Question

State clearly how photoelectric equation is obtained using the photon pictu.re of electromagnetic radiation.

Answer 1

Einstein’s photoelectric equation,

hv = K_max + Φ

Where

h = Planck’s constant

v = frequency

 

${\displaystyle K_{max}=\frac{1}{2}m{v}_{max}^2=e{V}_0\left(\begin{array}{c}{V}_{max}=\text{maximum velocity of emitted photoelectron}\\ V_0=\text{Stopping potential}\end{array}\right)}$

Φ = Work function

According to Planck’s quantum theory, light radiations consist of small packets of energy. Einstein postulated that a photon of energy hv is absorbed by the electron of the metal surface, then the energy equal to Φ is used to liberate electron from the surface and rest of the energy hv − Φbecomes the kinetic energy of the electron.

∴ Energy of photon is,

E = hv

Where, h = Planck’s constant

v = frequency of light

The minimum energy required by the electron of a material to escape out of it, is work function ‘Φ’.

The additional energy acquired by the electron appears as the maximum kinetic energy ‘K_max’ of the electron.

i.e.,

K_max = hv − Φ

or, ${\displaystyle hv=K_{max}+\varphi }$ Einstein's photoelectric equation

K_max = eV₀.