Questions on the Photoelectric Effect

Q1.

(a) One quantity in the photoelectric equation is a characteristic property of the metal that emits photoelectrons. Name and define this quantity.

The name of the quantity is the work function. It is the minimum energy required to remove an electron from the surface of a metal.

Note that you must include the word 'minimum' and this minimum energy applies to electrons on the surface of the metal - where the least pull is experienced. Deeper ones would require more eergy to release them. Both bold words are needed for the mark.

(2 marks)

(b) A metal is illuminated with monochromatic light. Explain why the kinetic energy of the photoelectrons emitted has a range of values up to a certain maximum.

Each of the incident photons will have the same energy because the light is monochromatic and the energy of each photon is given by the equations E = hf. If an incident photon is absorbed by an electron it will transfer all its energy to that electron. Some of that energy will be used to overcome the pull of the metal stucture on the electron. The rest of the energy will become kinetic energy of the electron. If the electron is at the surface it will not need as much energy to escape from the metal as one deeper within the structure. It will only need the work fundction of the metal to escape from the surface. Its kinetic energy wil therefore be a large amount compared to an electron below the surface that has to do work in order to reach the surface before leaving the surface and losing the work function quantity of energy. So the maximum energy a photoelectron can have is that given to it by the photon, less the work function. Electrons coming from deeper inside the metal will be emitted with less kinetic energy than those that were already at the surface.

Main points:

• incident photon has fixed energy because the source is monochromatic
• photon loses all its energy in to a single electron
• electron loses various amounts of energy in order to reach the surface of metal
• electron transfers 'work function' energy to escape from the surface
• electrons have a maximum kinetic energy = (photon energy) − work function

(3 marks max)

(c) A gold surface is illuminated with monochromatic ultraviolet light of frequency 1.8 × 10¹⁵ Hz. The maximum kinetic energy of the emitted photoelectrons is 4.2 × 10^–19 J. Calculate, for gold:

(i) the work function, in J,

hf = Φ + E_K(max)

Φ =hf - E_K(max)

Φ = (6.63 x 10^-34 x 1.8 × 10¹⁵) - 4.2 × 10^–19

Φ = 7.73 x 10^-19

Φ = 7.7 x 10^-19 J

(ii) the threshold frequency.

The threshold frequency will be the frequency of a photon that just has enough energy to overcome the work function - but no more. Therefore the electron will have no kineic energy.

hf₀ = Φ

f₀ = Φ/h

f₀ = 7.73 x 10^-19/ (6.63 x 10^-34 )

f₀ = 1.2 x 10 ¹⁵ Hz

(5 marks)

(Total 10 marks)