What is the minimum frequency of electromagnetic radiation needed for a photon to ionise an atom of sodium? ( An atom of sodium has an ionisation energy of 5.15 eV.)

First, let's define what the ionisation energy is. The ionisation energy is the minimum amount of energy required to remove an electron from the ground state of an atom. That means, if we give an electron in the sodium atom enough energy (using light or heat for example) we can actually cause it to be ejected completely from the atom.The question asks, what frequency of electromagnetic radiation (light) do we need to achieve this? We are told that an atom of sodium has an ionisation energy of 5.15 eV (electron volts - a unit of energy), and therefore to remove the electron using light, the photon must also have this amount of energy (or more!). We use the famous expression for the energy of a photon: E = hf where h is Planck's constant, f is the frequency of the photon and E is the energy. Rearranging the equation for the frequency gives: f = E/h. Now, subbing in the values: f = (5.15 x 1.6 x10^-19)/6.63x10^-34 gives the final answer of f = 1.24 x 10^15 Hz. It is important to remember to multiply the energy in eV by the electronic charge to convert it into Joules (so that our equation is all in SI units).(NB. This is a good question because it brings up a number of interesting concepts, such as the quantisation of light, photon absorption/ionisation which has a number of interesting applications that could be discussed with the student to give a deeper understanding and appreciation of the science and finally unit conversions from eV to Joules.)