Question

What is “Work function”?

Answer 1

Hint- Work function plays an important role in solid-state physics. It can be defined as the minimum energy that is required to remove an electron from its surface.

Complete step by step answer:
At room temperature in metals, the electrons in the outer orbit of an atom are loosely bound to the nucleus and these are called “free electrons”. These electrons cannot leave the metal surface on their own. As soon as an electron finds to leave the metal surface an appositive charge is developed on the metal surface. This positive charge pulls back a free-electron trying to leave the metal surface. This force forms a “surface barrier” for electrons. The free electrons can leave the metal surface only if external energy is supplied to it to overcome the surface barrier. The process of liberation of electrons from a metal surface is called “Electron emission”.
We need additional energy for the removal of an electron to overcome the surface barrier of the metal is called the work function of the metal. The minimum energy required for an electron to just escape from the metal surface is called “work function”. It is denoted by $\left({\varphi }_0\right)$.
There are certain factors that the work function depends on.
The work function depends on:
(i) the nature of the metal
(ii) the conditions of the metal surface.
It is measured by a unit of energy called electron volt (eV).
Therefore, from the above description we are able to understand the definition of the work function.

Additional information: Let us consider the work function of some metals

Metal	Work function	Metal	Work function
Cs	2.14	Al	4.28
K	2.30	Hg	4.49
Na	2.75	Cu	4.65
Ca	3.20	Ag	4.70
Mo	4.17	Ni	5.15
Pb	4.25	Pt	5.65

Let us now consider Einstein’s photoelectric equation.
When light is incident on metal, the photons having energy collide with electrons at the surface of the metal. During these collisions, the energy of the photon is completely transferred to the electron. If this energy is sufficient, the electrons are ejected out of the metal instantaneously. The minimum energy needed for the electron to come out of the metal surface is called work function. If the energy of the incident photon exceeds the work function, the electrons are emitted with a maximum kinetic energy.
$$\text{h}\nu \text{ = }{\varphi }_0+{\text{K}}_{\text{max}}$$
$${\text{K}}_{\text{max}}=\text{h}\nu -{\varphi }_0$$

Note: The dependency of the work function is on the configuration of the atoms. A material’s work function can be measured with kelvin probe (KP) and PES values. PES is the measurement of the absolute work function and KP gives the potential difference between the surface and the probe.