Question

Derive the Dr Broglie wave equation for dual nature of light
De Broglie equation.
wave length=h/m frequency or wave length=h/p
in= wavelength
h = planck's constant
m=mass
v=velocita
p= momentum
​

Answer 1

Derivation of de-Broglie Equation

The wavelength of the wave associated with any material particle was calculated by analogy with photon.

In case of photon, if it is assumed to have wave character, its energy is given by

E = hv …(i)

(According to the Planck’s quantum theory)

Where nth frequency of the wave and ‘h’ is is Planck’s constant

If the photon is supposed to have particle character, its energy is given by

E = mc2 ….… (ii)

(according to Einstein’s equation)

where ‘m’ is the mass of photon, ‘c’ is the velocity of light.

By equating (i) and (ii)

hv = mc2

But v = c/λ

h c/λ = mc2

(or) λ = h /mc

The above equation is applicable to material particle if the mass and velocity of photon is replaced by the mass and velocity of material particle. Thus for any material particle like electron.

λ = h/mv or λ = where mv = p is the momentum of the particle.