Photoelectric equation

When working with the photoelectric effect, we can link together:

• the incident photon energy
• the work function of the metal
• the maximum kinetic energy of the emitted electrons

Linking them all together is the photoelectric equation!

E_\text{photon}=\phi+E_\text{kmax}

Where:

• E_\text{photon} is the energy of the incident photon (in joules)
• \phi is the work function of the metal (in joules)
• E_\text{kmax} is the maximum kinetic energy of the emitted electrons (in joules). They may have less kinetic energy than this, but they can’t have more. See threshold frequency for an explanation on why.

Calculating from frequency

If we don’t have the photon energy but instead have the frequency of the incident light, we can calculate the energy of the photon using the equation:

E_\text{photon} = hf

And then just substitute that into the photoelectric equation. In one single equation, we can replace E_\text{photon} with hf to get:

hf = \phi + E_\text{kmax}

Calculating from wavelength

To calculate from the wavelength, we need to use three equations…

• First, convert to frequency:
  • The speed of any EM wave is 3.00\times10^8ms^{-1}
  • So we can calculate the frequency of the incident light using f=\frac{3.00\times10^8}{\lambda} (\lambda is the wavelength).
• Then calculate the energy of the photon using E_\text{photon} = hf.
• We finally substitute that into the photoelectric equation to get our final equation.

In one single equation, we get:

\frac{hc}{\lambda} = \phi + E_\text{kmax}

c is the speed of light: 3.00\times10^8ms^{-1}.