Question

Work function of aluminium is 4.2 eV. If two photons, each of energy 2.5 eV, are incidents on its surface, will the emission of electrons take place? Justify.

Answer 1

Hint: This phenomena in which electrons escape out from the metal by hitting photons is known as photoelectric effect. It is one photon one electron concept based phenomena in which simultaneously the energy of the photon is used to escape the electron from metal and due to more energy provides kinetic energy to the electron.

Complete step by step solution:
Photons are the packets of moving energy in a form of light. When these interact with some metal surfaces it shows a phenomena called photoelectric effect. In which energy of photon is absorbed by metal simultaneously and electrons are emitted and some velocity is given to the electron. But there are some conditions of the photoelectric effect and one of them is work function. Work function is the least energy that is required to escape out the electron from any metal.

So, it is given that Work function of aluminium is 4.2 eV, and two photons, each of energy 2.5 eV are incidents on its surface. In this case, by total energy it can achieve the work function limit. But ejection of electrons is a simultaneous process and for escaping out of an electron we have to hit those photons in the same place at the same time and it seems to be impossible. So, there will not be an emission of electrons.

Note: We can learn that if the energy of photons hitting the metal surface must be greater than or equal to the work function to eject out or give some velocity to the electron. If there is not sufficient energy in a photon, the energy of two photons can’t be added at the moment, when the photons collide with the electron. Thus, all the energy of the photon will be dissipated or wasted as the energy generated is not sufficient to knock it out.