Question

Derive de-Broglie’s equation. What is its significance?

Answer 1

According to the Einstein mass energy equivalence,
 E = mc²  --------eq(i) 
where, c is the velocity of the light and m is the mass. 

According to the Planck, photon of the light having the Energy E is associated with the wave of the Frequency ν as ⇒
 E = hν  --------eq(ii)

From eq(i) and eq(ii), 
 mc² = hν

Now,  we know, 
 c = ν (or f ) × λ 
where, λ is the wavelength. 
∴ ν = c/λ

Thus,
mc² =  hc/λ
λ = hc/mc²
λ = h/mc 

Now, this equation is only valid for the Photons. 
Therefore, Chemist, de-Broglie suggested that if we substitute the velocity of the Particles in place of the velocity of the light, then this equation can be valid for the Particles too. 

  ∴ λ = h/mu
Where, u is the velocity of the Particles. 

This Proved relation is also known as the de-Broglie Equation.

This equation can also be written as λ = h/p
where, p is the momentum. 

Hope it helps.

Answer 2

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