CAIE A-Level Physics 22 Quantum Physics

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: 2]

Define magnetic flux.

product of (magnetic) flux density and (cross-sectional) area

M1

direction of flux normal to (plane of the) area

A1

or

(magnetic) flux density × area × $\sin \theta$

(M1)

where $\theta$ is angle between direction of flux and (plane of the) area

(A1)

[Maximum number: 9]

(a)

Explain what is meant by the photoelectric effect.

[ 2 ]

(b)

One wavelength of electromagnetic radiation emitted from a mercury vapour lamp is 436 nm . Calculate the photon energy corresponding to this wavelength.
energy =

[ 2 ]

$E=h c / \lambda$ $=\left(6.63 \times 10^{-34} \times 3.00 \times 10^{8}\right) /\left(436 \times 10^{-9}\right)$ $=4.56 \times 10^{-19} \mathrm{~J}\left(4.6 \times 10^{-19} \mathrm{~J}\right) \quad$ A1

(c)

Light from the lamp in (b) is incident, separately, on the surfaces of caesium and tungsten metal.

Data for the work function energies of caesium and tungsten metal are given in Fig. 10.1.

Fig. 10.1

Calculate the threshold wavelength for photoelectric emission from

[ 3 ]

(i)

caesium, nm

[ 2 ]

$\Phi=h c / \lambda_{0}$

\begin{aligned} \lambda_{0} & =\left(6.63 \times 10^{-34} \times 3.00 \times 10^{8}\right) /\left(1.4 \times 1.60 \times 10^{-19}\right) \\ & =890 \mathrm{~nm} \end{aligned}

(ii)

tungsten.

threshold wavelength =nm [1]

[ 1 ]

$\lambda_{0}=\left(6.63 \times 10^{-34} \times 3.00 \times 10^{8}\right) /\left(4.5 \times 1.60 \times 10^{-19}\right)$

=280 \mathrm{~nm}

(d)

Use your answers in (c) to state and explain whether the radiation from the mercury lamp of wavelength 436 nm will give rise to photoelectric emission from each of the metals.
caesium:
tungsten:

[ 2 ]

caesium:
wavelength of photon less than threshold wavelength (or v.v.)
or
$\lambda_{0}=890 \mathrm{~nm}>436 \mathrm{~nm}$
so yes
tungsten:
wavelength of photon greater than threshold wavelength (or v.v.)
or
$\lambda_{0}=280 \mathrm{~nm}<436 \mathrm{~nm}$
so no

[Maximum number: 9]

(a)

State an effect, one in each case, that provides evidence for

[ 2 ]

(i)

the wave nature of a particle,

[ 1 ]

(ii)

the particulate nature of electromagnetic radiation.

[ 1 ]

(b)

Four electron energy levels in an isolated atom are shown in Fig. 12.1.

Fig. 12.1

For the emission spectrum associated with these energy levels,

[ 3 ]

(i)

on Fig. 12.1, mark with an arrow the transition that gives rise to the shortest wavelength,

[ 1 ]

(ii)

show that the wavelength of the transition in (i) is $4.35 \times 10^{-7} \mathrm{~m}$ .

[ 2 ]

$E=h c / \lambda$ or E=h f and $c=f \lambda$

\lambda=\left(6.63 \times 10^{-34} \times 3.00 \times 10^{8}\right) /\left[(3.40-0.54) \times 1.60 \times 10^{-19}\right]=4.35 \times 10^{-7} \mathrm{~m}

(c)

State what is meant by the de Broglie wavelength.

[ 2 ]

(d)

Calculate the speed of an electron having a de Broglie wavelength equal to the wavelength in (b)(ii).

speed =

$\mathrm{ms}^{-1}$

[ 2 ]

$\lambda=h / m v$

\begin{aligned} v & =\left(6.63 \times 10^{-34}\right) /\left(9.11 \times 10^{-31} \times 4.35 \times 10^{-7}\right) \\ & =1.67 \times 10^{3} \mathrm{~ms}^{-1} \end{aligned}

[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.

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Covered syllabus points

22. Quantum physics question 1

22. Quantum physics question 2

Question (a)

Question (b)

Question (c)

Question (i)

Question (ii)

Question (d)

22. Quantum physics question 3

Question (a)

Question (i)

Question (ii)

Question (b)

Question (i)

Question (ii)

Question (c)

Question (d)

22. Quantum physics question 4