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dense.","correct":false,"explanation":"The early universe was not cold and sparse; its enormous temperature and density are fundamental predictions of the Big Bang theory."},{"text":"It was extremely hot and spread out.","correct":false,"explanation":"The early universe was not cool and spread out. It began in an extremely hot, dense state before expansion reduced its density."},{"text":"It was extremely cold and spread out.","correct":false,"explanation":"Reversing both conditions contradicts the model: the early universe was extremely hot and dense, not cold and spread out."}]},{"id":"79a3228f-a9fc-4877-b89c-5a6d12876454","cardType":"basic","points":2,"front":"How does the Big Bang theory describe the change in the universe's temperature and volume over time?","back":"The universe has expanded and cooled.","mcqOptions":[{"text":"The universe has expanded and cooled.","correct":true,"explanation":"As space expands, matter and galaxies become more widely separated, while the universe’s energy is distributed over a larger volume and its temperature falls."},{"text":"The universe has contracted and heated.","correct":false,"explanation":"The universe has not contracted and heated overall. Big Bang evidence indicates continuing expansion accompanied by cooling since the early hot state."},{"text":"The universe has expanded and heated.","correct":false,"explanation":"Expansion is correct, but the universe has cooled rather than heated as its contents and radiation have become more spread out."},{"text":"The universe has contracted and cooled.","correct":false,"explanation":"Cooling is correct, but the universe has expanded rather than contracted; distant galaxies are generally receding as space increases."}]},{"id":"08524fc5-cd98-410d-ab4b-b11eaadc9d17","cardType":"cloze","points":null,"front":"The Big Bang was not an explosion into empty space; instead, the [ ] has increased over time.","back":"The Big Bang was not an explosion into empty space; instead, the space between galaxies has increased over time.","mcqOptions":[{"text":"space between galaxies","correct":true,"explanation":"The expansion is an increase in the space separating galaxies themselves, rather than an explosion spreading matter into pre-existing empty space."},{"text":"galaxies themselves","correct":false,"explanation":"Galaxies are not generally growing larger because of cosmic expansion. The increasing separation is mainly due to the expansion of space between them."},{"text":"amount of matter","correct":false,"explanation":"The Big Bang describes expanding space, not an increase in the amount of matter between galaxies. Matter is not continually created in this way."},{"text":"temperature of space","correct":false,"explanation":"The universe has cooled over time, but temperature is not the quantity that increases to separate galaxies; the space between them expands."}]},{"id":"f06c9312-7017-4476-9097-61fc6f3483eb","cardType":"basic","points":2,"front":"What happens to the observed wavelength and frequency of a wave if the source moves away from the observer?","back":"

Wavelength increases
Frequency decreases

","mcqOptions":[{"text":"

Wavelength increases
Frequency decreases

","correct":true,"explanation":"A source moving away makes successive wavefronts arrive farther apart, increasing the observed wavelength and reducing the observed frequency."},{"text":"

Wavelength decreases
Frequency increases

","correct":false,"explanation":"This reverses the Doppler effect. A receding source produces longer wavelengths and lower frequencies, whereas shorter wavelengths and higher frequencies indicate approach."},{"text":"

Wavelength decreases
Frequency decreases

","correct":false,"explanation":"The wavelength change is reversed here. Moving away stretches the waves, so wavelength increases; because wave speed is constant, frequency decreases."},{"text":"

Wavelength increases
Frequency increases

","correct":false,"explanation":"The frequency change is reversed here. A receding source produces fewer wavefronts per second, so frequency decreases while wavelength increases."}]},{"id":"108277df-07f1-4668-a324-6dad19ddcc0c","cardType":"basic","points":2,"front":"What happens to the observed wavelength and frequency of a wave if the source moves towards the observer?","back":"

Wavelength decreases
Frequency increases

","mcqOptions":[{"text":"

Wavelength decreases
Frequency increases

","correct":true,"explanation":"When the source approaches, successive wavefronts are compressed before reaching the observer, so wavelength decreases and frequency increases."},{"text":"

Wavelength increases
Frequency decreases

","correct":false,"explanation":"This describes a source moving away, not towards the observer. Approach compresses the wavefronts, decreasing wavelength and increasing frequency."},{"text":"

Wavelength decreases
Frequency decreases

","correct":false,"explanation":"The wavelength change is correct, but approaching wavefronts arrive more frequently, so frequency increases rather than decreases."},{"text":"

Wavelength increases
Frequency increases

","correct":false,"explanation":"The frequency change is correct, but an approaching source compresses the wavefronts, so wavelength decreases rather than increases."}]},{"id":"bc5798ea-2cb9-4dcf-a444-f8abdc2cbc3b","cardType":"basic","points":1,"front":"In terms of spectral lines, how is red-shift identified?","back":"The observed wavelength is longer than the reference wavelength (measured on Earth).","mcqOptions":[{"text":"The observed wavelength is longer than the reference wavelength (measured on Earth).","correct":true,"explanation":"Red-shift means the spectral line is displaced towards longer wavelengths compared with the same reference line measured from a source on Earth."},{"text":"The observed wavelength is shorter than the reference wavelength (measured on Earth).","correct":false,"explanation":"A shorter observed wavelength is blue-shift, usually indicating approach. Red-shift specifically requires the observed wavelength to be longer than the reference."},{"text":"The observed frequency is longer than the reference frequency (measured on Earth).","correct":false,"explanation":"Red-shift compares wavelengths, not frequencies. The observed wavelength is longer than the reference wavelength; its frequency is correspondingly lower."},{"text":"The observed wavelength is equal to the reference wavelength (measured on Earth).","correct":false,"explanation":"The reference measurement provides the comparison, but red-shift occurs when the observed wavelength is longer, not shorter, than that reference."}]},{"id":"66137779-36c0-48ee-bf39-b1fe5fdcbd4a","cardType":"cloze","points":null,"front":"Red-shift indicates that a galaxy is [ ] (moving away) from Earth.","back":"Red-shift indicates that a galaxy is receding (moving away) from Earth.","mcqOptions":[{"text":"receding","correct":true,"explanation":"Receding means moving away from Earth. A galaxy moving away produces red-shift because its observed light has a longer wavelength than its reference wavelength."},{"text":"approaching","correct":false,"explanation":"Approaching means moving towards Earth and produces blue-shift, with shorter observed wavelengths. Red-shift instead indicates that the galaxy is receding."},{"text":"stationary","correct":false,"explanation":"Stationary means not moving relative to Earth and would not produce a Doppler red-shift. Red-shift indicates motion away, or recession."},{"text":"orbiting","correct":false,"explanation":"Orbiting describes motion around another object, not specifically motion away from Earth. Red-shift in this context indicates that the galaxy is receding."}]},{"id":"2046ebe9-1f03-440c-872d-18e165d34ce3","cardType":"basic","points":1,"front":"State the equation linking red-shift, galaxy velocity, and the speed of light.","back":"$$$\\frac{\\lambda - \\lambda_0}{\\lambda_0} = \\frac{\\Delta\\lambda}{\\lambda_0} = \\frac{v}{c}$$","mcqOptions":[{"text":"$$$\\frac{\\lambda - \\lambda_0}{\\lambda_0} = \\frac{\\Delta\\lambda}{\\lambda_0} = \\frac{v}{c}$$","correct":true,"explanation":"Red-shift is the change in wavelength divided by the original wavelength, and for speeds much smaller than light speed this fractional change equals the galaxy’s velocity divided by the speed of light."},{"text":"$$$\\frac{\\lambda_0 - \\lambda}{\\lambda_0} = \\frac{\\Delta\\lambda}{\\lambda_0} = \\frac{v}{c}$$","correct":false,"explanation":"The wavelength increases for a receding galaxy, so the change is observed wavelength minus original wavelength. Reversing the subtraction gives the wrong sign for red-shift."},{"text":"$$$\\frac{\\lambda - \\lambda_0}{\\lambda_0} = \\frac{\\Delta\\lambda}{\\lambda_0} = \\frac{c}{v}$$","correct":false,"explanation":"The fractional wavelength change is proportional to velocity divided by light speed, not the inverse. Swapping these quantities would predict larger red-shifts for slower galaxies."},{"text":"$$$\\frac{\\lambda - \\lambda_0}{\\lambda} = \\frac{\\Delta\\lambda}{\\lambda_0} = \\frac{v}{c}$$","correct":false,"explanation":"Red-shift uses the original emitted wavelength as the denominator. Using the observed wavelength instead changes the fractional measurement and does not give the standard equation."}]},{"id":"49d980e9-89af-4f00-97fd-e9fb5433ae1a","cardType":"basic","points":2,"front":"In the red-shift equation $\\frac{\\Delta\\lambda}{\\lambda_0} = \\frac{v}{c}$, what do the symbols $\\lambda_0$ and $c$ represent?","back":"

$\\lambda_0$: reference wavelength
$c$: speed of light ($3.0 \\times 10^8$ m/s)

","mcqOptions":[{"text":"

$\\lambda_0$: reference wavelength
$c$: speed of light ($3.0 \\times 10^8$ m/s)

","correct":true,"explanation":"The subscript zero identifies the unshifted laboratory wavelength used for comparison, while $c$ is the speed of light in a vacuum, approximately $3.0 \\times 10^8$ m/s."},{"text":"

$\\lambda_0$: observed wavelength
$c$: speed of sound ($3.4 \\times 10^2$ m/s)

","correct":false,"explanation":"This confuses the reference wavelength with the measured wavelength and light with sound. The equation uses the unshifted reference wavelength and the speed of light, $3.0 \\times 10^8$ m/s."},{"text":"

$\\lambda_0$: reference frequency
$c$: recession velocity ($3.0 \\times 10^5$ m/s)

","correct":false,"explanation":"Frequency is a different wave quantity, and the listed value is not the speed of light. Here $\\lambda_0$ is the reference wavelength and $c$ is $3.0 \\times 10^8$ m/s."},{"text":"

$\\lambda_0$: change in wavelength
$c$: velocity of the galaxy ($3.0 \\times 10^8$ m/s)

","correct":false,"explanation":"The wavelength change is $\\Delta\\lambda$, not $\\lambda_0$, and $c$ is not the galaxy’s velocity. The symbols represent reference wavelength and the speed of light respectively."}]},{"id":"63f4cb76-d1e3-4e02-96a1-ca49d993ec39","cardType":"basic","points":1,"front":"How is the change in wavelength ($\\Delta\\lambda$) calculated for the red-shift equation?","back":"$$$\\Delta\\lambda = \\text{observed wavelength} - \\text{reference wavelength}$$","mcqOptions":[{"text":"$$$\\Delta\\lambda = \\text{observed wavelength} - \\text{reference wavelength}$$","correct":true,"explanation":"The wavelength change is the final measured value minus the original reference value. A red-shift therefore gives a positive $\\Delta\\lambda$ because the observed wavelength is longer."},{"text":"$$$\\Delta\\lambda = \\text{reference wavelength} - \\text{observed wavelength}$$","correct":false,"explanation":"Reversing the subtraction gives a negative value for a red-shift, even though the observed wavelength has increased. The correct order is observed wavelength minus reference wavelength."},{"text":"$$$\\Delta\\lambda = \\text{observed wavelength} + \\text{reference wavelength}$$","correct":false,"explanation":"Adding the two wavelengths gives their total, not the change between them. The change must be calculated by subtracting the reference wavelength from the observed wavelength."},{"text":"$$$\\Delta\\lambda = \\frac{\\text{observed wavelength}}{\\text{reference wavelength}}$$","correct":false,"explanation":"Dividing the wavelengths produces a dimensionless ratio rather than a wavelength change. $\\Delta\\lambda$ is found by subtracting the reference wavelength from the observed wavelength."}]},{"id":"0662d0ea-44f1-423b-8c1f-123847aee2a2","cardType":"basic","points":2,"front":"How does the distance of a galaxy generally affect its red-shift and recession velocity?","back":"More distant galaxies have a greater red-shift and a higher recession velocity.","mcqOptions":[{"text":"More distant galaxies have a greater red-shift and a higher recession velocity.","correct":true,"explanation":"Observations show that greater galaxy distances generally correspond to larger red-shifts. Through the red-shift equation, a larger red-shift also indicates a higher recession velocity."},{"text":"More distant galaxies have a smaller red-shift and a lower recession velocity.","correct":false,"explanation":"This reverses the observed distance-red-shift relationship. More distant galaxies generally show greater red-shifts, indicating that they are receding at higher velocities."},{"text":"More distant galaxies have a greater blue-shift and a higher approach velocity.","correct":false,"explanation":"Blue-shift indicates motion towards the observer, not the general recession of distant galaxies. More distant galaxies generally have greater red-shifts and higher recession velocities."},{"text":"More distant galaxies have a constant red-shift and an equal recession velocity.","correct":false,"explanation":"The expansion of the universe does not give all galaxies the same observed shift or velocity. More distant galaxies generally have greater red-shifts and higher recession velocities."}]},{"id":"be6a53f8-d3d0-4d75-985b-47773ca0d90b","cardType":"cloze","points":null,"front":"A larger red-shift ratio ($\\frac{\\Delta\\lambda}{\\lambda_0}$) indicates a [ ] recession velocity.","back":"A larger red-shift ratio ($\\frac{\\Delta\\lambda}{\\lambda_0}$) indicates a greater recession velocity.","mcqOptions":[{"text":"greater","correct":true,"explanation":"The equation gives $v=c\\Delta\\lambda/\\lambda_0$, so recession velocity is directly proportional to the red-shift ratio. A larger positive ratio therefore means a greater recession velocity."},{"text":"smaller","correct":false,"explanation":"This reverses the direct proportionality in the red-shift equation. Because $v=c\\Delta\\lambda/\\lambda_0$, a larger red-shift ratio indicates a greater, not smaller, recession velocity."},{"text":"constant","correct":false,"explanation":"Recession velocity is not fixed when the red-shift ratio changes. Since the ratio equals $v/c$, increasing it corresponds to a greater recession velocity."},{"text":"zero","correct":false,"explanation":"A zero recession velocity corresponds to zero red-shift ratio, not a larger ratio. A larger positive ratio indicates a greater recession velocity."}]},{"id":"02cf2d26-b14b-4890-a892-1ae7139ed377","cardType":"basic","points":2,"front":"Name the two main pieces of evidence for the Big Bang theory.","back":"

Red-shift of distant galaxies
Cosmic Microwave Background (CMB) radiation

","mcqOptions":[{"text":"

Red-shift of distant galaxies
Cosmic Microwave Background (CMB) radiation

","correct":true,"explanation":"Distant galaxies are systematically red-shifted, showing cosmic expansion, while the CMB is cooled remnant radiation from the early universe. Together they strongly support the Big Bang model."},{"text":"

Blue-shift of distant galaxies
Cosmic Microwave Background (CMB) radiation

","correct":false,"explanation":"A general blue-shift would imply galaxies approaching rather than an expanding universe. The two principal observations are red-shift of distant galaxies and Cosmic Microwave Background radiation."},{"text":"

Red-shift of distant galaxies
Dark matter around galaxies

","correct":false,"explanation":"Dark matter is inferred from gravitational effects but is not one of these two principal Big Bang observations. The required evidence is galactic red-shift and Cosmic Microwave Background radiation."},{"text":"

Sunspots on nearby stars
Radio waves from pulsars

","correct":false,"explanation":"Sunspots and radio waves from pulsars are local astrophysical phenomena, not the main evidence for the universe’s origin. The accepted pair is galactic red-shift and CMB radiation."}]},{"id":"a9f5734b-8dd9-4946-ba5f-30ab5603a024","cardType":"basic","points":3,"front":"Explain the logical link between red-shift and the Big Bang theory.","back":"Red-shift shows galaxies move apart (expansion); reversing this suggests the universe was once smaller, hotter, and denser.","mcqOptions":[{"text":"Red-shift shows galaxies move apart (expansion); reversing this suggests the universe was once smaller, hotter, and denser.","correct":true,"explanation":"Systematic red-shift indicates that galaxies are receding and space is expanding. Extrapolating this expansion backwards implies that the universe began in a smaller, hotter and denser state."},{"text":"Red-shift shows galaxies move apart (expansion); reversing this suggests the universe was once larger, cooler, and less dense.","correct":false,"explanation":"This reverses the backward extrapolation of cosmic expansion. If galaxies are moving apart now, the earlier universe must have been smaller, hotter and denser, not larger and cooler."},{"text":"Red-shift shows galaxies move together (contraction); reversing this suggests the universe was once larger, cooler, and less dense.","correct":false,"explanation":"Red-shift indicates recession rather than galaxies moving together. Reversing the observed expansion leads to an earlier universe that was smaller, hotter and denser."},{"text":"Red-shift shows galaxies move apart (expansion); reversing this suggests the universe was always the same size and density.","correct":false,"explanation":"Cosmic expansion means conditions change when extrapolated backwards, so a constant-sized universe does not follow. Red-shift implies an earlier universe that was smaller, hotter and denser."}]},{"id":"d8d9780f-62a7-4916-9b32-03022b7413f2","cardType":"cloze","points":null,"front":"Cosmic microwave background radiation (CMB) is detected arriving from [ ] in space.","back":"Cosmic microwave background radiation (CMB) is detected arriving from all directions in space.","mcqOptions":[{"text":"all directions","correct":true,"explanation":"The CMB is nearly uniform across the whole sky because it is remnant radiation from the early universe, rather than radiation emitted by one localised object."},{"text":"a single direction","correct":false,"explanation":"The CMB is not concentrated in one region of the sky. It is detected from all directions because its source is the hot early universe as a whole."},{"text":"distant stars","correct":false,"explanation":"Individual distant stars emit electromagnetic radiation, but they are not the source of the background. CMB radiation is detected arriving from all directions in space."},{"text":"the Milky Way","correct":false,"explanation":"The CMB did not originate within our galaxy; it is remnant radiation from the early universe. Consequently, it is observed arriving from all directions in space."}]},{"id":"bafdef43-22a2-4bc1-858c-aabda9823edd","cardType":"basic","points":2,"front":"Why is the leftover radiation from the early universe now detected as microwaves?","back":"The expansion of the universe stretched the original high-energy radiation to longer wavelengths.","mcqOptions":[{"text":"The expansion of the universe stretched the original high-energy radiation to longer wavelengths.","correct":true,"explanation":"As the universe expanded, space stretched the radiation’s wavelengths. The initially short-wavelength, high-energy radiation was red-shifted until it reached the microwave region of the spectrum."},{"text":"The expansion of the universe compressed the original high-energy radiation to shorter wavelengths.","correct":false,"explanation":"Expansion stretches radiation rather than compressing it. The early high-energy radiation lost energy through cosmological red-shift and is now observed at longer microwave wavelengths."},{"text":"The expansion of the universe energised the original low-energy radiation to shorter wavelengths.","correct":false,"explanation":"Cosmic expansion does not increase the radiation’s energy or shorten its wavelength. It stretches wavelengths, reducing photon energy until the remnant radiation lies in the microwave region."},{"text":"The expansion of the universe absorbed the original high-energy radiation at shorter wavelengths.","correct":false,"explanation":"Absorption by galaxies does not explain the nearly uniform microwave background. Expansion stretched the original high-energy radiation to longer wavelengths through cosmological red-shift."}]},{"id":"cf255250-7d04-4f79-882d-9ec257491687","cardType":"basic","points":2,"front":"How does CMB radiation specifically support the Big Bang theory?","back":"The theory predicted leftover radiation from a hot, dense early stage; the CMB matches this prediction.","mcqOptions":[{"text":"The theory predicted leftover radiation from a hot, dense early stage; the CMB matches this prediction.","correct":true,"explanation":"A hot, dense early universe should leave behind cooled thermal radiation. The observed CMB has the predicted properties, providing strong evidence for the Big Bang model."},{"text":"The theory predicted radiation produced by the first generation of stars; the CMB matches this prediction.","correct":false,"explanation":"This confuses the CMB with radiation emitted by stars. The CMB is leftover radiation from the hot, dense early universe, matching a prediction of the Big Bang theory."},{"text":"The theory predicted leftover radiation from a cold, empty early stage; the CMB matches this prediction.","correct":false,"explanation":"The early universe was hot and dense, not cold and empty. The CMB supports the Big Bang because it is the predicted remnant of that initial hot stage."},{"text":"The theory predicted radiation coming only from nearby galaxies; the CMB matches this prediction.","correct":false,"explanation":"The CMB arrives almost uniformly from every direction rather than only from nearby galaxies. It is relic radiation from the hot early universe, as the Big Bang theory predicted."}]},{"id":"1c5e5a0a-a28d-4813-9569-e9470668a864","cardType":"cloze","points":null,"front":"Red-shift does not mean a galaxy looks red; it means the pattern of [ ] has shifted toward the red end of the spectrum.","back":"Red-shift does not mean a galaxy looks red; it means the pattern of spectral lines has shifted toward the red end of the spectrum.","mcqOptions":[{"text":"spectral lines","correct":true,"explanation":"Spectral lines occur at characteristic wavelengths for particular elements. Red-shift means this entire recognisable pattern is displaced toward longer, redder wavelengths."},{"text":"light intensity","correct":false,"explanation":"Red-shift is identified by the displacement of spectral lines, not by an overall change in light intensity. Brightness can change without indicating motion away from Earth."},{"text":"wave amplitudes","correct":false,"explanation":"Wave amplitudes affect the intensity of light rather than its red-shift. Red-shift is measured by comparing the observed pattern of spectral lines with its laboratory wavelengths."},{"text":"absorption levels","correct":false,"explanation":"Absorption levels describe how strongly wavelengths are absorbed, not where their identifying pattern appears. The spectral lines themselves shift toward the red end during red-shift."}]},{"id":"c1fa3bcc-c885-4ff1-af17-19080e3aa8f7","cardType":"cloze","points":null,"front":"Red-shift does not mean a galaxy looks red; it means the pattern of spectral lines has shifted toward the [ ] of the spectrum.","back":"Red-shift does not mean a galaxy looks red; it means the pattern of spectral lines has shifted toward the red end of the spectrum.","mcqOptions":[{"text":"red end","correct":true,"explanation":"The red end corresponds to longer wavelengths. A shift of spectral lines in that direction indicates that the galaxy is moving away from the observer."},{"text":"blue end","correct":false,"explanation":"A shift toward the blue end is blue-shift, which indicates motion toward the observer. Receding galaxies instead show spectral lines shifted toward the red end."},{"text":"ultraviolet end","correct":false,"explanation":"Ultraviolet wavelengths are shorter than visible wavelengths, so this would not describe red-shift. Red-shift moves the spectral-line pattern toward the longer-wavelength red end."},{"text":"central region","correct":false,"explanation":"Red-shift specifies a directional displacement rather than movement toward the spectrum’s centre. The lines move toward the longer-wavelength red end when a galaxy recedes."}]},{"id":"c4a678f2-1850-4442-9002-2fb03ba18271","cardType":"basic","points":2,"front":"Does red-shift show that Earth is the centre of the universe? Explain.","back":"No; space is expanding everywhere, so observers in any galaxy would see others moving away.","mcqOptions":[{"text":"No; space is expanding everywhere, so observers in any galaxy would see others moving away.","correct":true,"explanation":"Cosmic expansion has no unique central galaxy. From any galaxy, sufficiently distant galaxies would generally appear to recede as the space between galaxies expands."},{"text":"Yes; galaxies are moving away from Earth, so Earth occupies the fixed centre of the universe.","correct":false,"explanation":"Seeing other galaxies recede does not make Earth a fixed centre. Uniform expansion means observers in any galaxy would also see sufficiently distant galaxies moving away."},{"text":"No; the Milky Way remains stationary, so only distant galaxies are carried outward by expansion.","correct":false,"explanation":"The Milky Way is not a stationary reference point outside cosmic expansion. Red-shift supports expansion everywhere, with observers in any galaxy seeing other distant galaxies recede."},{"text":"Yes; expansion begins near Earth, so observers in our galaxy see all others moving away.","correct":false,"explanation":"Earth’s location does not cause universal expansion. The recession pattern follows from space expanding throughout the universe, and the same general pattern would be observed from any galaxy."}]},{"id":"d94715fc-0d60-4641-9295-f9d02e50e295","cardType":"cloze","points":null,"front":"To find the velocity of a galaxy using red-shift, use the rearranged formula: $\\text{[...]}$.","back":"To find the velocity of a galaxy using red-shift, use the rearranged formula: $\\boxed{v = c \\times \\frac{\\Delta\\lambda}{\\lambda_0}}$.","mcqOptions":[{"text":"$$v = c \\times \\frac{\\Delta\\lambda}{\\lambda_0}$","correct":true,"explanation":"For small cosmological red-shifts, $rac{\\Delta\\lambda}{\\lambda_0}=rac{v}{c}$. Multiplying the fractional wavelength change by the speed of light therefore gives the galaxy’s recession velocity."},{"text":"$$v = c \\times \\frac{\\lambda_0}{\\Delta\\lambda}$","correct":false,"explanation":"This reverses the wavelength fraction, giving a larger velocity when the measured shift becomes smaller. The correct rearrangement is $v=c\\times\\frac{\\Delta\\lambda}{\\lambda_0}$."},{"text":"$$v = \\frac{\\Delta\\lambda}{c \\times \\lambda_0}$","correct":false,"explanation":"This divides by the speed of light instead of multiplying by it, producing incorrect dimensions for velocity. The required formula is $v=c\\times\\frac{\\Delta\\lambda}{\\lambda_0}$."},{"text":"$$v = c \\times \\frac{\\Delta\\lambda}{\\lambda}$","correct":false,"explanation":"Using the observed wavelength in the denominator confuses $lambda$ with the rest wavelength. The standard low-red-shift relation uses $lambda_0$, giving $v=c\\times\\frac{Deltalambda}{lambda_0}$."}]}]}],"examCountdown":{"examDate":"2027-05-25","paperLabel":"Paper 1"},"heading":"Cosmology","title":"Cosmology Flashcards","topbar":{"backHref":"/igcse/physics/edexcel/flashcards"},"topicSidebar":"$L37"}]}],"topicId":"e07ffe2b-8690-594b-af77-ae23a8501f9f","walled":"$L38"}],"$L39","$L3a"]