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

 

`K_max = 1/2mv_max^2 = eV_0 ((V_max = \text { maximum velocity of emitted photoelectron} ),(V_0 = \text { Stopping potential}))`

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, `hv = K_max +phi` Einstein's photoelectric equation

K_max = eV₀.