is the name of the property that all particles possess, which results in a particle having ‘angular momentum’ without it rotating?",[1131],[1435],"Quantum tunneling",{"id":1437,"data":1438,"type":24,"maxContentLevel":35,"version":25,"reviews":1442},"f5771ff0-19bf-4ada-913d-843792868337",{"type":24,"title":1439,"markdownContent":1440,"audioMediaId":1441},"Unravelling Quantum Entanglement page 3","A laser beam fired through certain crystals can cause individual photons to split into a pair of ‘entangled’ photons, with opposing spin states. Once entangled and separated by a vast distance, actions performed on one can affect the other.\n\nIf Photon A is observed and takes on an up-spin state, entangled Photon B – now far away – mysteriously takes up a state relative to that of Photon B, in this case a down-spin state! This transfer of state between the entangled photons happens instantaneously, regardless of the distance between them.","ada67cdf-0b44-42eb-90e4-788ab5a4f12d",[1443],{"id":1444,"data":1445,"type":69,"version":24,"maxContentLevel":35},"669b8f34-1baa-480f-a39c-6574ade9aa81",{"type":69,"reviewType":28,"spacingBehaviour":24,"clozeQuestion":1446,"clozeWords":1448},[1447],"Spin' is a uniquely quantum quality that does not describe a particle's physical rotation but instead its angular momentum.",[1131],{"id":1450,"data":1451,"type":27,"maxContentLevel":35,"version":25,"orbs":1454},"86c92b27-70ed-4513-8112-32c31b118c6b",{"type":27,"title":1452,"tagline":1453},"Practical Uses of Quantum Physics Today","The contemporary world of quantum, and where it's headed.",[1455,1528],{"id":1456,"data":1457,"type":25,"version":25,"maxContentLevel":35,"summaryPage":1459,"introPage":1468,"pages":1475},"02b8f164-65fc-4e2f-896a-b4998e1c0c40",{"type":25,"title":1458},"Quantum Technologies",{"id":1460,"data":1461,"type":35,"maxContentLevel":35,"version":24},"119762b3-7838-45c1-86cf-9e6701e3b330",{"type":35,"title":1462,"summary":1463},"Quantum Technologies summary",[1464,1465,1466,1467],"Toasters glow red due to the quantum nature of energy","Qubits in quantum computers can be in multiple states at once","Quantum computers can process many operations simultaneously","Atomic clocks use electron transitions for extreme time accuracy",{"id":1469,"data":1470,"type":53,"maxContentLevel":35,"version":24},"89869d21-6b30-4f42-97ff-e15dd52c4f31",{"type":53,"title":1471,"intro":1472},"Quantum Technologies intro",[1473,1474],"How does a qubit differ from a classical bit?","Why are quantum computers expected to revolutionize climate change modeling?",[1476,1490,1514],{"id":1477,"data":1478,"type":24,"maxContentLevel":35,"version":25,"reviews":1482},"450d5862-d8ef-49dd-87ab-1e15ac24355d",{"type":24,"title":1479,"markdownContent":1480,"audioMediaId":1481},"Quantum Technologies page 1","We will now embark on a whistle-stop tour of the major ways quantum ideas are being utilized to enhance our lives or develop new and exciting technologies that push the boundary of what’s possible. While some more imaginative applications of quantum physics may seem far off, many current technologies already employ quantum principles. To illustrate how this field’s influence can be found everywhere – even in the places you’d least expect – let’s quickly talk about a common kitchen appliance that demonstrates one of the phenomena that inspired the founding of quantum mechanics.\n\nToasters contain a metallic element which glows red when it heats up. Any material in fact, when heated to the same temperature will glow red, then yellow, and finally white as it gets hotter. The restricted range of visible light wavelengths being emitted from the heated elements is a direct result of the quantum nature of energy! It’s in fact one of the things which tipped physicists off!","5675ae10-72ad-4485-90ae-e9a1e21414ec",[1483],{"id":1484,"data":1485,"type":69,"version":24,"maxContentLevel":35},"187cb0c3-fd69-45a6-aec4-6b354133c6a0",{"type":69,"reviewType":24,"spacingBehaviour":24,"activeRecallQuestion":1486,"activeRecallAnswers":1488},[1487],"Why do toasters illustrate the existence of quantum phenomena?",[1489],"They demonstrate the photoelectric effect, because whatever the material being heated up, the colour is always the same shade of orange",{"id":1491,"data":1492,"type":24,"maxContentLevel":35,"version":25,"reviews":1496},"5fad096b-10ad-4cb7-992c-10971b7c7102",{"type":24,"title":1493,"markdownContent":1494,"audioMediaId":1495},"Quantum Technologies page 2","Quantum computing leverages quantum phenomena such as quantum bits – or ‘qubits’ – superposition and entanglement to perform data operations at lightning speed. In classical computing, a ‘bit’ is a unit of information which is stored as either 1 or 0. A qubit on the other hand is a two-level quantum system which can either be in the 1 state, the 0 state, or some combination of both states via superposition, allowing for information to be processed far more quickly.\n\n![Graph](image://496a4afc-3007-4159-91f6-9451d82bfe35 \"A quantum computer. Image credit: IBM\")\n\nQubits can be used to tackle extremely difficult tasks which ordinary computers simply cannot perform on their own. This added flexibility means that quantum computers can process numerous operations at the same time rather than one by one as our usual computers do. There’s a reason this new breed of computer is predicted to have a huge impact on understanding climate change and the vast amount of data that needs to be processed to model it!","7ab3bbb7-38e4-4924-b3be-d89ced0b301c",[1497,1506],{"id":1498,"data":1499,"type":69,"version":24,"maxContentLevel":35},"a41043e4-050f-433a-9b7c-5f7d1874e45a",{"type":69,"reviewType":25,"spacingBehaviour":24,"binaryQuestion":1500,"binaryCorrect":1502,"binaryIncorrect":1504},[1501],"What is the name of the unit of information used in quantum computing?",[1503],"Qubit",[1505],"Bit",{"id":1507,"data":1508,"type":69,"version":24,"maxContentLevel":35},"4ede42ad-a419-4976-9e66-22ffe04c30b4",{"type":69,"reviewType":25,"spacingBehaviour":24,"binaryQuestion":1509,"binaryCorrect":1511,"binaryIncorrect":1512},[1510],"What is a unit of information stored as either 1 or 0 in classical computing?",[1505],[1513],"Byte",{"id":1515,"data":1516,"type":24,"maxContentLevel":35,"version":25,"reviews":1520},"34e37615-557c-4824-aaca-e6b3346a59d2",{"type":24,"title":1517,"markdownContent":1518,"audioMediaId":1519},"Quantum Technologies page 3","As we know, when atoms are exposed to particular frequencies of electromagnetic radiation, the electrons orbiting the atom’s nucleus are made to “jump” between well-known, discrete energy states. Clocks based on this jumping in theory would offer an extremely precise way to measure time. That’s exactly why the quantum clock – more commonly known as an ‘atomic clock’ – has been successfully built!\n\n![Graph](image://22aa91a4-22ec-42f2-bf44-ea16c5a276fb \"A classical clock. Image: Public domain via Pxfuel\")\n\nJust as a classical clock is an apparatus that counts a repetitive event – for example, a mechanical clock with a pendulum that swings once every second or an electronic clock that uses a vibrating quartz crystal to keep time – an atomic clock relies on the quantum transitions of electrons to achieve an unfathomable level of accuracy. Using this technology, time can be measured within a margin of error of just one second in up to 100 million years! They are integral to Global Positioning Systems (GPS) and are also used to send signals to spacecraft to determine their position.","e6e844d4-8c3d-4bdb-8858-012dd6a03dc6",[1521],{"id":1522,"data":1523,"type":69,"version":24,"maxContentLevel":35},"bb9d9e5e-6d65-492f-9e9f-70fb08909038",{"type":69,"reviewType":24,"spacingBehaviour":24,"activeRecallQuestion":1524,"activeRecallAnswers":1526},[1525],"How does an atomic clock measure time?",[1527],"By counting the quantum transitions of electrons",{"id":1529,"data":1530,"type":25,"version":25,"maxContentLevel":35,"summaryPage":1532,"introPage":1541,"pages":1548},"694ddf0d-0176-487e-8ada-7081d167773e",{"type":25,"title":1531},"Quantum Physics in Light and Time",{"id":1533,"data":1534,"type":35,"maxContentLevel":35,"version":24},"47e4ab37-8c0b-4c88-ac11-d4719be4592b",{"type":35,"title":1535,"summary":1536},"Quantum Physics in Light and Time summary",[1537,1538,1539,1540],"Lasers emit light because their waves are perfectly synchronized","Fluorescent bulbs glow due to quantum energy jumps in mercury atoms","Semiconductors use quantum effects to control electrical conductivity","MRI scans use particle spin to create detailed body images",{"id":1542,"data":1543,"type":53,"maxContentLevel":35,"version":24},"b8f34dd5-1020-44ed-bdb4-a4752d82216b",{"type":53,"title":1544,"intro":1545},"Quantum Physics in Light and Time intro",[1546,1547],"How do semiconductors use quantum mechanics to control electrical conductivity?","What quantum property does MRI use to create body images?",[1549,1572,1586],{"id":1550,"data":1551,"type":24,"maxContentLevel":35,"version":25,"reviews":1555},"e260ba1c-84d0-49e0-b678-7cd8641797e8",{"type":24,"title":1552,"markdownContent":1553,"audioMediaId":1554},"Quantum Physics in Light and Time page 1","Lasers are only able to emit a concentrated beam of light because all the individual light waves – using the term ‘wave’ loosely now that we know the dual nature of light! – are ‘coherent’. Coherent in this scientific sense means that each of these light waves have completely identical frequencies and waveforms, i.e., they are in perfect synchronization with each other. To generate laser light that meets this stringent definition we rely on a technique called ‘stimulated emission’.\n\n![Graph](image://d6c8e743-6864-4c22-9e02-6071b6cdaa87 \"A laser used for experiments. Image: Public domain via picryl\")\n\nIn stimulated emission, a photon is used to stimulate an already excited atomic electron to drop down to a lower quantum energy state and release two identical photons in the process which are travelling coherently. By repeating this process countless times in a reflective chamber, we can amass a huge number of photons which are coherent and once emitted together form what we know as a laser. The word ‘laser’ is an acronym which stands for “Light Amplification by Stimulated Emission of Radiation”!","2577ce45-a126-4aaf-bc0d-75572358dd72",[1556,1563],{"id":1557,"data":1558,"type":69,"version":24,"maxContentLevel":35},"b1527327-d9fb-4420-b315-2529681ce0f1",{"type":69,"reviewType":28,"spacingBehaviour":24,"clozeQuestion":1559,"clozeWords":1561},[1560],"Laser light is generated by a process called stimulated emission, which involves photons.",[1562],"stimulated",{"id":1564,"data":1565,"type":69,"version":24,"maxContentLevel":35},"ebade149-864d-4ae2-99d0-1d8e5c8f83f0",{"type":69,"reviewType":25,"spacingBehaviour":24,"binaryQuestion":1566,"binaryCorrect":1568,"binaryIncorrect":1570},[1567],"What is \"Laser\" an acronym for?",[1569],"Light Amplification by Stimulated Emission of Radiation",[1571],"Light Aided by Stimulated Electrode Rows",{"id":1573,"data":1574,"type":24,"maxContentLevel":35,"version":25,"reviews":1578},"3cad787a-581e-432d-bd35-be8fcdabf870",{"type":24,"title":1575,"markdownContent":1576,"audioMediaId":1577},"Quantum Physics in Light and Time page 2","You may be surprised to hear that the ubiquitous fluorescent bulb only works because of quantum phenomena! They contain electrodes which eject high-energy electrons when heated up. These electrons in turn bombard a tiny sample of mercury placed inside of the bulb, supplying energy to the electrons in the mercury atoms and causing them to jump up to a higher energy quantum state.\n\n![Graph](image://3d4415f9-8714-4ac6-8781-cea7c67b7177 \"Fluorescent bulbs. Image: Public domain via Freepik\")\n\nThe inherent instability present in an ‘excited atom’ ensures that these electrons eventually return to their stable ground state, in the process emitting electromagnetic radiation in the form of visible light photons. The production of these photons in the bulb, as dictated by the theory of quantum mechanics, provides the light which we see radiated from the bulb!","2302e565-81af-44b1-ac73-e48537eff804",[1579],{"id":1580,"data":1581,"type":69,"version":24,"maxContentLevel":35},"895a14c1-46fd-4ca9-9754-3821d18970f2",{"type":69,"reviewType":24,"spacingBehaviour":24,"activeRecallQuestion":1582,"activeRecallAnswers":1584},[1583],"How does a fluorescent bulb produce light?",[1585],"By supplying energy to the electrons in a tiny sample of mercury",{"id":1587,"data":1588,"type":24,"maxContentLevel":35,"version":25,"reviews":1592},"171a4ae7-f5a6-43a5-8613-4350643ef4ad",{"type":24,"title":1589,"markdownContent":1590,"audioMediaId":1591},"Quantum Physics in Light and Time page 3","Before closing out this Pathway, there are two hugely influential areas which simply would not be possible without an understanding of quantum mechanics.\n\n![Graph](image://c20d886a-2b60-43e6-9d4b-fe071f4abee3 \"Delocalized electrons in a semiconductor. Image: Public domain\")\n\nThe first of these applications is in ‘semiconductors’, which are materials which possess an electrical conductivity somewhere between that of a conductor – which has ample shared or ‘delocalized’ electrons in its atomic structure and can carry a current with ease – and an insulator, which prevents the flow of electricity. Semiconductors are complex, and function via quantum effects to accommodate a wide range of possible currents and voltages, making them vital in all sorts of everyday electronics such as computers, TVs, and phones.\n\nSecondly, there’s Magnetic Resonance Imaging (MRI). This medical imaging technique uses the quantum property of particle ‘spin’ in hydrogen protons to infer whether each small area of the body is composed of water or fat, culminating in a beautifully clear image of a slice of the body.","bcb6da4f-e42b-4cb7-a9b2-10e67dccf5bd",[1593],{"id":1594,"data":1595,"type":69,"version":24,"maxContentLevel":35},"92af64aa-3553-4d9c-b996-a1c489752c8c",{"type":69,"reviewType":35,"spacingBehaviour":24,"multiChoiceQuestion":1596,"multiChoiceCorrect":1598,"multiChoiceIncorrect":1600,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[1597],"What medical imaging technique uses the quantum property of particle ‘spin’ in hydrogen protons?",[1599],"Magnetic Resonance Imaging (MRI)",[1601,1602,1603],"X-ray Imaging","Ultrasound Imaging","Gamma Ray Imaging",{"left":4,"top":4,"width":1605,"height":1605,"rotate":4,"vFlip":6,"hFlip":6,"body":1606},24,"\u003Cpath fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"round\" stroke-linejoin=\"round\" stroke-width=\"2\" d=\"m9 18l6-6l-6-6\"/>",{"left":4,"top":4,"width":1605,"height":1605,"rotate":4,"vFlip":6,"hFlip":6,"body":1608},"\u003Cg fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"round\" stroke-linejoin=\"round\" stroke-width=\"2\">\u003Cpath d=\"M12.586 2.586A2 2 0 0 0 11.172 2H4a2 2 0 0 0-2 2v7.172a2 2 0 0 0 .586 1.414l8.704 8.704a2.426 2.426 0 0 0 3.42 0l6.58-6.58a2.426 2.426 0 0 0 0-3.42z\"/>\u003Ccircle cx=\"7.5\" cy=\"7.5\" r=\".5\" fill=\"currentColor\"/>\u003C/g>",1778179168644]