Question

Work function of a metal is the:
A. Energy required by an electron to get absorbed in the metal surface
B. Minimum energy required by an electron to escape from the metal surface
C. Energy required by an electron to be retained in the metal surface
D. Maximum energy required by an electron to escape from the metal surface

Answer 1

Hint: The work function in solid-state physics is the minimal thermodynamic work required to extract an electron from a solid to a point directly beyond the solid surface in the vacuum.

Complete step by step answer:
Work function is a type of energy which measures how closely a given metal retains its electrons, that is how much lower the energy of the electron is in the metal when it is present.
Work functions depend on a surface’s structure and chemical composition. Different crystallographic surfaces of the same metal or compound, for instance may have varying work functions. A surface’s chemical changes may have much greater implications.
Its unit is given by electron volt or $eV$.
The work function is the difference between the energy in the conduction band and the vacuum of the most excited electrons. It is the energy needed to expel an electron from the conduction band to the outside of the metal.
Mathematically work function is given by-
$h\upsilon = W + E$, where $h = $ Planck’s constant, $\upsilon = $frequency of the incident photon, $W = $ work function, $E = $maximum possible kinetic energy.
If the photon does not overcome the work function, no energy will be emitted.

So, the correct answer is “Option B”.

Note:
The behaviour of electrons in metal varies with temperature and is primarily expressed by the work function of electrons. Also the work function depends on the kinetic energy of the electrons. The kinetic energy of the electron expelled is equal to the working function of the metal derived from the launched photon’s energy.
The energy of the photon must be greater than the working function in order for photoelectric effect to occur. As the incident light’s wavelength reduces but is smaller than the cut-off wavelength, the photo electron’s overall kinetic energy increases.