# Photoelectric effect

1887 – Heinrich Hertz discovered when light of a certain frequency on a metallic surface, electrons are emitted

If the light does not have a high enough frequency, no electrons are emitted no matter the intensity.

• The electrons were emitted immediately
• Increasing the intensity of the light increased the number of emitted electrons but not their maximum of KE
• Low frequency did not cause the ejection of electrons, no matter what the intensity of the light
• A weak high frequency will eject only a few electrons, but their maximum KE are greater than those for intense light of lower frequencies

### Particle model

The energy of the ejected electrons was:

• Proportional to the frequency of the illuminating light
• Independent of the intensity of the light

Light therefore acted as a particle, and does not act as a wave in this instance.

If it were a wave, the energy of the electrons would depend on the amplitude/intensity, not the frequency.

### Work function

W = the minimum amount of energy required to release an electron from a metal.

W = hfo

Where fo is the minimum frequency needed to eject electrons, h = Planck’s constant

EKE max = 0.5 mv2 = hf – W

The KE of the electron is equal to the energy of the photon minus the amount of energy needed to remove it from the atom

### Stopping voltage

Light on the negative plate (cathode)
The ejected electrons will move towards the positive plate.

The energy that it gains as it moves across a field of potential difference is given by:

E = qv = eV

That is, the energy that an electron gains across an electric field of a pd of 1 V is one eV.

Light on the positive plate (anode)

• Electrons will be ejected from the +ve plate and towards the -ve plate
• However, the electric field will force the electrons back towards the +ve plate
• The voltage that just stops the fastest electrons from hitting the -ve plate is called the stopping voltage
• The energy that the field removes from the electron is equal to their KE

eVo = KE = hf – W

Where e = charge on electron; Vo = stopping voltage