# What is important to know to be able to calculate the number of photoelectrons produced by a beam of light?

Mar 31, 2016

Intensity of the beam of light (possibly also the cross sectional area of the beam), frequency of the light and work function of the metal's surface.

#### Explanation:

In order to calculate the number of photoelectons we would need to know whether the photons in the light had sufficient energy to release electrons from the metal and if they did then how many would be released. Photons react one to one with electrons, therefore the number of photons capable of releasing electrons will correspond exactly with the number of electrons released.

There is a minimum energy required to release electrons from a metal, it is called the work function (symbol φ). Photons must have energy greater than this to release electrons.

In order to calculate the number of photons in a beam of light we can use the intensity to calculate the total energy arriving per unit time (per unit area) in the beam and then divide that by the energy of each photon.

The total energy delivered by a beam of light in one second would be calculated as follows:
$E = I \cdot A \cdot 1$
Where I is the intensity and A is the cross sectional area of the beam.

Photon energy is related to frequency by this equation :
${E}_{p} = h f$

Total number of photons arriving at the metal in the beam every second would be given by this:
$n = \frac{E}{E} _ p$

The above calculations are very straightforward for sources of monochromatic light, i.e. light with only one colour which means it only has one frequency present. But most sources of light have multiple frequencies. In that case the calculations would need to be repeated for each frequency of light that has photons with energy above the work function.