Derive de-Broglie equation.

Explanation

De- Broglie combined the following two equations of energy of which one represents wave character (hu) and the other represents the particle nature `(mc^(2))` .
(i) Planck's quantum hypothesis : E = hv
(ii) Einsteins mass-energy relationship :
E = `mc^(2)`
From (i) and (ii)
hn` = mc^(2)`
`hc//lambda= mc^(2)`
`lambda = h //mc`
The equation represents the wavelength of photons whose momentum is given by mc (Photons have zero rest mass)
For a particle of matter mass m and moving with a velocity v, the equation can be written as
` lambda = h //mv `
This is valid only when the particle travels at speeds much less than the speed of light .