QCAA Physics Quantum Theory
15 sample questions with marking guides and sample answers
Estimate the de Broglie wavelength for a standard men's basketball travelling at 10.0 m s.
Reveal Answer
Using de Broglie's equation,
Taking the mass of a standard men's basketball as approximately
then
So the estimated de Broglie wavelength is approximately
| Descriptor | Marks |
|---|---|
Estimates mass of basketball | 1 |
Substitutes for in equation (using 0.60 kg) | 1 |
Calculates answer | 1 |
2 significant figures | 1 |
Experiments have been carried out by scientists to investigate cathode rays.
Assess the contribution of the results of these experiments in developing an understanding of the existence and properties of electrons.
Reveal Answer
Experimental results and their interpretation have played an essential role in developing and understanding of both the existence and properties of electrons.
It was demonstrated that cathode rays could be deflected by an electric field in a manner consistent with negatively charged particles. This experiment also allowed the deduction that the cathode rays were not electromagnetic waves because the latter would not be deflected by an electric field.
The combined effect of changing the magnitudes of electric and magnetic fields through which the electrons passed was measured and from this the charge-to-mass ratio of the electron was calculated.
| Descriptor | Marks |
|---|---|
| 5 |
| 4 |
| 3 |
| 2 |
Provides some relevant information | 1 |
None of the above | 0 |
Describe what happens when light is shone onto a metallic surface in the context of the photoelectric effect.
Reveal Answer
Light with energy equivalent to has the ability to produce photoelectrons from a metallic surface.
When the frequency of light is below the threshold frequency for the metallic surface, the light will be reflected with no transfer of energy.
When the frequency of light is above the threshold frequency for the metallic surface, the energy of the photons will be absorbed and photoelectrons with kinetic energy proportional to the excess energy will be released.
The intensity of incident light is proportional to the number of photoelectrons for frequencies greater than the threshold frequency.
| Descriptor | Marks |
|---|---|
Identifies incident light has energy equivalent to | 1 |
Describes transfer of energy when frequency of light is below the threshold frequency | 1 |
Describes transfer of energy when frequency of light is above the threshold frequency | 1 |
Identifies relationship between intensity of incident light and resultant photoelectrons | 1 |
Outline TWO ways in which Schrödinger's model of electron behaviour is different from electron behaviour in the atomic models of Rutherford and Bohr.
Reveal Answer
In contrast to Bohr's idea of fixed orbits, Schrdinger described orbitals as probabilities of electrons as being in particular locations.
Unlike Rutherford's model in which electrons were imagined as particles orbiting the nucleus, Schrdinger described the electrons as waves, based on the work of de Broglie.
| Descriptor | Marks |
|---|---|
Outlines TWO ways in which Schrödinger's model differs from those of Rutherford and Bohr | 3 |
| 2 |
Provides some relevant information | 1 |
None of the above | 0 |
After coherent light has been passed through a double slit, the observation of an interference pattern on a screen is explained by the
wave nature of light.
equal width of the slits.
discrete packets of photons.
distance from the slits to the screen.
Reveal Answer
wave nature of light.
Interference is a fundamental property of waves where overlapping wavefronts add constructively or destructively; this experiment is the classic evidence for the wave nature of light.
equal width of the slits.
While slit width affects the diffraction envelope and contrast, the interference pattern itself is caused by wave superposition, which can occur even if the slits are not perfectly equal in width.
discrete packets of photons.
Discrete packets (photons) refer to the particle nature of light; if light behaved strictly as classical particles, it would form two distinct bands rather than an interference pattern.
distance from the slits to the screen.
The distance to the screen affects the spacing of the fringes (scale), but it is not the fundamental cause of the interference phenomenon itself.
Which one of the following is closest to the de Broglie wavelength of a motor car moving at ?
Reveal Answer
Correct. Using the de Broglie wavelength formula , we calculate .
Incorrect. This result is off by a factor of 10, which would occur if the velocity was instead of .
Incorrect. This answer is off by a factor of 100, likely due to a miscalculation of the momentum denominator .
Incorrect. This is approximately the value of Planck's constant (), which means the momentum was incorrectly treated as .
Determine the wavelength of an electromagnetic wave with an energy of J.
m
m
m
m
Reveal Answer
m
This incorrect value results from simply multiplying the energy by the speed of light (), ignoring Planck's constant and the correct formula.
m
This answer is obtained by dividing Planck's constant by the energy () but neglecting to multiply by the speed of light ().
m
Using the relationship , substitute Planck's constant ( Js) and the speed of light ( m/s) to find m.
m
This value represents the wavenumber ( m), which is the reciprocal of the wavelength rather than the wavelength itself.
Discuss the nature of light by describing evidence from two key experiments.
Reveal Answer
Young's double slit experiment and black-body radiation both provide evidence for the behaviour of light.
In Young's double slit experiment, the interference patterns formed as light passed between the two slits demonstrates the wave nature of light.
In contrast, black-body radiation demonstrates the quantised nature of light as electrons can only absorb or emit energy in discrete amounts.
Therefore, light has some wave properties and some particle properties.
| Descriptor | Marks |
|---|---|
Identifies evidence for the nature of light comes from Young's double slit experiment | 1 |
Identifies evidence for the nature of light comes from black-body radiation | 1 |
Describes evidence for wave nature of light | 1 |
Describes evidence for photons | 1 |
Concludes light has the properties of both waves and particles | 1 |
Many scientists have performed experiments to explore the interaction of light and matter.
Analyse how evidence from at least THREE such experiments has contributed to our understanding of physics.
Reveal Answer
Answers could include:
Reference to:
- Black body radiation experiments and the development of quantum physics
- Photoelectric experiments and the development of quantum physics
- Spectroscopy experiments and the development of astrophysics and the atomic model
- Polarisation experiments and the development of the wave nature of light
- Interference and diffraction and the development of the wave model of light
- Cosmic gamma rays and the development of theory of special relativity and/or the standard model.
| Descriptor | Marks |
|---|---|
| 8 |
| 7 |
The student response meets all criteria of the 5-mark band, and additionally meets the majority of criteria in the 7-mark band. | 6 |
| 5 |
The student response meets all criteria of the 3-mark band, and additionally meets the majority of criteria in the 5-mark band. | 4 |
Provides some information about evidence from an experiment AND/OR a link to physics | 3 |
The student response meets all criteria of the 1-mark band, and additionally meets the majority of criteria in the 3-mark band. | 2 |
Provides some relevant information | 1 |
None of the above | 0 |
Neutrons are subatomic particles and, like electrons, they can exhibit both particle-like and wave-like behaviour. Ignore any relativistic effects.
A beam of neutrons that can be used for scientific experiments is produced by a nuclear research reactor.
The mass of a neutron is .
The de Broglie wavelength of the neutrons produced by the nuclear reactor is .
Calculate the speed of the neutrons.
Reveal Answer
| Descriptor | Marks |
|---|---|
Shows correct substitution into the de Broglie wavelength formula, e.g. | 1 |
Calculates the correct speed of | 1 |
The neutron beam is sent through a crystal with an interatomic spacing of .
Would you expect to observe a diffraction pattern? Justify your answer.
Reveal Answer
The ratio of . As this ratio is close to 1, we would expect to be able to observe a diffraction pattern.
| Descriptor | Marks |
|---|---|
Calculates the ratio as and identifies that it is close to 1 | 1 |
Concludes that a diffraction pattern is expected to be observed | 1 |
Consider an electron beam with the same de Broglie wavelength as the neutron beam, .
Which will have the greater speed: an electron in the electron beam or a neutron in the neutron beam? Justify your answer.
Reveal Answer
The electron will have the greater speed.
The product of mass and velocity must remain constant for wavelength to remain constant, so if mass decreases, velocity must increase.
| Descriptor | Marks |
|---|---|
States that the electron will have the greater speed | 1 |
Provides correct reasoning based on the de Broglie wavelength formula, explaining that for a constant wavelength, the product of mass and velocity must remain constant, so a smaller mass requires a greater velocity | 1 |
The maximum kinetic energy of an electron ejected from a metallic surface can be increased by
using a positively ionised metal.
using a metal with a larger work function.
increasing the intensity of the incident light.
decreasing the wavelength of the incident light.
Reveal Answer
using a positively ionised metal.
Using a positively ionised metal would increase the electrostatic attraction on the electrons, effectively increasing the energy required to escape and decreasing the kinetic energy.
using a metal with a larger work function.
According to the photoelectric equation , increasing the work function () reduces the remaining energy available for kinetic energy.
increasing the intensity of the incident light.
Increasing intensity increases the number of photons and ejected electrons (photocurrent), but does not change the energy of individual photons or the maximum kinetic energy of the electrons.
decreasing the wavelength of the incident light.
Photon energy is inversely proportional to wavelength (). Decreasing the wavelength increases the incident photon energy, thereby increasing the maximum kinetic energy of the ejected electrons.
Photons are
gauge bosons that exhibit wave characteristics.
particles that can only travel in a medium.
mediators of the weak nuclear force.
leptons with no charge.
Reveal Answer
gauge bosons that exhibit wave characteristics.
Photons are the gauge bosons responsible for the electromagnetic force and exhibit wave-particle duality, displaying properties of both waves and particles.
particles that can only travel in a medium.
Unlike mechanical waves (like sound), photons are electromagnetic radiation and can travel through a vacuum without requiring a physical medium.
mediators of the weak nuclear force.
Photons mediate the electromagnetic force, whereas the weak nuclear force is mediated by and bosons.
leptons with no charge.
Photons are bosons, not leptons; leptons are a different family of particles that includes electrons and neutrinos.
Incident light with a frequency of Hz is shone onto a metal surface with a work function of J.
Determine the kinetic energy of a photoelectron ejected from the metal surface.
eV
eV
eV
eV
Reveal Answer
eV
This is the correct answer. First, calculate the photon energy J. Subtract the work function to find the kinetic energy in Joules ( J), then divide by J/eV to convert to electron-volts.
eV
This option is incorrect. It appears to confuse the numerical value of the frequency () with the final energy, ignoring Planck's constant and the necessary unit conversions.
eV
This option represents the kinetic energy in Joules ( J), not electron-volts. To obtain the correct answer in eV, you must divide this value by the elementary charge ( J/eV).
eV
This value is extremely small and physically unrealistic for the kinetic energy of a photoelectron in this context. It likely results from an arithmetic error or incorrect formula application.
The Bohr atomic model describes an atom as
the smallest particle of any substance.
a small dense nucleus orbited by electrons.
electrons scattered throughout a sphere of positively charged fluid.
a small positive nucleus surrounded by negative electrons in set orbits of fixed energy.
Reveal Answer
the smallest particle of any substance.
This describes John Dalton's early atomic theory, which viewed atoms as indivisible spheres, rather than the internal structure proposed by Bohr.
a small dense nucleus orbited by electrons.
This describes Rutherford's planetary model. While similar, it fails to include Bohr's key innovation: that electrons are restricted to specific, quantized orbits.
electrons scattered throughout a sphere of positively charged fluid.
This describes J.J. Thomson's "Plum Pudding" model, which was disproved by Rutherford before Bohr developed his model.
a small positive nucleus surrounded by negative electrons in set orbits of fixed energy.
The Bohr model refined the nuclear model by proposing that electrons move in specific, circular orbits (shells) with fixed, quantized energy levels around the nucleus.
Which one of the following best provides evidence of light behaving as a particle?
photoelectric effect
white light passing through a prism
diffraction of light through a single slit
interference of light passing through a double slit
Reveal Answer
photoelectric effect
The photoelectric effect demonstrates that light energy is absorbed and emitted in discrete quantized packets called photons, providing direct evidence of its particle nature.
white light passing through a prism
White light passing through a prism demonstrates dispersion and refraction, which are phenomena explained by the wave nature of light and its varying wavelengths.
diffraction of light through a single slit
Diffraction is the bending of light as it passes through a slit, which is a classic characteristic of waves rather than particles.
interference of light passing through a double slit
Interference patterns are created by the superposition of overlapping waves, providing foundational evidence for the wave model of light.