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HSC Physics · Module 7 flashcards
The Nature of Light
84 cards. Work out each answer first, then open the card to check it and see the working.
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Maxwell's equations predicted that electromagnetic waves travel through a vacuum at a speed determined by …Show answer
Answer: the electric and magnetic constants of free space
Maxwell showed c = 1/√(μ0ε0), which gave a value matching the measured speed of light.
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A metal has a work function of 2.3 eV. What is its threshold frequency?Show answer
Answer: 5.6 × 1014 Hz
f0 = W/h = (2.3 × 1.602 × 10-19)/(6.626 × 10-34) = 5.6 × 1014 Hz.
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A muon at rest has a lifetime of 2.2 μs. What lifetime would an observer measure for a muon moving at 0.98c?Show answer
Answer: 11 μs
γ = 1/√(1 − 0.98²) = 5.03. t = γt0 = 5.03 × 2.2 = 11 μs.
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Hertz's experiments with radio waves were important because they showed that the waves …Show answer
Answer: could be reflected, refracted and polarised like light
Hertz generated and detected radio waves and showed they had the same wave properties as light, confirming Maxwell's prediction of electromagnetic waves.
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A spaceship is 100 m long in its own rest frame. It passes Earth at 0.60c. What length does an observer on Earth measure?Show answer
Answer: 80 m
γ = 1/√(1 − 0.36) = 1.25. L = L0/γ = 100/1.25 = 80 m.
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The null result of the Michelson–Morley experiment …Show answer
Answer: provided no evidence for the existence of the aether
The experiment looked for a change in the speed of light due to Earth's motion through the aether. No shift was found, so no aether motion was detected.
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Rømer's estimate of the speed of light was based on …Show answer
Answer: timing variations in the eclipses of Jupiter's moon Io
Rømer noticed Io's eclipses appeared late when Earth was far from Jupiter and early when near, and attributed the difference to light's travel time across Earth's orbit.
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A diffraction grating has 500 lines per mm. At what angle does the second-order maximum of 600 nm light appear?Show answer
Answer: 36.9°
d = 1/500 000 = 2.0 × 10-6 m. sinθ = mλ/d = 2 × 6.0 × 10-7/2.0 × 10-6 = 0.60, so θ = 36.9°.
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Light of frequency 8.0 × 1014 Hz falls on a metal of work function 2.0 eV. What is the maximum kinetic energy of the photoelectrons?Show answer
Answer: 1.3 eV
Ephoton = hf = 6.626 × 10-34 × 8.0 × 1014 = 5.3 × 10-19 J = 3.3 eV. KEmax = 3.3 − 2.0 = 1.3 eV.
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A spacecraft travels at 0.80c. The crew measure the journey as taking 10 years. How long does the journey take according to observers on Earth?Show answer
Answer: 16.7 years
γ = 1/√(1 − 0.64) = 1.67. The crew measure proper time, so Earth measures t = γt0 = 16.7 years.
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What is the energy of a photon of wavelength 400 nm?Show answer
Answer: 5.0 × 10-19 J
E = hc/λ = 6.626 × 10-34 × 3.0 × 108/4.0 × 10-7 = 5.0 × 10-19 J (about 3.1 eV).
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In a photoelectric experiment the stopping voltage is 1.5 V. What is the maximum kinetic energy of the photoelectrons?Show answer
Answer: 2.4 × 10-19 J
KEmax = eVstop = 1.602 × 10-19 × 1.5 = 2.4 × 10-19 J (that is, 1.5 eV).
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A particle moves at 0.60c. By what factor is its relativistic momentum greater than the classical value mv?Show answer
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Fizeau measured the speed of light using …Show answer
Answer: a rotating toothed wheel and a distant mirror
Light passed through a gap in a spinning wheel, reflected from a mirror kilometres away, and was blocked by the next tooth at a particular rotation rate, giving the travel time.
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A hot dense solid such as a tungsten filament produces …Show answer
Answer: a continuous spectrum
Closely packed atoms in a hot solid interact so strongly that all wavelengths are emitted. Line spectra come from low-pressure gases.
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According to special relativity, two events that are simultaneous in one inertial frame …Show answer
Answer: may not be simultaneous in a frame moving relative to the first
Because c is the same for all observers, observers in relative motion can disagree about whether spatially separated events occurred at the same time.
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Maxwell's main contribution to the understanding of light was to …Show answer
Answer: unify electricity, magnetism and light as electromagnetic waves
Maxwell's equations predicted self-propagating electric and magnetic waves at a speed equal to that of light, identifying light as an electromagnetic wave.
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The rotation of a star can be detected from its spectrum because …Show answer
Answer: the lines are broadened as one edge approaches and the other recedes
Light from the approaching limb is blue-shifted and from the receding limb red-shifted, smearing each line over a range of wavelengths.
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In a double-slit experiment, the slit separation is increased while wavelength and screen distance are unchanged. The fringe spacing …Show answer
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The Sun converts 4.3 × 109 kg of mass into energy each second. What is its power output?Show answer
Answer: 3.9 × 1026 W
P = (Δm/Δt)c² = 4.3 × 109 × 9.0 × 1016 = 3.9 × 1026 W.
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In Hertz's experiment, a spark jumped across the gap of a distant loop of wire. This demonstrated that …Show answer
Answer: electromagnetic waves had travelled from the transmitter to the receiver
The receiving loop was not connected to the transmitter. The spark showed that an oscillating electromagnetic wave had induced a current in it.
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A hot gas at low pressure produces …Show answer
Answer: an emission spectrum of discrete bright lines
Isolated atoms emit only the wavelengths matching their energy level differences.
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Light can be polarised. This shows that light is …Show answer
Answer: a transverse wave
Only transverse waves have an oscillation direction perpendicular to travel that can be filtered by a polariser.
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A metal has a work function of 4.5 eV. What is the longest wavelength that will eject electrons? (hc = 1240 eV nm) …Show answer
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The proper time between two events is measured by …Show answer
Answer: an observer for whom the events happen at the same place
Proper time is the shortest time interval, measured by the clock that is present at both events. Every other observer measures a longer, dilated interval.
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In an electromagnetic wave, the electric and magnetic fields are …Show answer
Answer: perpendicular to each other and both perpendicular to the direction of travel
E, B and the direction of propagation are mutually perpendicular, and E and B oscillate in phase.
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Compared with a double slit, a diffraction grating with many slits produces …Show answer
Answer: sharper, brighter maxima
More slits means more waves adding constructively at the maxima and cancelling more completely between them, giving narrow bright lines.
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The maximum kinetic energy of photoelectrons depends on …Show answer
Answer: the frequency of the light and the work function of the metal
KEmax = hf − W. Intensity affects how many electrons leave, not their energy.
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The proper length of an object is measured …Show answer
Answer: in the frame in which the object is at rest
Proper length is the longest length. Any observer moving relative to the object measures a contracted length L = L0/γ.
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A star's spectral lines are blue-shifted. The star is …Show answer
Answer: moving towards Earth
A shift to shorter wavelengths indicates a source approaching the observer.
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In a double-slit experiment, d = 0.50 mm, the screen is 2.0 m away and bright fringes are 2.4 mm apart. The wavelength is …Show answer
Answer: 600 nm
λ = dΔy/L = 5.0 × 10-4 × 2.4 × 10-3/2.0 = 6.0 × 10-7 m = 600 nm.
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A 2.0 W laser emits light of wavelength 500 nm. How many photons does it emit per second?Show answer
Answer: 5.0 × 1018
Ephoton = hc/λ = 3.97 × 10-19 J. N = 2.0/3.97 × 10-19 = 5.0 × 1018 per second.
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Why can no object with mass reach the speed of light?Show answer
Answer: The energy required becomes infinite as v approaches c
γ → ∞ as v → c, so the kinetic energy (γ − 1)mc² and the required work become unbounded.
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Hertz measured the speed of the radio waves he produced by …Show answer
Answer: setting up standing waves and measuring their wavelength, then using v = fλ
Reflecting the waves created standing waves. The node spacing gave the wavelength, and the known oscillator frequency gave the speed, which equalled c.
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A black body at 10 000 K has its peak emission at about (b = 2.898 × 10-3 m K) …Show answer
Answer: 290 nm
λmax = b/T = 2.898 × 10-3/10 000 = 2.9 × 10-7 m = 290 nm (ultraviolet).
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Plane-polarised light of intensity I0 passes through an analyser whose axis is at 45° to the polarisation direction. The transmitted intensity is …Show answer
Answer: I0/2
Malus' law: I = I0 cos²45° = I0 × 0.5. (For unpolarised light there would be an extra factor of ½.)
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In the twin paradox, one twin travels to a distant star at high speed and returns. On return …Show answer
Answer: the travelling twin is younger
The travelling twin's clock runs slow relative to Earth. The situation is not symmetric because the traveller changes frames when turning around.
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The dark Fraunhofer lines in the Sun's spectrum reveal …Show answer
Answer: the elements present in the Sun's outer atmosphere
Each element absorbs at its own set of wavelengths, so the pattern of dark lines identifies which elements are present in the cooler outer layers.
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The SI unit of Planck's constant is …Show answer
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The condition for a bright fringe in a double-slit pattern is …Show answer
Answer: d sinθ = mλ
Constructive interference needs a path difference d sinθ equal to a whole number of wavelengths.
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Light of 300 nm falls on a metal of work function 2.3 eV. The stopping voltage is about (hc = 1240 eV nm) …Show answer
Answer: 1.8 V
Ephoton = 1240/300 = 4.13 eV. KEmax = 4.13 − 2.3 = 1.8 eV, so Vstop = 1.8 V.
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A spacecraft travels at 0.80c to a star 8.0 light-years away (Earth frame). According to the crew the trip takes …Show answer
Answer: 6.0 years
Earth frame: t = 8.0/0.80 = 10 years. γ = 1.67, so crew time = 10/1.67 = 6.0 years. (Equivalently the distance contracts to 4.8 ly.)
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Using the measured values of μ0 and ε0, Maxwell calculated the speed of electromagnetic waves to be about …Show answer
Answer: 3.0 × 108 m s-1
c = 1/√(μ0ε0) ≈ 3.0 × 108 m s-1, matching the known speed of light.
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A hydrogen line with rest wavelength 656.3 nm is observed at 656.5 nm from a star. The star's radial speed is about …Show answer
Answer: 9 × 104 m s-1
v = c Δλ/λ = 3.0 × 108 × 0.2/656.3 = 9.1 × 104 m s-1, receding (red shift).
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A diffraction grating is replaced with one having more lines per millimetre. For the same light, the first-order maximum appears at …Show answer
Answer: a larger angle
More lines per mm means smaller slit spacing d. sinθ = λ/d increases.
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A photon has energy 2.0 eV. Its wavelength is about (hc = 1240 eV nm) …Show answer
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An observer on Earth sees a spaceship's clock running slow. An observer on the spaceship sees Earth's clock …Show answer
Answer: running slow
Time dilation is symmetric between inertial frames: each sees the other's clock as slow, because each sees the other as moving.
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The radial velocity of a star is determined from its spectrum by measuring …Show answer
Answer: the Doppler shift of the lines
The amount of shift Δλ/λ = v/c gives the speed towards or away from the observer.
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Classical physics predicted that a black body should emit unlimited energy at short wavelengths. This failed prediction is called …Show answer
Answer: the ultraviolet catastrophe
Planck resolved it by proposing that energy is emitted in packets E = hf, which suppresses high-frequency emission.
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In Young's experiment, a dark fringe occurs where the path difference from the two slits is …Show answer
Answer: half a wavelength
A half-wavelength path difference puts the waves out of phase so they cancel.
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A 1.0 m rod moves at 0.9c in a direction perpendicular to its length. An observer at rest measures its length as …Show answer
Answer: 1.0 m
Length contraction occurs only along the direction of motion. Perpendicular dimensions are unchanged.
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Hertz showed that his radio waves were polarised by …Show answer
Answer: rotating the receiving loop and observing the spark strength change
The spark in the detector depended on the orientation of the receiver relative to the transmitter, which is the signature of a polarised transverse wave.
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A blue star compared with a red star is …Show answer
Answer: hotter
Wien's law: hotter objects peak at shorter wavelengths. Blue stars have surface temperatures above about 10 000 K; red stars below about 3500 K.
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Unpolarised light passes through a single ideal polarising filter. The transmitted intensity is …Show answer
Answer: one half
Averaging cos²θ over all orientations gives ½. Malus' law applies only after the light is already polarised.
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A muon has a proper lifetime of 2.2 μs and travels at 0.995c (γ = 10). What distance does it travel in the laboratory frame before decaying?Show answer
Answer: 6600 m
Lab lifetime = 10 × 2.2 μs = 22 μs. Distance = 0.995 × 3.0 × 108 × 22 × 10-6 = 6.6 × 10³ m.
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Rømer's observations showed that the timing of Io's eclipses …Show answer
Answer: varied with the Earth–Jupiter distance
The eclipses lagged when Earth was further away because the light had further to travel. The lag gave a finite speed for light.
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The visible emission lines of hydrogen are described by …Show answer
Answer: the Balmer formula
Balmer found an empirical formula for the visible lines; Rydberg generalised it and Bohr later derived it.
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A grating with 300 lines per mm is illuminated with 650 nm light. The first-order maximum appears at …Show answer
Answer: 11°
d = 1/300 000 = 3.33 × 10-6 m. sinθ = 6.5 × 10-7/3.33 × 10-6 = 0.195, θ = 11°.
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The energy equivalent of the electron's rest mass is about …Show answer
Answer: 8.2 × 10-14 J (0.51 MeV)
E = mc² = 9.109 × 10-31 × 9.0 × 1016 = 8.2 × 10-14 J ≈ 0.51 MeV.
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According to Maxwell, a changing electric field …Show answer
Answer: produces a magnetic field
This is the key addition Maxwell made to Ampère's law. Together with Faraday's law it allows E and B to regenerate each other as a travelling wave.
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A star's spectrum peaks at 250 nm. Its surface temperature is about (b = 2.898 × 10-3 m K) …Show answer
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When white light is used in a double-slit experiment, the central fringe is …Show answer
Answer: white, with coloured fringes either side
All wavelengths have zero path difference at the centre, so they all add constructively. Away from centre, different wavelengths peak at different positions.
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Light of 500 nm (2.48 eV) falls on a metal with work function 2.0 eV. The emitted electrons have maximum kinetic energy …Show answer
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Einstein's two postulates of special relativity are that the laws of physics are the same in all inertial frames, and that …Show answer
Answer: the speed of light in a vacuum is the same for all observers
The constancy of c for all inertial observers, regardless of the motion of the source, leads directly to time dilation and length contraction.
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Hertz detected waves across his laboratory. This showed that the waves …Show answer
Answer: travelled through air at a finite speed, later measured as c
No conductor linked transmitter and receiver. The waves propagated through space, as Maxwell's theory required.
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A star's spectrum peaks at 700 nm. Its surface temperature is about (b = 2.898 × 10-3 m K) …Show answer
Answer: 4100 K
T = 2.898 × 10-3/7.0 × 10-7 = 4100 K — a cool orange-red star.
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In a double-slit experiment the light source is changed from red to blue, all else unchanged. The fringes become …Show answer
Answer: closer together
Δy = λL/d. Blue light has a shorter wavelength, so the spacing decreases.
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Red light of 700 nm (1.77 eV) shines on a metal with work function 2.3 eV. The result is …Show answer
Answer: no electrons emitted, however bright the light
Each photon has less energy than the work function. No single photon can free an electron, and intensity does not change the energy per photon.
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A clock on a spaceship moving at 0.50c records one hour. An Earth observer measures the same interval as …Show answer
Answer: 69 minutes
γ = 1/√(1 − 0.25) = 1.155. t = 1.155 × 60 = 69 minutes.
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Arranged in order of increasing frequency, the electromagnetic spectrum runs …Show answer
Answer: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma
Radio has the longest wavelength and lowest frequency; gamma the shortest wavelength and highest frequency.
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The Sun is a class G star with a surface temperature of about …Show answer
Answer: 5800 K
Its spectrum peaks near 500 nm, which by Wien's law corresponds to about 5800 K.
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Plane-polarised light passes through an analyser at 30° to its polarisation direction. The fraction transmitted is …Show answer
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The energy of a photon is …Show answer
Answer: inversely proportional to its wavelength
E = hf = hc/λ.
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A spaceship is 50 m long at rest. Moving at 0.90c, its length as measured by a stationary observer is …Show answer
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The Michelson–Morley experiment was designed to detect …Show answer
Answer: the motion of Earth through the aether via a shift in interference fringes
If light moved relative to a stationary aether, rotating the apparatus should have shifted the fringes. No shift was seen.
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An absorption spectrum appears as …Show answer
Answer: dark lines on a continuous spectrum
A cooler gas in front of a continuous source removes specific wavelengths, leaving gaps.
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A diffraction grating has 600 lines per millimetre. Its slit spacing is …Show answer
Answer: 1.67 × 10-6 m
d = 1 mm/600 = 1.0 × 10-3/600 = 1.67 × 10-6 m.
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In the photoelectric effect, the energy of an absorbed photon is shared between …Show answer
Answer: the work function and the electron's kinetic energy
hf = W + KEmax. The work function is the minimum energy to free the electron; the rest is kinetic energy.
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The energy released when 2.0 g of matter is entirely converted to energy is …Show answer
Answer: 1.8 × 1014 J
E = mc² = 2.0 × 10-3 × 9.0 × 1016 = 1.8 × 1014 J.
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Light passes through two polarisers whose axes are at 90° to each other. The transmitted intensity is …Show answer
Answer: zero
After the first polariser the light is polarised. Malus' law: I = I1 cos²90° = 0.
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Planck's quantum hypothesis was introduced to explain …Show answer
Answer: the shape of the black body spectrum
Treating energy as emitted in multiples of hf gave a curve matching experiment and removed the ultraviolet catastrophe.
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A black body at 3000 K has its peak emission at about (b = 2.898 × 10-3 m K) …Show answer
Answer: 970 nm
λmax = 2.898 × 10-3/3000 = 9.7 × 10-7 m = 970 nm (infrared).
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Einstein's photoelectric equation is …Show answer
Answer: KEmax = hf − W
The electron gains hf from one photon and spends W escaping the metal; the rest is kinetic energy.
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The Lorentz factor γ for an object moving at 0.99c is about …Show answer
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