Monochromatic radiation is incident on a clean metal surface. The frequency of the radiation is below the threshold frequency of the metal.
What observation provides evidence against a purely classical wave model of light?
Photoelectrons are emitted with greater maximum kinetic energy when the intensity is increased.
Photoelectrons are emitted after a measurable delay at high intensity.
Photoelectrons are emitted only if the illuminated area is increased.
No photoelectrons are emitted even when the intensity is increased.
A metal has work function . The Planck constant is .
What is the threshold frequency of the metal?
Light of wavelength is incident on a metal of work function . The photon energy may be found using .
What is the stopping potential for the emitted photoelectrons?
An electron and a proton are each accelerated from rest through the same potential difference. Relativistic effects are negligible.
What comparison of their de Broglie wavelengths is correct?
The electron has the larger wavelength because its momentum is smaller.
The two wavelengths are equal because the potential difference is the same.
The electron has the smaller wavelength because its charge is negative.
The proton has the larger wavelength because its mass is larger.
Electrons are accelerated through a potential difference and produce diffraction rings from a thin graphite film. The accelerating potential difference is then increased to .
The effect on the ring diameters is that they

remain unchanged.
double.
halve.
become four times larger.
Electrons are sent one at a time through a double-slit arrangement. A detector screen records many individual electron arrivals. A device is then added that can determine which slit each electron passes through.
What is the expected result when the path information is obtained?
Each electron spreads uniformly over the screen and the interference pattern becomes sharper.
No electrons reach the screen because the measurement absorbs them all.
Each electron is still detected at a localized point, but the interference pattern disappears.
The same interference pattern remains because each electron passes through only one slit.
Two X-ray photons of different initial wavelengths are Compton scattered by free electrons through the same scattering angle.
What comparison of the wavelength shifts is correct?
Both wavelength shifts are zero.
The two wavelength shifts are equal.
The photon with the shorter initial wavelength has the larger shift.
The photon with the longer initial wavelength has the larger shift.
Compton scattering is often considered more direct evidence for the particle nature of light than the photoelectric effect.
What is the reason for this?
The incident photon is completely absorbed and cannot be detected after the interaction.
The scattered photon can be observed with changed wavelength and direction after the interaction.
The electron remains at rest, showing that only photon energy changes.
The effect occurs only when the light intensity is above a threshold value.
In Compton scattering, an incident photon scatters from an electron that is initially at rest. The scattered photon has a longer wavelength than the incident photon.
What change has occurred to the photon?
Its energy and momentum magnitude have both increased.
Its energy has increased but its momentum magnitude has decreased.
Its energy and momentum magnitude have both decreased.
Its energy has decreased but its momentum magnitude has increased.
The graph shows the maximum kinetic energy of photoelectrons against frequency for two metals, X and Y. The threshold frequency of X is lower than that of Y.
What comparison is correct for radiation of the same frequency above both threshold frequencies?

Metal Y gives the greater maximum kinetic energy and the two lines have the same gradient.
Metal X gives the greater maximum kinetic energy and the two lines have the same gradient.
Metal Y gives the greater maximum kinetic energy and line Y has the greater gradient.
Metal X gives the greater maximum kinetic energy and line X has the greater gradient.
A beam of electrons of de Broglie wavelength is incident normally on a narrow slit of width .
The approximate angular position of the first minimum in the diffraction pattern is
An X-ray photon is Compton scattered by an electron through an angle of . The Compton wavelength of the electron is .
What is the wavelength shift of the photon?
A clean metal surface is illuminated by monochromatic radiation. No photoelectrons are emitted when the frequency is below a certain value, even when the intensity is very large.
Outline why this observation is inconsistent with a purely classical wave model of light.
The frequency is then set above the threshold frequency and the intensity is increased. Explain the effect on the photoelectric current and on the maximum kinetic energy of the photoelectrons.
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A metal has a threshold frequency of . Radiation of frequency is incident on the metal.
State the energy condition for emission at the threshold frequency.
Calculate the maximum kinetic energy of the emitted photoelectrons in electronvolts.
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Electrons are sent through a double-slit apparatus one at a time. Each electron is recorded as a small dot at a definite position on a screen. After many electrons have been recorded, alternating bright and dark bands are visible.
Outline the particle-like evidence in this observation.
Explain the wave-like evidence in this observation.
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A proton and an electron are each accelerated from rest through the same potential difference. Non-relativistic motion may be assumed.
Determine the ratio of their de Broglie wavelengths.
Suggest why proton diffraction is less easily observed in the same apparatus.
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An X-ray photon is Compton-scattered by an electron that may be treated as initially free and at rest.

State the expression for the momentum of a photon in terms of its wavelength.
Explain why the wavelength of the scattered photon is greater than that of the incident photon.
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Several metal surfaces are illuminated by monochromatic sources. The observations record whether photoelectrons are emitted.
| Metal | Work function / J | Emission at 4.0×10^14 Hz | Emission at 1.0×10^15 Hz |
|---|---|---|---|
| Magnesium | 4.0 × 10^-19 | No | Yes |
| Platinum | 9.0 × 10^-19 | No | No |
| Sodium | 3.7 × 10^-19 | No | Yes |
| Zinc | 6.0 × 10^-19 | No | Yes |
Identify the metal with the largest threshold frequency.
For sodium, calculate the threshold frequency using the data in the table.
Suggest why one sample of the same metal might have a higher measured threshold frequency than another sample.
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In a photoelectric experiment, the stopping potential is measured for different frequencies of incident light. A straight-line graph of against is obtained. Two points on the best-fit line are and .

Determine a value for the Planck constant from these data.
Determine the threshold frequency and the work function in electronvolts.
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Radiation of wavelength is incident on a potassium surface. The stopping potential is .

Calculate the maximum kinetic energy of the photoelectrons in joules.
Calculate the work function of potassium in electronvolts.
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A beam of electrons with momentum passes through a narrow slit of width . A detector is moved in a circular arc around the slit to measure the electron intensity at different angles.

State the condition for the first minimum in the diffracted electron intensity.
Calculate the angle of the first minimum.
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Electrons are accelerated from rest through a potential difference of and then pass through a thin graphite film, producing diffraction rings on a screen.

Calculate the de Broglie wavelength of the electrons.
State the effect on the diffraction ring radii when the accelerating potential difference is increased.
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An X-ray photon of wavelength is scattered by a free electron through an angle of .
Calculate the Compton wavelength shift.
Calculate the wavelength of the scattered photon.
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The spectrum of X-rays scattered from a carbon target is measured at several scattering angles. At a non-zero scattering angle, two peaks are observed in the detected intensity.

Identify the peak that provides evidence for Compton scattering by electrons.
Explain the presence of a peak at the original incident wavelength.
Describe how the shifted peak changes as the scattering angle increases.
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A photoelectric cell is illuminated with monochromatic light of different frequencies. For each frequency the stopping potential is measured for a clean metal cathode.

Determine the threshold frequency of the metal.
Calculate the work function of the metal in joules.
Explain why increasing the intensity at a fixed frequency above threshold would not change the stopping potential.
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The current in a photoelectric cell is measured as the collector potential is varied. Curves are shown for two intensities at the same frequency and for a third curve at a higher frequency.

State how the graph shows that one pair of curves corresponds to the same incident frequency.
Explain why the saturation current is larger for one of these two curves.
Explain why the curve for the higher frequency has a larger magnitude of stopping potential.
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An experiment sends electrons through a double-slit apparatus one at a time. The screen is recorded after increasing numbers of detected electrons.

State the feature of the images that shows particle-like behaviour.
State the feature of the images that shows wave-like behaviour.
Explain why adding a detector to determine which slit each electron passes through would change the final pattern.
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The table gives the momentum of three moving objects that might be directed at a crystal with atomic spacing of order .
| Object | Momentum / kg m s^-1 |
|---|---|
| electron | 6.6 × 10^-24 |
| neutron | 3.3 × 10^-24 |
| tennis ball | 6.6 × 10^-2 |
Calculate the de Broglie wavelength of the electron with momentum .
Identify which object in the table is least likely to show observable diffraction by the crystal.
Compare how the table supports wave-particle duality for matter.
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Two experiments are compared as evidence for the particle nature of light: the photoelectric effect and Compton scattering.
| Experiment | Incident frequency / 10^14 Hz | Stopping potential / V | Scattering angle / ° | Incident wavelength / pm | Scattered wavelength / pm |
|---|---|---|---|---|---|
| Photoelectric effect | 5.00 | 0.00 | — | — | — |
| Photoelectric effect | 5.50 | 0.00 | — | — | — |
| Photoelectric effect | 6.00 | 0.21 | — | — | — |
| Photoelectric effect | 6.50 | 0.41 | — | — | — |
| Photoelectric effect | 7.00 | 0.62 | — | — | — |
| Compton scattering | — | — | 0 | 71.0 | 71.0 |
| Compton scattering | — | — | 45 | 71.0 | 71.7 |
| Compton scattering | — | — | 90 | 71.0 | 73.4 |
| Compton scattering | — | — | 135 | 71.0 | 75.1 |
| Compton scattering | — | — | 180 | 71.0 | 75.9 |
State one measured quantity in each experiment that provides evidence for photons.
Explain why the Bohr model is not an appropriate explanation of the photoelectric effect for a metal surface.
Discuss why Compton scattering is often considered more direct evidence for photon momentum than the photoelectric effect.
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Compton scattering is often described as a collision between a photon and an electron, but the analogy with a collision between two solid balls is limited.
Compare Compton scattering with a collision between two solid balls.
Discuss why Compton scattering gives more direct evidence for the particle nature of light than the photoelectric effect.
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A very low-intensity ultraviolet beam and a high-intensity red beam are each incident on a zinc surface. The table summarizes the observed emission.
| Beam | Frequency / 10^14 Hz | Intensity | Photoelectrons observed? | Delay / s |
|---|---|---|---|---|
| red | 4.5 | high | no | — |
| ultraviolet | 12.0 | very low | yes | <1×10^-9 |
Identify the observation that shows the threshold frequency is not an intensity effect.
Explain why the absence of a measurable time delay supports the photon model.
Evaluate the claim that these observations are explained by the classical wave model of light.
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Electrons are accelerated from rest through a potential difference before passing through a thin graphite film. The diameter of one diffraction ring is measured for different accelerating potentials.

State the relationship between the ring diameter and the accelerating potential shown by the graph.
Calculate the de Broglie wavelength of electrons accelerated through .
Explain why the observation of rings is evidence for the wave nature of electrons.
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A beam of electrons passes through a narrow slit. A movable detector measures the intensity at different angles from the central direction.

Identify the angular position of the first minimum on one side of the central maximum.
The de Broglie wavelength of the electrons is . Estimate the slit width.
Suggest why a detector placed at the first minimum records very few electrons even though individual electrons arrive as particles.
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X-rays are incident on a carbon target. The scattered spectrum is measured at a fixed scattering angle.

Identify which peak is due to Compton scattering by electrons that can be treated as free.
Determine the wavelength shift from the graph.
Explain why the shifted photon has lower energy than the incident photon.
Suggest why an unshifted peak is also observed.
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Compton scattering measurements are made at different photon scattering angles. The wavelength shift is plotted against .

State why the graph is expected to pass through the origin.
Determine the gradient of the graph and identify the physical constant it represents.
Calculate the expected wavelength shift for scattering through .
Explain why the shift does not depend on the incident wavelength in this model.
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A clean zinc plate is connected to a sensitive ammeter in a photoelectric cell. Very weak ultraviolet radiation causes an immediate current, but intense visible radiation causes no current.

The observations are compared with the predictions of a classical wave model of light.
Explain why the observation with weak ultraviolet radiation is inconsistent with a purely classical wave model.
Explain why intense visible radiation causes no current.
Ultraviolet radiation of wavelength is incident on the zinc. The stopping potential is . Calculate the work function of the zinc surface in electronvolts.
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The maximum kinetic energy of photoelectrons emitted from a metal is measured for different frequencies of incident light. The graph is a straight line. It crosses the frequency axis at and has when .

Use the graph information to interpret the photoelectric properties of the metal.
State the threshold frequency of the metal.
Calculate the work function of the metal in joules and in electronvolts.
Discuss how the graph would be affected by using light of the same frequency but greater intensity, and by using a different metal with a larger work function.
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An electron and a small dust grain both move in a laboratory. The electron speed is . The dust grain has mass and speed .
The de Broglie wavelengths of the two objects are compared.
Calculate the de Broglie wavelength of the electron.
Calculate the de Broglie wavelength of the dust grain.
Compare and contrast the likelihood of observing diffraction for the electron and the dust grain using ordinary laboratory apertures or crystals.
Explain how the comparison illustrates wave-particle duality for matter.
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A Compton scattering event is represented by the directions of the incident photon, the scattered photon and the recoil electron. The incident and scattered photon wavelengths are given.

Calculate the energy transferred from the photon when and .
State what happens to the energy calculated in part (a).
Explain how the event is similar to and different from a collision between two solid balls.
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Two monochromatic beams, A and B, are incident separately on the same metal cathode in a photoelectric cell. The beams have the same intensity. The current-potential curves are shown.

The beam with the larger magnitude of stopping potential is considered.
Identify which beam has the shorter wavelength.
Explain your answer to (a)(i).
Beam B is now used with twice the original intensity but unchanged wavelength. On the same axes, sketch the new current-potential curve for beam B.
Evaluate whether the Bohr model of the atom can explain these photoelectric observations for a metal surface.
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Electrons are accelerated from rest through a potential difference of and directed at a thin crystalline film. A detector records the first minimum in electron intensity at an angle of from the incident beam direction.

Assume the first minimum satisfies , where is the effective spacing causing diffraction.
Calculate the de Broglie wavelength of the electrons.
Estimate the spacing in the film.
Discuss how this experiment provides evidence for the wave nature of matter.
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Electrons are sent one at a time through a double-slit arrangement. Each electron produces one localized dot on a screen. After many electrons have arrived, a pattern of bright and dark bands is observed. A detector is then placed near the slits to determine which slit each electron passes through.

The pattern is first observed with no which-path detector operating.
Explain why the observations cannot be described using only a classical particle model.
Explain why the observations cannot be described using only a classical wave model.
Evaluate the effect of operating the which-path detector on the interference pattern.
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X-ray photons of wavelength are incident on a carbon target. Scattered photons are detected at to the incident direction. Treat the scattering electrons as free.

Use the Compton shift equation for the scattered photon.
Calculate the wavelength shift of the photon.
Calculate the wavelength of the scattered photon and the energy transferred to the electron.
Explain why Compton scattering is evidence for the particle nature of light.
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An electron beam is used to investigate a regular array of atoms in a thin solid film. The effective aperture spacing is . The electrons are accelerated from rest through .

detector is moved around the film to find positions of minimum intensity.
Describe how the detector should be used to identify a diffraction minimum.
State why a minimum is evidence for wave behaviour rather than only geometrical spreading.
Use the de Broglie model to predict the first-minimum angle using .
Calculate the de Broglie wavelength of the electrons.
Calculate the first-minimum angle.
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In a photoelectric experiment, two measurements of stopping potential are made for the same metal surface. At the stopping potential is . At the stopping potential is .

The data are used to test Einstein's photoelectric equation.
Show that the data give a value of Planck's constant close to the accepted value.
Determine the work function and threshold frequency of the metal.
Evaluate the claim that increasing the intensity of the light used in these measurements would increase the stopping potential.
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A Compton scattering experiment records the spectrum of X-rays scattered from a graphite target. At a fixed scattering angle, the spectrum contains one peak at the incident wavelength and a second peak at a longer wavelength. In another run, the wavelength shift of the second peak is .

The two peaks in the scattered spectrum are considered.
Explain the origin of the peak at the incident wavelength.
Explain why the second peak occurs at a longer wavelength.
Calculate the scattering angle for the run in which the wavelength shift is .
Evaluate the usefulness of comparing Compton scattering with a collision between two solid balls.
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Gamma-ray photons of wavelength are Compton scattered by free electrons. Scattered photons are observed at angles of and to the incident direction.
The angle dependence of the Compton shift is investigated.
Calculate the wavelength shifts for scattering angles of and .
For the scattering event, estimate the kinetic energy gained by the recoil electron.
Discuss why Compton scattering is most easily observed using X-rays or gamma rays rather than visible light.
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A student claims: "The photoelectric effect proves that light is only a particle, and electron diffraction proves that electrons are only waves." An electron diffraction tube uses a crystalline target with atomic spacings of about .
Evaluate the student's claim using evidence from quantum physics.
Explain the evidence for particle-like behaviour in the photoelectric effect.
Explain why electron diffraction does not mean that electrons are only waves.
The diffraction tube is adjusted so the electron de Broglie wavelength is about .
Estimate the accelerating potential difference needed for electrons starting from rest.
Explain what happens to the diffraction pattern if the accelerating potential difference is increased.
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