Photoelectric emission

Photoelectric emission is a process during which electrons are ejected from a metal surface by electromagnetic radiation, (e.g. ultraviolet).

If a clean, positively charged zinc plate is exposed to intense white light it will not discharge.

If a clean, negatively charged zinc plate is exposed to intense white light it will not discharge. No matter how intense the light the plate will not discharge, or whether the plate is positively or negatively charged, the plate will not discharge.

If a clean, positively charged zinc plate is exposed to an ultraviolet source it will not discharge.

However, if a clean, negatively charged zinc plate is exposed to an ultraviolet source it will discharge.

Only if the plate is negatively charged and the source has a high enough frequency will it discharge. The intensity of the source only affects how long it takes the plate to discharge.

The above points lead to the following conclusions:

• the plate is not being discharged by ionization (the positive one would also discharge)
• the total amount of energy from the source does not determine whether the plate discharges or not

This leads to the theory that the beams of light and ultraviolet are made up of individual units called photons.

Before an electron can be removed from a negatively charged plate each photon must have enough energy on its own to remove it.

Photons and energy

The energy of a photon depends on its frequency. Whether or not photoelectric emission takes place depends on the energy of the photon and the type of metal being tested.

The energy of a photon is directly proportional to its frequency. This gives rise to the equation E = hf

E is the energy of the photon

h is Planck's constant (6.63 × 10^-34 Js)

f is the frequency of the radiation.

The minimum frequency required to cause photoelectric emission is called the threshold frequency, f_o

The minimum energy required to remove an electron from a metal is called the work function, W

These are related by the equation W = h f_o

Different metals have different work functions. This means it is easier to remove electrons from some metals than others.

In turn, this means that the minimum frequency of photon needed to remove an electron from one metal can be lower than for another metal.

In short, the smaller the work function the lower the threshold frequency.

When an electron is ejected from a metal surface it will have kinetic energy. The amount of kinetic energy the electron will have depends on the difference between the energy of the photon and the work function of the metal.

The kinetic energy of the electron is equal to the energy of the photon minus the work function of the metal, E_k = E - W

This means that E_k= hf - h f_o

or

E_k= h(f - f_o)