IB Physics HL E 2 Quantum Physics Questions

Practise IB Physics HL E.2 by applying photon, matter-wave, uncertainty and quantum-state models to evidence from spectra and microscopic experiments.

Exam points

Relate photon energy, frequency and wavelength to transitions, photoelectric evidence and spectra.
Apply de Broglie wavelength, momentum and uncertainty relationships to microscopic systems.
Interpret quantum-state, probability and measurement evidence while evaluating model limits.

Covered syllabus points

E.2.1 (HL)—Photoelectric effect E.2.2 (HL)—Threshold frequency E.2.3 (HL)—Photoelectric equation E.2.4 (HL)—Particle diffraction E.2.5 (HL)—Matter wave-particle duality E.2.6 (HL)—de Broglie wavelength E.2.7 (HL)—Compton scattering E.2.8 (HL)—Photon wavelength increase E.2.9 (HL)—Compton wavelength shift

[Maximum number: 10]

This question is in two parts. Part 1 is about photoelectricity. Part 2 is about electrical and magnetic force fields.
Part 1 Photoelectricity

(a)

State what is meant by work function.

[ 1 ]

(b)

The diagram shows part of an experimental arrangement used to investigate the photoelectric effect.

[ 4 ]

(i)

Explain how the maximum kinetic energy of the emitted electrons is determined experimentally.

[ 2 ]

(ii)

On the diagram, draw the power supply and other necessary components needed in order to carry out the experiment in (b)(i).

[ 2 ]

(c)

Using results obtained with the apparatus in (b), the following graph was drawn. The graph shows how the maximum kinetic energy of the photoelectrons varies with the frequency of the incident radiation.

State how the graph can be used to determine

[ 3 ]

(i)

a value for the Planck constant.

[ 1 ]

(ii)

the work function of the material.

[ 1 ]

(iii)

the threshold wavelength of the material.

[ 1 ]

$\quad \lambda_{0}=\frac{c}{\text { frequency intercept }}$ or $\frac{h c}{\text { max ke intercept }}$ ;

(d)

In an experiment, light at a particular frequency is incident on a surface and electrons are emitted. Explain what happens to the number of electrons emitted per second when the intensity of this light is increased.

[ 2 ]

[Maximum number: 10]

This question is in two parts. Part 1 is about the oscillation of a mass. Part 2 is about the photoelectric effect.
Part 1 Oscillation of a mass
A mass of 0.80 kg rests on a frictionless surface and is connected to two identical springs both of which are fixed at their other ends. A force of 0.030 N is required to extend or compress each spring by 1.0 mm . When the mass is at rest in the centre of the arrangement, the springs are not extended.

(a)

Part 2 Photoelectric effect
A student carries out a photoelectric experiment in which radiation is incident on a metal surface in a vacuum.

Explain why photoelectrons are not emitted from the metal surface unless the frequency of incident light exceeds a minimum value.

[ 2 ]

(b)

A graph of the results of the experiment show how the maximum kinetic energy $E_{\text {max }}$ of the emitted photoelectrons varies with the frequency f of the incident radiation.

Use the graph to

[ 6 ]

(i)

identify the minimum value of the frequency $f_{0}$ for photoelectrons to be emitted.

[ 1 ]

(value of intercept on f-axis $=) 9.3 \times 10^{14} \mathrm{~Hz}$ ;
Allow answers in the range of 9.0 to 9.5, but with correct power of ten.

(ii)

determine the Planck constant.

[ 3 ]

attempted use of gradient $\left(\frac{h}{e}\right)$ to evaluate h;
eg $\frac{2.4}{6 \times 10^{14}}=4 \times 10^{-15} \mathrm{eVs}$ ; (allow answers in the range of 3.9 to $4.2 \times 10^{-15}$ ) $6.4 \times 10^{-34} \mathrm{Js}$ ; (allow ECF, eg answers in the range of 6.2 to $6.7 \times 10^{-34}$ )

Marking guidance:

Do not allow a bald answer of $6.6 \times 10^{-34}$ as value is known.
or
use of y-intercept $=\frac{-h f_{0}}{e}$ ;
$h=\frac{3.77 \times 1.6 \times 10^{-19}}{0.93 \times 10^{15}} ;($ allow intercept between -3.6 and -3.8 eV)
$6.4 \times 10^{-34} \mathrm{Js}$ ; (allow ECF, eg answers in the range of 6.0 to $6.8 \times 10^{-34}$ )
Do not allow a bald answer of $6.6 \times 10^{-34}$ as value is known.

(iii)

calculate the work function, in eV , for the metal surface.

[ 2 ]

$E=6.62 \times 10^{-34} \times 9.3 \times 10^{14}\left(=6.2 \times 10^{-19} \mathrm{~J}\right)$ ;
an answer in the range of 3.4 to 4.0 eV ;
(allow ECF from (e)(i) and (e)(ii))
or
identifies y intercept as work function;
an answer in the range of 3.6 to 3.8 eV ;

(c)

The student repeats the experiment with a different metal surface that has a smaller value for the work function. On the graph in (e), draw a line to show how $E_{\text {max }}$ varies with f.

[ 2 ]

[Maximum number: 5]

This question is in two parts. Part 1 is about thermal properties of matter. Part 2 is about quantum physics.

Part 1 Thermal properties of matter

(a)

Part 2 Quantum physics

The diagram shows the end of an electron diffraction tube.

A pattern forms when diffracted electrons are incident on a fluorescent layer at the end of the tube.

Explain how the pattern demonstrates that electrons have wave properties.

[ 3 ]

(b)

Electrons are accelerated to a speed of $3.6 \times 10^{7} \mathrm{~m} \mathrm{~s}^{-1}$ by the electric field between the cathode and the anode.

[ 2 ]

(i)

Calculate the de Broglie wavelength of the electrons.

[ 2 ]

$\left(p=m_{\mathrm{e}} v=\right) 3.28 \times 10^{-23} \mathrm{Ns}$ ;

\lambda=\left(\frac{\mathrm{h}}{\mathrm{p}}=\frac{6.63 \times 10^{-34}}{3.28 \times 10^{-23}}=\right) 2.02 \times 10^{-11} \mathrm{~m} ;

[Maximum number: 3]

This question is in two parts. Part 1 is about thermal properties of matter. Part 2 is about quantum physics.

Part 1 Thermal properties of matter

Part 2 Quantum physics

The diagram shows the end of an electron diffraction tube.

A pattern forms when diffracted electrons are incident on a fluorescent layer at the end of the tube.

Explain how the pattern demonstrates that electrons have wave properties.

[Maximum number: 2]

This question is in two parts. Part 1 is about momentum and energy. Part 2 is about the de Broglie hypothesis and radioactive decay.

Describe the de Broglie hypothesis.

[Maximum number: 5]

(a)

The existence of atomic energy levels can be understood by applying the de Broglie hypothesis to an electron confined to move in one dimension in a box of length L.

[ 4 ]

(i)

State the de Broglie hypothesis as it applies to an electron.

[ 1 ]

(ii)

Show that the energy $E_{\mathrm{n}}$ of the electron in the box is given by

E_{\mathrm{n}}=\frac{n^{2} h^{2}}{8 m_{\mathrm{e}} L^{2}}

where $n=1,2,3 \ldots, h$ is the Planck constant and $m_{\mathrm{e}}$ is the mass of the electron.

[ 3 ]

(b)

The magnitude of the least energy that an electron in the hydrogen atom can have is $2.2 \times 10^{-18} \mathrm{~J}$ . Estimate, using the equation in (b)(ii), the radius of the hydrogen atom.

[ 1 ]

$1.7 \times 10^{-10} \mathrm{~m}$ ;

[Maximum number: 3]

(a)

Outline why Compton scattering offers better evidence for the particle nature of light than the photoelectric effect.

A photon of wavelength $6.40 \times 10^{-12} \mathrm{~m}$ and energy 0.194 MeV is incident on an electron at rest. The photon scatters at an angle $\theta$ with wavelength $7.47 \times 10^{-12} \mathrm{~m}$ . The electron recoils.

[ 2 ]

(b)

Calculate the kinetic energy of the recoiling electron.

[ 1 ]

$E=\lessdot 0.194-0.166=>0.028 \mathrm{MeV} \quad$

Accept 0.024 from the value given as show that.

Allow ECF from c) i)

Accept $4.5 \times 10^{-15} \mathrm{~J}$ .

(c)

Show that the energy of the scattered photon is about 0.17 MeV .

[ 1 ]

$E=<\frac{h c}{\lambda}=>\frac{1.24 \times 10^{-6}}{7.47 \times 10^{-12}}$ OR 0.166 MeV

(d)

For an electron, $\frac{h}{m_{\mathrm{e}} c}=2.43 \times 10^{-12} \mathrm{~m}$ . Determine $\theta$ .

[ 2 ]

$7.47 \times 10^{-12}-6.40 \times 10^{-12}=2.43 \times 10^{-12}(1-\cos \theta)^{}$

« $\cos \theta=0.5597$ so » $\theta=56.0^{\underline{\mathrm{o}}}$

Accept angle in radians ( 0.98 « rad »).

Award [2] if 56 « ${ }^{\circ}$ » or 0.98 « rad» are seen as the answer without working

[Maximum number: 2]

Outline why the wavelength of the scattered photon is longer than that of the incident photon.

The photon loses energy / transfers energy to the electron

$E=\frac{h c}{\lambda} /$ lower energy implies longer wavelength

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Covered syllabus points

Question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question (c)

Question (i)

Question (ii)

Question (iii)

Question (d)

Question 2

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

Question (c)

Question 3

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Question (b)

Question (i)

Question 4

Question 5

Question 6

Question (a)

Question (i)

Question (ii)

Question (b)

Question 7

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Question (c)

Question (d)

Question 8