CAIE A-Level Physics A2 22 Quantum Physics Questions

Practise analysing photon energy and momentum, photoelectric emission, wave-particle evidence, de Broglie matter waves and quantised line spectra.

Exam points

calculate and interpret photon energy and momentum, including energy, frequency, wavelength and radiation-force relationships
explain and calculate photoelectric emission using threshold conditions, work function and maximum kinetic energy
use photoelectric, interference and diffraction evidence to evaluate wave�particle duality and apply de Broglie wavelength
interpret atomic energy levels and emission or absorption spectra as quantised transitions
calculate photon frequency or energy from an atomic energy-level difference

Covered syllabus points

22.1 Energy and momentum of a photon 22.2 Photoelectric effect 22.3 Wave–particle duality 22.4 Energy levels in atoms and line spectra

[Maximum number: 9]

(a)

State what is meant by:

[ 3 ]

(i)

the photoelectric effect

[ 2 ]

(ii)

work function energy.

[ 1 ]

(b)

A polished calcium plate in a vacuum is investigated by illuminating the surface with light.

It is found that no photoelectric current is produced when the frequency of the light is less than $6.93 \times 10^{14} \mathrm{~Hz}$ .

[ 6 ]

(i)

State the name of the frequency below which no photoelectric current is produced.

[ 1 ]

(ii)

Explain how the photon model of electromagnetic radiation accounts for this phenomenon.

[ 3 ]

(iii)

Calculate the work function energy, in eV , of calcium.
work function energy = eV

[ 2 ]

work function $=h f_{0}=6.63 \times 10^{-34} \times 6.93 \times 10^{14}$ $\begin{aligned} =4.59 \times 10^{-19}(\mathrm{~J}) =4.59 \times 10^{-19} / 1.60 \times 10^{-19}(\mathrm{eV}) =2.87 \mathrm{eV} \end{aligned}$

[Maximum number: 7]

(a)

State one piece of experimental evidence for:

[ 2 ]

(i)

the particulate nature of electromagnetic radiation

[ 1 ]

(ii)

the wave nature of matter.

[ 1 ]

(b)

Calculate the de Broglie wavelength $\lambda$ of an alpha-particle moving at a speed of $6.2 \times 10^{7} \mathrm{~m} \mathrm{~s}^{-1}$ .

\lambda=

[ 2 ]

$\lambda=h / p$ $\begin{aligned} p =4 \times 1.66 \times 10^{-27} \times 6.2 \times 10^{7} \left.=4.1 \times 10^{-19} \mathrm{~N} \mathrm{~s}\right) \end{aligned}$ $\begin{aligned} \lambda =6.63 \times 10^{-34} / 4.1 \times 10^{-19} =1.6 \times 10^{-15} \mathrm{~m} \end{aligned}$

(c)

The speed v of the alpha-particle in (b)(i) is gradually reduced to zero.

On Fig. 8.1, sketch the variation with v of $\lambda$ .

Fig. 8.1

[ 2 ]

line with negative gradient throughout
curve asymptotic to both axes with non-zero $\lambda$ at $v=6.2 \times 10^{7} \mathrm{~m} \mathrm{~s}^{-1}$

(d)

Suggest an explanation for why people are not observed to diffract when they walk through a doorway.

[ 1 ]

[Maximum number: 3]

Some of the electron energy bands in a solid are illustrated in Fig. 12.1.

Fig. 12.1

In isolated atoms, electron energy levels have discrete values. Suggest why, in a solid, there are energy bands, rather than discrete energy levels.

[Maximum number: 7]

(a)

State what is meant by a photon.

[ 2 ]

(b)

For an accelerating voltage of 32 kV in Fig. 8.1, determine:

[ 5 ]

(i)

the maximum momentum of an X-ray photon produced at the target

maximum photon momentum =

[ 2 ]

momentum =E / c
momentum $=\left(0.032 \times 1.60 \times 10^{-13}\right) /\left(3.00 \times 10^{8}\right)$ $=1.7 \times 10^{-23} \mathrm{~N} \mathrm{~s}$

(ii)

the minimum wavelength of X-rays produced at the target.

minimum wavelength =m [3]

[ 3 ]

E=h f and $\lambda=c / f$ $\begin{aligned} \lambda =h c / E =\left(6.63 \times 10^{-34} \times 3.00 \times 10^{8}\right) /\left(0.032 \times 1.60 \times 10^{-13}\right) \end{aligned}$ $\lambda=3.9 \times 10^{-11} \mathrm{~m}$

All question bank results loaded

Covered syllabus points

Question 1

Question (a)

Question (i)

Question (ii)

Question (b)

Question (i)

Question (ii)

Question (iii)

Question 2

Question (a)

Question (i)

Question (ii)

Question (b)

Question (c)

Question (d)

Question 3

Question 4

Question (a)

Question (b)

Question (i)

Question (ii)