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BPhO R1 S1 · Section 1

Photons and the Photoelectric Effect

8 questions — reveal each final answer.

2012 · fPhotons and the Photoelectric Effect

A lithium surface, with work function energy $\mathrm{W}=3.7 \times 10^{-19} \mathrm{~J}$, is irradiated with photons of frequency $f=6.3 \times 10^{14} \mathrm{~Hz}$. The loss of photoelectrons from the surface causes the metal to acquire a positive potential, $V$. What will this potential be when the metal prevents the loss of further electrons? [4]

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Final result
  • The surface charges positively until its potential equals the maximum kinetic energy per unit charge, $V = K_{\text{max}}/e \approx 0.30 \, \mathrm{V}$, at which point even the fastest electrons can no longer escape.

Worked solutions are in the book.

2016 · jPhotons and the Photoelectric Effect

The maximum kinetic energy of photoelectrons ejected from a tungsten surface by monochromatic light of wavelength $248 \mathrm{~nm}$ is $8.60 \times 10^{-20} \mathrm{~J}$.

What is the value of the work function, $W$, of tungsten? [3]

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Final result
  • The work function is the photon energy $hf = 8.02 \times 10^{-19}\,\text{J}$ minus the measured maximum kinetic energy $8.60 \times 10^{-20}\,\text{J}$, giving $W = 7.16 \times 10^{-19}\,\text{J}$ ($\approx 4.5\,\text{eV}$).

Worked solutions are in the book.

2017 · jPhotons and the Photoelectric Effect

Calculate the number of photons emitted in a one nanosecond $\left(10^{-9} \mathrm{~s}\right)$ pulse of light from a $0.5 \mathrm{~mW}$ laser of wavelength $639 \mathrm{~nm}$. [3]

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Final result
  • The number of photons emitted in a one nanosecond pulse of light from the laser is $1.61 \times 10^6$.

Worked solutions are in the book.

2019 · pPhotons and the Photoelectric Effect

An electrically isolated copper sphere of radius $2 \mathrm{~mm}$ is illuminated by light of wavelength $150 \mathrm{~nm}$. Determine

(i) the maximum electric potential that the copper sphere can reach

(ii) the number of electrons lost reaching the maximum potential

(Work function of copper $=4.5 \mathrm{eV}$ ) [4]

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Final result
  • The sphere charges up until its potential cancels the electrons' maximum kinetic energy, giving $V_{\text{max}} = 3.79\, \text{V}$.

Worked solutions are in the book.

2021 · pPhotons and the Photoelectric Effect

In the photoelectric effect, an electrode is placed $0.10 \mathrm{~m}$ from a clean sodium surface, which has a work function of $2.28 \mathrm{eV}$. Light of wavelength $400 \mathrm{~nm}$ is shone on the surface and electrons are emitted.

(i) What is the shortest time it takes the most energetic photoelectrons to reach the electrode after illumination is started?

(ii) If a stopping potential of $0.50 \mathrm{~V}$ is applied between a plane electrode parallel to the photoemissive surface to produce a uniform electric field, what is now the shortest time it takes the most energetic photoelectrons to reach the electrode after illumination is started? [6]

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Final result
  • (i) With no field the electrons coast at constant speed, giving a crossing time of about $1.86 \times 10^{-7} \, \mathrm{s}$.

Worked solutions are in the book.

2022 · pPhotons and the Photoelectric Effect

One spectral line in hydrogen is caused by photons with an energy of $2.55 \mathrm{eV}$. The same line is redshifted in the spectrum of a distant galaxy by $5.4 \mathrm{~nm}$. Calculate

(i) the wavelength of the photon,

(ii) the speed of recession of the galaxy,

(iii) the distance to the galaxy.

How far away is the galaxy? Give your answer in megaparsecs (Mpc).

The Hubble constant, $H_{0}=70 \mathrm{~km} \mathrm{~s}^{-1} \mathrm{Mpc}^{-1}$. [3]

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Final result
  • The emitted wavelength is $\lambda = 487\,\mathrm{nm}$; the small redshift $\Delta\lambda = 5.4\,\mathrm{nm}$ gives a non-relativistic recession speed $v = c\,\Delta\lambda/\lambda \approx 3.3 \times 10^{3}\,\mathrm{km\,s^{-1}}$, and Hubble's law then places the galaxy at $d = v/H_0 \approx 47.5\,\mathrm{Mpc}$.

Worked solutions are in the book.

2023 · iPhotons and the Photoelectric Effect

An $8 \mathrm{~W}$ beam of light is shone on a surface at normal incidence. The surface reflects $50 \%$ of the incident light and absorbs the other $50 \%$.
(i) What is the average force exerted on the surface by the radiation?
Hint: the momentum of a photon, $p$, is given by its energy, $E$, divided by the speed of light, $c$. i.e. $p=\frac{E}{c}$
(ii) The average wavelength of the light is $600 \mathrm{~nm}$ and the beam covers an area of $12 \mathrm{~cm}^2$ when it is incident on the surface. Calculate the volume density of photons in the beam. [4]

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Final result
  • The key idea is that reflected photons reverse their momentum (factor of 2) while absorbed photons only deliver theirs (factor of 1), so the half-and-half beam gives a total force of $4 \times 10^{-8}\,\mathrm{N}$.

Worked solutions are in the book.

2025 · aPhotons and the Photoelectric Effect

An Einstein is a unit corresponding to a mole of photons. How long does it take for a $630\,\text{nm}$ and $0.50\,\text{mW}$ laser to release an Einstein? [3]

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Final result
  • It takes $t \approx 3.8\times10^{8}\,\text{s}$ (about 12 years) for such a low-power laser to emit an Einstein of photons.

Worked solutions are in the book.

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