CAIE A-Level Physics A2 22.2 Photoelectric Effect Questions

Practise analysing photoelectric emission, threshold quantities, photon energy, work function, Einstein’s equation and graph effects of frequency and intensity.

Exam points

explain photoelectric emission and determine threshold conditions from frequency or wavelength
use photon energy and work function to explain the energy of emitted electrons
calculate or rearrange the Einstein photoelectric equation for maximum kinetic energy
interpret photoelectric graphs and distinguish frequency effects on electron energy from intensity effects on current

Covered syllabus points

22.2.1—Photoelectrons may be emitted from a metal surface when it is illuminated by 22.2.2—The terms threshold frequency and threshold wavelength 22.2.3—Photoelectric emission in terms of photon energy and work function energy 22.2.4—Hf = Φ + 1/2 mvmax 2 22.2.5—Why the maximum kinetic energy of photoelectrons is independent of

[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: 3]

(a)

Light of a single wavelength is incident on the surface of different metals. The work function energy of the metals is given in Table 7.1.

Table 7.1

[ 3 ]

(i)

Explain the term threshold wavelength.

[ 1 ]

(ii)

For the metals in Table 7.1, calculate the value of the largest threshold wavelength.
threshold wavelength = m

[ 2 ]

$\text { work function }=2.26 \times 1.60 \times 10^{-19}(\mathrm{~J})$ $E=h c / \lambda$ so
$\left(2.26 \times 1.60 \times 10^{-19}\right)=\left(6.63 \times 10^{-34} \times 3.00 \times 10^{8}\right) / \lambda_{0}$ $\lambda_{0}=5.50 \times 10^{-7} \mathrm{~m}$

[Maximum number: 6]

(a)

When the surface of a metal plate is illuminated with electromagnetic radiation, electrons are sometimes emitted from the metal.

[ 4 ]

(i)

State the name of this phenomenon.

[ 1 ]

(ii)

It is observed that this phenomenon occurs only when the frequency of the electromagnetic radiation is greater than a certain minimum value, regardless of the intensity of the radiation.

Explain how this observation provides evidence for the existence of photons.

[ 3 ]

(b)

Fig. 8.1 shows the variation of the maximum kinetic energy of the emitted electrons in (b) with the frequency of the incident radiation.

Fig. 8.1

State the name of the quantity represented by:

[ 2 ]

(i)

the gradient of the line in Fig. 8.1

[ 1 ]

(ii)

the y-intercept of the extrapolated line in Fig. 8.1.

[ 1 ]

[Maximum number: 2]

State what is meant by:

the photoelectric effect

[Maximum number: 3]

When the surface of a metal plate is illuminated with electromagnetic radiation, electrons are sometimes emitted from the metal.

[Maximum number: 3]

The work function energy of a clean metal surface is $5.5 \times 10^{-19} \mathrm{~J}$ .

Electromagnetic radiation of wavelength 280 nm is incident on the metal surface. The metal is in a vacuum.

Calculate:
1. the photon energy
photon energy =
2. the maximum speed $v_{\text {MAX }}$ of the electrons emitted from the surface.

v_{\mathrm{MAX}}=

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

1. photon energy $=h c / \lambda$ $\begin{aligned} =\left(6.63 \times 10^{-34} \times 3.00 \times 10^{8}\right) /\left(280 \times 10^{-9}\right) =7.1 \times 10^{-19} \mathrm{~J} \end{aligned}$
2. electron energy $=(7.1-5.5) \times 10^{-19} \mathrm{~J}$ $1 / 2 \times 9.11 \times 10^{-31} \times v^{2}=(7.1-5.5) \times 10^{-19}$ $v=5.9 \times 10^{5} \mathrm{~m} \mathrm{~s}^{-1}$

[Maximum number: 3]

Electromagnetic radiation of a single constant frequency is incident on a metal surface. This causes an electron to be emitted.

Explain why the maximum kinetic energy of the electron is independent of the intensity of the incident radiation.

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Covered syllabus points

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Question 2

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Question 3

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