E.2 Quantum physics
Practice exam-style IB Physics questions for Quantum physics, aligned with the syllabus and grouped by topic.
Question 1
Monochromatic light causes photoelectric emission from a clean metal surface. The frequency of the light is kept constant above the threshold frequency and the intensity is doubled.
A.
It becomes zero because electrons are emitted more rapidly.
B.
It remains unchanged because the photon energy is unchanged.
C.
It increases by a factor of √2 because intensity is proportional to amplitude squared.
D.
It doubles because the photons arrive with twice the energy.
Question 2
A metal has threshold frequency f₀. Radiation of frequency 0.9f₀ is incident on the metal with very high intensity.
A.
Photoelectrons are emitted with zero maximum kinetic energy.
B.
Photoelectrons are emitted with kinetic energy proportional to intensity.
C.
No photoelectrons are emitted.
D.
Photoelectrons are emitted after a measurable delay.
Question 3
A beam of electrons passes through a thin crystalline film and forms concentric rings on a fluorescent screen.
A.
The electrons have zero momentum after passing through the film.
B.
The electrons are converted into photons in the film.
C.
The electrons behave as waves during propagation through the crystal.
D.
The electrons have a continuous range of electric charge.
Question 4
Electrons pass one at a time through a double-slit arrangement. Individual dots appear on a detector, and after many electrons an interference pattern is observed.
A.
The detector changes the electron charge into electromagnetic radiation.
B.
Each electron is detected locally, while the probability distribution shows wave-like interference.
C.
Each electron splits permanently into two smaller electrons at the slits.
D.
The pattern appears only because electrons collide with each other in the beam.
Question 5
A purely classical wave model of light predicts energy is delivered continuously to electrons in a metal.
A.
Light travels at the same speed in vacuum for different frequencies.
B.
Emission occurs without measurable delay above the threshold frequency, even at low intensity.
C.
Metals conduct electricity in the dark.
D.
Electrons have negative charge.
Question 6
Photoelectric emission is observed from a clean metal surface.
Define photoelectric emission.
[1]
State what is meant by a photoelectron.
[1]
State why increasing the intensity of light at fixed frequency above threshold increases the photoelectric current.
[1]
Question 7
The work function of a metal is 2.0 eV. Light of photon energy 5.0 eV is incident on the metal.
A.
3.0 eV
B.
7.0 eV
C.
2.0 eV
D.
5.0 eV
Question 8
A graph of maximum kinetic energy Emax against incident frequency f is obtained for photoelectrons emitted from a metal.
A.
The threshold frequency of the metal
B.
The elementary charge
C.
The work function of the metal
D.
The Planck constant
Question 9
A non-relativistic electron is accelerated from rest through a potential difference V. The potential difference is increased to 4V.
A.
It remains unchanged.
B.
It becomes one half of its original value.
C.
It doubles.
D.
It becomes one quarter of its original value.
Question 10
Compton scattering of X-rays by electrons is described using conservation of energy and momentum.
A.
The electron remains stationary after the interaction.
B.
The photon wavelength decreases after scattering.
C.
A photon has momentum h/λ.
D.
A photon has charge e.
Question 11
An X-ray photon undergoes Compton scattering from a nearly free electron through a non-zero angle.
A.
Its wavelength decreases and its energy increases.
B.
Its frequency increases while its speed decreases.
C.
Its wavelength remains constant and its direction changes.
D.
Its wavelength increases and its energy decreases.
Question 12
For Compton scattering from a free electron, the scattering angle of the photon is increased from 30° to 120°.
A.
It remains unchanged because it is independent of angle.
B.
It decreases because the scattered photon travels farther from the original direction.
C.
It increases because 1 − cos θ increases.
D.
It becomes negative because the photon loses energy.
Question 13
Particles with de Broglie wavelength λ pass through a single slit of width a. The first minimum in detected intensity occurs at angle θ.
A.
a cos θ = λ
B.
a sin θ = λ/2
C.
a sin θ = λ
D.
λ sin θ = a
Question 14
Compton scattering is often regarded as more direct evidence for photon particle behaviour than the photoelectric effect.
A.
The scattered photon remains after the interaction with measurable energy and direction.
B.
The electron does not recoil in Compton scattering.
C.
The incident photon is always absorbed completely by the target electron.
D.
The wavelength shift is independent of scattering angle.
Question 15
A metal has a threshold frequency of 6.4 × 10¹⁴ Hz.
Calculate the work function of the metal in joules.
[1]
State the maximum kinetic energy of an emitted electron when the incident frequency is exactly 6.4 × 10¹⁴ Hz.
[1]
Question 16
A metal surface is illuminated by red light of high intensity and no photoelectrons are emitted. Ultraviolet light of much lower intensity causes immediate emission.
Explain these observations using the photon model.
[1]
Question 17
A graph of maximum kinetic energy Emax against incident frequency f is used to determine properties of a metal.
State how the Planck constant can be obtained from the graph.
[1]
State how the work function can be obtained from the graph.
[1]
State how the threshold frequency can be obtained from the graph.
[1]
Question 18
A beam of electrons forms an interference pattern even when the apparatus is adjusted so that electrons pass through it one at a time.
State the particle-like aspect of the observation.
[1]
State the wave-like aspect of the observation.
[1]
Explain why attempting to determine the path of each electron removes the interference pattern.
[1]
Question 19
In Compton scattering, an X-ray photon is scattered by a loosely bound electron.
State the expression for the momentum of a photon of wavelength λ.
[1]
Explain why the electron recoils after the interaction.
[1]
State one way in which Compton scattering differs from a collision between two solid balls.
[1]
Question 20
A Compton scattering spectrum from a carbon target contains one peak at the incident wavelength and another peak at a longer wavelength.
State the origin of the shifted peak.
[1]
State the origin of the unshifted peak.
[1]
Explain why the shifted peak is at a longer wavelength.
[1]
Question 21
The Bohr model successfully explains some features of hydrogen spectra.
State the physical system described by the Bohr model.
[1]
Explain why the Bohr model is not an adequate explanation of the photoelectric effect in metals.
[1]
Question 22
The table gives threshold frequencies for three different clean metal surfaces.
| Metal surface | Threshold frequency / Hz |
|---|---|
| Clean sodium | 5.5 × 10^14 |
| Clean zinc | 1.0 × 10^15 |
| Clean caesium | 5.1 × 10^14 |
Determine which metal has the largest work function.
[1]
Calculate the work function of one metal selected from the table.
[1]
Suggest one reason why a measured threshold frequency may differ from a published value.
[1]
Question 23
The stopping potential for photoelectrons emitted from a metal is 1.8 V.
A.
1.8 eV
B.
0.56 eV
C.
3.6 eV
D.
1.8 J
Question 24
A photon is Compton scattered through 90° by an electron. The electron Compton wavelength is λC = h/(mec).
A.
0
B.
2λC
C.
λC
D.
λC/2
Question 25
Two particles have the same speed. Particle X has mass m and particle Y has mass 4m.
A.
1
B.
4
C.
1/4
D.
2
Question 26
Light of wavelength 250 nm is incident on a metal with work function 3.1 eV.
Calculate the photon energy in eV.
[1]
Calculate the maximum kinetic energy of the emitted photoelectrons in eV.
[1]
State one reason why not all emitted electrons have this maximum kinetic energy.
[1]
Question 27
Photoelectrons from a metal are stopped by a potential difference of 2.6 V.
Calculate the maximum kinetic energy of the photoelectrons in joules.
[1]
Calculate the maximum speed of the photoelectrons. [2]
Use me = 9.11 × 10⁻³¹ kg and e = 1.60 × 10⁻¹⁹ C.
[1]
Question 28
Electrons are incident normally on a narrow slit of width a. A detector is moved along a distant arc centred on the slit.
State the approximate condition for an intensity minimum at angle θn.
[1]
Explain why a minimum is observed at this angle.
[1]
State how the angle of the first minimum changes if the electron speed is increased.
[1]
Question 29
A non-relativistic neutron of mass 1.67 × 10⁻²⁷ kg moves with speed 2.0 × 10³ m s⁻¹.
Calculate its de Broglie wavelength.
[1]
State why this wavelength could be relevant for diffraction by a crystal.
[1]
Question 30
Electrons are accelerated from rest through a potential difference of 150 V.
Show that the electron momentum is given by p = √(2meeV).
[1]
Calculate the de Broglie wavelength of the electrons.
[1]
State the effect on the diffraction ring diameter if the accelerating potential is increased.
[1]
Question 31
An X-ray photon is Compton scattered by a free electron through 120°. The electron Compton wavelength is 2.43 × 10⁻¹² m.
Calculate the wavelength shift.
[1]
The incident wavelength is 7.10 × 10⁻¹¹ m. Calculate the scattered wavelength.
[1]
State whether the scattered photon has a higher or lower frequency than the incident photon.
[1]
Question 32
Compare the effects of increasing the frequency and increasing the intensity of light incident on a metal surface when the frequency is above threshold.
State the effect of increasing frequency on maximum kinetic energy.
[1]
State the effect of increasing intensity on maximum kinetic energy.
[1]
State the effect of increasing intensity on photoelectric current.
[1]
Explain the photon-model reason for the difference between
[1]
and (c).
[1]
Question 33
A student measures the stopping potential Vs for different frequencies f of light incident on a metal surface. The data are plotted as Vs against f.
State the physical meaning of the frequency-axis intercept.
[1]
Use the graph to determine the Planck constant.
[1]
Suggest one experimental reason why the plotted points may not lie exactly on a straight line.
[1]
Explain why changing the intensity of the light would not change the gradient.
[1]
Question 34
The graph shows photocurrent I against collector potential V for a photoelectric cell at two different light intensities but the same frequency.
Identify the curve corresponding to the greater intensity.
[1]
State how the stopping potential compares for the two curves.
[1]
Explain the answer to (b).
[1]
Sketch on the graph the expected curve for the same intensity as the lower curve but a higher frequency.
[1]
Question 35
Electrons are accelerated through different potential differences V and passed through a thin graphite film. The diameter D of one diffraction ring is measured.
Describe the trend shown by the graph.
[1]
Explain why D decreases as V increases.
[1]
Use the graph to determine whether D is more nearly proportional to 1/V or to 1/√V.
[1]
Suggest one reason for uncertainty in measuring D.
[1]
Question 36
A student varies the intensity of light incident on a metal for two different frequencies. The table records whether photoelectrons are detected.
| Light intensity / W m^-2 | Current at 4.5 × 10^14 Hz / nA | Current at 7.5 × 10^14 Hz / nA |
|---|---|---|
| 20 | 0.00 | 0.80 |
| 50 | 0.00 | 2.00 |
| 100 | 0.00 | 4.00 |
Identify which frequency is below the threshold frequency.
[1]
Explain how the data support a photon model of light.
[1]
State one additional measurement that would allow the work function to be determined.
[1]
Question 37
The diagram shows the build-up of detections on a screen for electrons sent one at a time through a two-slit apparatus.
Describe the pattern after a small number of electrons.
[1]
Describe the pattern after a very large number of electrons.
[1]
Explain how the data show both particle-like and wave-like behaviour.
[1]
Question 38
A student proposes a scattering experiment to demonstrate the wave nature of matter using electrons and a thin graphite film.
State what pattern should be observed on a fluorescent screen if electrons diffract.
[1]
Suggest why graphite is suitable for the experiment.
[1]
Explain why the pattern changes when the accelerating voltage is decreased.
[1]
Question 39
A beam of neutral atoms passes through a single slit. A detector measures particle arrival rate as a function of angle from the central direction.
Identify the angular position of the first minimum from the graph.
[1]
Use the first minimum to determine the de Broglie wavelength of the atoms.
[1]
Explain why the intensity is not zero everywhere away from the central direction.
[1]
State one change to the apparatus that would increase the angle of the first minimum.
[1]
Question 40
X-rays of a fixed incident wavelength are scattered by a carbon target. The table gives the measured wavelength of the Compton-shifted peak at several scattering angles.
| Scattering angle θ / ° | Shifted wavelength λf / 10^-11 m |
|---|---|
| 0 | 7.10 |
| 30 | 7.13 |
| 45 | 7.17 |
| 60 | 7.22 |
| 75 | 7.26 |
| 90 | 7.34 |
| 120 | 7.46 |
| 150 | 7.55 |
Describe how the shifted wavelength varies with scattering angle.
[1]
Use the data to determine a value for the electron Compton wavelength h/(mec).
[1]
State whether the shift should depend on the incident wavelength according to the Compton equation.
[1]
Suggest why an unshifted peak may also be present in the spectrum.
[1]
Question 41
The graph shows X-ray spectra measured after scattering from a target at three different angles.
Identify the peak that corresponds to Compton scattering at the largest angle.
[1]
Describe the change in the separation between the shifted and unshifted peaks as angle increases.
[1]
Explain the change described in (b).
[1]
State what happens to the kinetic energy of the recoil electron at larger scattering angles.
[1]
Question 42
A Compton scattering experiment records the energies and directions of an incident X-ray photon, the scattered photon and the recoil electron.
From the vector diagram, state whether momentum is conserved in one dimension or two dimensions.
[1]
Use the diagram to explain why the electron recoil direction is not generally the same as the scattered photon direction.
[1]
Evaluate why these data provide evidence for photon particle behaviour.
[1]
State one limitation of describing the interaction as a collision between two solid balls.
[1]
Question 43
A student claims that the photoelectric effect can be fully explained by treating light as a classical wave with sufficiently large intensity.
Outline two key observations from the photoelectric effect.
[1]
Evaluate the student’s claim using Einstein’s photon explanation.
[1]
Question 44
A photoelectric experiment uses a variable-frequency source and a stopping potential measurement.
Derive the relationship between stopping potential Vs and frequency f.
[1]
Explain how the experiment can be used to determine both the Planck constant and the work function, including the effect of changing intensity.
[1]
Question 45
Wave–particle duality is used to describe both light and matter.
Describe one observation showing particle behaviour of light and one observation showing wave behaviour of matter.
[1]
Discuss how a single-electron interference experiment illustrates wave–particle duality and the role of measurement.
[1]
Question 46
An experiment is designed to demonstrate diffraction of particles using a collimated electron beam and a narrow slit.
State the de Broglie relation and the condition for the nth single-slit minimum.
[1]
Explain how the experiment provides evidence for the wave nature of matter and predict how the pattern changes when electron momentum is increased.
[1]
Question 47
Compton scattering is sometimes described as a collision between a photon and an electron.
State two conserved quantities in Compton scattering.
[1]
Evaluate the usefulness and limitations of the collision analogy, and explain why Compton scattering is evidence for the particle nature of light.
[1]
Question 48
An incident X-ray photon of wavelength λi is Compton scattered by a free electron initially at rest.
Calculate the wavelength shift for scattering angles of 0° and 180° in terms of the electron Compton wavelength λC = h/(mec).
[1]
Analyze the physical meaning of these two limiting cases, including energy transfer to the electron.
[1]
Question 49
The de Broglie wavelength is important for microscopic particles but normally unobservable for everyday objects.
Calculate the de Broglie wavelength of a 0.050 kg ball moving at 20 m s⁻¹.
[1]
Discuss why diffraction is observable for electrons accelerated through modest voltages but not for the ball in (a).
[1]
Question 50
The photoelectric effect and Compton scattering both support the particle model of light.
Outline how each phenomenon involves electrons.
[1]
Compare and contrast the evidence for photons provided by the two phenomena.
[1]
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