What does Quantum Physics cover in IB Physics?

This topic explores the wave-particle duality of light and matter, and the experimental evidence supporting these concepts. The photoelectric effect demonstrates light's particle nature, where the maximum kinetic energy of photoelectrons is E_max = hf - Phi. Matter exhibits wave-like properties, with a de Broglie wavelength given by λ = (h)/(p).

Is Quantum Physics SL or HL?

Quantum Physics is HL only. SL students are not examined on it.

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FourtyFive has 17 Quantum Physics questions. Every answer you write is marked mark by mark, IB-style, and you see where each mark was won or lost. Every part has a hint, the AI tutor helps you through the step you are stuck on, and your Study Profile picks what to practise next.

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Topic E.2 · HL only

Quantum Physics: notes and practice questions

Q: How do I revise Quantum Physics for IB Physics?

Start from the core idea: this topic explores the wave-particle duality of light and matter, and the experimental evidence supporting these concepts. In the exam: hL Paper 1A and HL Paper 2. The three standard shapes are a photoelectric stopping-potential-against-frequency graph with the gradient giving h and the intercept giving the work function, a de Broglie wavelength calculation for an accelerated electron, and a Compton shift calculation at a stated scattering angle. Then practise exam-style questions, easiest first, writing out every step of your working before you check it.

9 min read Jump to 17 practice questions

Summary

This topic explores the wave-particle duality of light and matter, and the experimental evidence supporting these concepts.
The photoelectric effect demonstrates light's particle nature, where the maximum kinetic energy of photoelectrons is $E_{\text{max}} = hf - \Phi$ .
Matter exhibits wave-like properties, with a de Broglie wavelength given by $\lambda = \frac{h}{p}$ .
Compton scattering provides further evidence for the particle nature of light, showing a shift in photon wavelength $\Delta\lambda = \frac{h}{m_e c}(1 - \cos \theta)$ .
These phenomena challenge classical wave theory and support the quantum model.

How it is examined

HL Paper 1A and HL Paper 2. The three standard shapes are a photoelectric stopping-potential-against-frequency graph with the gradient giving h and the intercept giving the work function, a de Broglie wavelength calculation for an accelerated electron, and a Compton shift calculation at a stated scattering angle.

Given in the booklet

$E_\text{max} = hf - \Phi$ , $\lambda = h/p$ , the Compton shift formula, plus h, $m_\text{e}$ and c. Work functions of named metals are supplied in the question. The stopping-potential relation $eV_\text{s} = E_\text{max}$ is not printed and has to be reasoned from the definition of potential difference.

Key ideas

There is no standard level content in E.2.

Not assessed

The derivation of the Compton formula is not required.

Guiding questions

How can light be used to create an electric current?
What is meant by wave-particle duality?

Linking questions

How can particles diffract?
What are the defining features and behaviours of waves?
What evidence indicates the diffraction of a wave?
How is photon scattering off an electron similar to and how is it different from the collision of two solid balls?
Can the Bohr model help explain the photoelectric effect? (NOS)
How did the explanation of the photoelectric effect lead to the falsification that light was purely a wave? (NOS)
Why is Compton scattering more convincing evidence for the particle nature of light than that from the photoelectric effect? (NOS)

Practice questions

17 questions · 2 easy · 12 medium · 3 hard

Showing 17 of 17

Question 1

EasyPaper 1A · calculator1 mark

The black-body radiation spectrum for a star with a surface temperature of $5000 \text{ K}$ is shown. The intensity units are arbitrary.

Graph showing the black-body radiation spectrum for a star at 5000 K, with intensity on the y-axis and wavelength on the x-axis. The curve has a single peak.

Later in its life cycle, the star's surface temperature increases to $7500 \text{ K}$ . Which graph shows the new radiation spectrum? The original spectrum is shown as a dashed line.

Graph showing the new curve with its peak at a shorter wavelength and a higher intensity than the original dashed curve.

Graph showing the new curve with its peak at a longer wavelength and a higher intensity than the original dashed curve.

Graph showing the new curve with its peak at a shorter wavelength and a lower intensity than the original dashed curve.

Graph showing the new curve with its peak at a longer wavelength and a lower intensity than the original dashed curve.

Question 2

MediumPaper 2 · calculator8 marks

(a)

This question is about the wave nature of matter.

(a) State the de Broglie hypothesis.

[2]

(b)(i)

(b)(i) The Davisson-Germer experiment provided evidence for the wave nature of electrons. Outline the experimental setup.

[3]

(b)(ii)

(b)(ii) Explain how the results of this experiment support the de Broglie hypothesis.

[3]

Question 3

HardPaper 2 · calculator12 marks

(a)

In an experiment to investigate the photoelectric effect, light of varying frequency $f$ is incident on a metal surface. For each frequency, the stopping potential $V_s$ required to prevent any photoelectrons from reaching the collector is measured. The data are used to plot a graph of the maximum kinetic energy $E_{k,max}$ of the photoelectrons against the frequency of the incident light. The graph is shown below.

A graph of Maximum Kinetic Energy (in J) on the y-axis against Frequency (in Hz) on the x-axis. The graph is a straight line with a positive slope. It intersects the x-axis at 6.0 x 10^14 Hz and passes through the point (10.0 x 10^14 Hz, 2.65 x 10^-19 J)

(a) Explain how this graph supports the particle model of light (the photon model) and contradicts the classical wave model.

[3]

(b)

(b) Use the graph to determine a value for Planck's constant.

[3]

(c)

[2]

(d)

(d) The light source is now changed so that the intensity of the incident light is doubled, but the frequency remains the same at $10.0 \times 10^{14}$ Hz. State and explain the effect of this change on:

i. the maximum kinetic energy of the photoelectrons.

ii. the photoelectric current.

[4]

Question 4

EasyPaper 1A · calculator1 mark

An X-ray photon is scattered by a stationary electron. The scattered photon moves at an angle of $120^\circ$ relative to its original direction.

What is the change in the wavelength of the photon?

A. $\frac{h}{2m_\text{e}c}$

B. $\frac{h}{m_\text{e}c}$

C. $\frac{3h}{2m_\text{e}c}$

D. $\frac{2h}{m_\text{e}c}$

Question 5

MediumPaper 2 · calculator6 marks

(a)(i)

3. This question is about the de Broglie wavelength.

In a research laboratory, physicists investigate the wave-particle duality of matter. They perform experiments with various particles and objects.

(a) Calculate:

i. the de Broglie wavelength of electrons moving at $0.1c$ (one-tenth the speed of light) in an electron microscope.

[2]

(a)(ii)

(a) Calculate:

ii. the de Broglie wavelength for protons accelerated to a speed of $5.00 \times 10^6$ m s $^{-1}$ in a particle accelerator.

[2]

(a)(iii)

(a) Calculate:

iii. the de Broglie wavelength of a tiny dust particle with a mass of $1.00 \times 10^{-12}$ kg drifting slowly at $1.00 \times 10^{-3}$ m s $^{-1}$ .

[2]

Question 6

HardPaper 2 · calculator12 marks

(a)

In a specialized medical imaging technique, high-energy X-rays are directed at a target to probe its atomic structure. During this process, a photon with an initial wavelength of $4.00 \times 10^{-12}$ m collides with a stationary electron in the target material. After the collision, the photon's wavelength is observed to have increased by exactly $1.21 \times 10^{-12}$ m.

(a) Calculate the wavelength of the photon after the collision.

[2]

(b)

(b) Deduce the angle through which the photon has been deflected in this collision.

[3]

(c)

(c) Explain whether the angle between the original direction of the photon and the final direction of the electron is greater, smaller or equal to your answer in (b).

[3]

(d)

(d) Determine the kinetic energy of the electron after the collision. Express your answer in keV.

[4]

Question 7

MediumPaper 1A · calculator1 mark

A photon of energy $E$ is incident on a metal surface with work function $\Phi$ . An electron is emitted from the surface.

What is the minimum de Broglie wavelength of the emitted electron? ( $m_e$ is the rest mass of the electron and $h$ is the Planck constant.)

A. $\frac{h}{\sqrt{2m_e(E - \Phi)}}$

B. $\frac{h}{\sqrt{2m_e E}}$

C. $\frac{h}{E - \Phi}$

D. $\frac{\sqrt{2m_e(E - \Phi)}}{h}$

Question 8

HardPaper 1A · calculator1 mark

In a photoelectric effect experiment, a graph of stopping potential $V_s$ is plotted against the wavelength $\lambda$ of the incident light for a particular metal surface. What is the magnitude of the gradient of the graph at wavelength $\lambda$ ?

A. $\frac{h}{e}$

B. $\frac{hc}{e}$

C. $\frac{hc}{e\lambda^2}$

D. $\frac{h}{e\lambda}$

Question 9

MediumPaper 1A · calculator1 mark

A gamma-ray photon is incident on a stationary proton. The photon is scattered inelastically by the proton.

What are the changes, if any, to the magnitude of the momentum and the speed of the photon?

	Magnitude of momentum	Speed
A.	Decreases	Decreases
B.	Decreases	Unchanged
C.	Unchanged	Decreases
D.	Unchanged	Unchanged

Question 10

MediumPaper 1A · calculator1 mark

An experiment investigates the photoelectric effect using a caesium metal surface. The graph shows the variation of the maximum kinetic energy $E_{k,max}$ of photoelectrons with the frequency $f$ of the incident light, represented by line C.

A graph of Ek,max vs f. A straight line, labelled C, with a positive slope intersects the positive f-axis and the negative Ek,max-axis.

The caesium surface is then replaced with a zinc surface, which has a larger work function. Which statement correctly describes the new graph for zinc?

A. The new graph will be a line parallel to C, but shifted to the left.

B. The new graph will be a line parallel to C, but shifted to the right.

C. The new graph will be a line with a steeper slope than C.

D. The new graph will be a line with a shallower slope than C.

Question 11

MediumPaper 1A · calculator1 mark

A beam of monochromatic light of intensity $I$ is incident on a metal plate. The source of light is changed. The wavelength of the new light is tripled. The number of photons incident on the plate per unit area per unit time is increased by a factor of six.

What is the new intensity of the light beam?

A. $\frac{I}{3}$

B. $2I$

C. $6I$

D. $18I$

Question 12

MediumPaper 1A · calculator1 mark

A tiny dust particle, with a mass of $2.0 \times 10^{-10} \text{ kg}$ , is observed to have a kinetic energy of $2.5 \times 10^{-9} \text{ J}$ . Which of the following expressions gives the de Broglie wavelength, in metres, of this dust particle?

A. $\frac{h}{1.0 \times 10^{-9}}$

B. $\frac{h}{7.1 \times 10^{-10}}$

C. $\frac{h}{2.0 \times 10^{-10}}$

D. $\frac{h}{2.5 \times 10^{-9}}$

Question 13

MediumPaper 1A · calculator1 mark

The photoelectric effect is the emission of electrons from a metal surface when electromagnetic radiation is incident on it. Which of the following are predictions of the classical wave model for this effect?

I. The maximum kinetic energy of an emitted electron increases as the intensity of the radiation increases.

II. There is a significant time delay between the radiation first striking the surface and the emission of the first electron, especially at low intensities.

III. Electron emission occurs for any frequency of radiation, provided the intensity is sufficiently high.

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

Question 14

MediumPaper 1A · calculator1 mark

An X-ray photon has an initial wavelength $\lambda_i$ . It scatters from a stationary electron and emerges with a final wavelength $\lambda_f$ . What is the kinetic energy of the electron after the scattering event?

A. $\frac{hc}{\lambda_f}$

B. $\frac{hc}{\lambda_i}$

C. $hc(\frac{1}{\lambda_i} - \frac{1}{\lambda_f})$

D. $hc(\frac{1}{\lambda_f} - \frac{1}{\lambda_i})$

Question 15

MediumPaper 1A · calculator1 mark

A proton and a deuteron are accelerated from rest through the same potential difference. The mass of a deuteron is approximately twice the mass of a proton, and they have the same magnitude of charge.

What are the values for the ratio of the final kinetic energies $\frac{E_{k, \text{proton}}}{E_{k, \text{deuteron}}}$ and the ratio of the final de Broglie wavelengths $\frac{\lambda_{\text{proton}}}{\lambda_{\text{deuteron}}}$ ?

A. Kinetic energy ratio = 1; Wavelength ratio = $\sqrt{2}$

B. Kinetic energy ratio = 1; Wavelength ratio = $\frac{1}{\sqrt{2}}$

C. Kinetic energy ratio = 2; Wavelength ratio = 2

D. Kinetic energy ratio = 1; Wavelength ratio = 1

Question 16

MediumPaper 1A · calculator1 mark

An experiment investigates the photoelectric effect for two different metals, Zinc (Zn) and Sodium (Na). The work function for Zinc is $4.3$ eV and for Sodium is $2.3$ eV.

Which graph shows the variation with light frequency $f$ of the maximum kinetic energy $E_{\text{max}}$ of photoelectrons emitted from both metals?

Four graphs of Emax vs frequency. Each graph shows two lines, Zn and Na, representing the photoelectric effect for the two different metals. In option A, the lines are parallel, but the line for Zn has a smaller x-intercept than Na. In option B, the lines are parallel, and the line for Na has a smaller x-intercept than Zn. In option C, the lines have different gradients and cross. In option D, the lines have different gradients and do not cross.

A. A

B. B

C. C

D. D

Question 17

MediumPaper 1A · calculator1 mark

Blue light incident on a metallic surface causes the emission of photoelectrons. The blue light is replaced by ultraviolet light of the same intensity.

What is the effect on the maximum kinetic energy of the photoelectrons and the rate of emission of photoelectrons?

A. Maximum kinetic energy increases and rate of emission increases

B. Maximum kinetic energy increases and rate of emission decreases

C. Maximum kinetic energy decreases and rate of emission increases

D. Maximum kinetic energy decreases and rate of emission decreases

Every Quantum Physics question, marked for you

Every answer is marked mark by mark, IB-style, and the AI tutor helps when you are stuck.

Where marks are lost

Stopping one step short of the conclusion. Two numbers and no sentence is two marks out of three.
Answering a procedure question with a platitude.
Losing precision in Paper 1B. Uniquely to this paper, quoting the right number badly loses marks.

Quantum Physics: notes and practice questions

How it is examined

Guiding questions

Linking questions