Question

derive the relationship between wavelength and momentum of an electron in an atom​

Answer 1

Answer:

According to Einstein's Special Relativity applied on an electron,

E = Pc

where, E is the energy of the electron

p is it's momentum of the electron

and c is the speed of light

Now,

According to Max Plank

E = h f

where

f is the frequency of the electron

and h is the Planck's constant

So,

Pc = hf

Now, f = c/lambda

So,

Pc = hc/lambda

or,

P = h/lambda

And this is the relation between momentum of the electron and it's wavelength.

This was first proposed by the French scientist De-Broglie.

He further went onto earn the Nobel prize in physics to his name due to development in the theory of quantum mechanics.