Question

The de Broglie wavelength of an electron accelerated through a potential difference V is directly proportional to V^n then n must be equal to

Answer 1

The value of n is equal to -1.

The de-Broglie's wavelength of a electron is given by - λ = h/p = h/mv

Kinetic energy of the electron = K = 1/2 mv²

Relationship between momentum and kinetic energy - p = √(2Km)

Now , λ = h/√(2Km)

K = qV [kinetic energy gained when a charge q is accelerated through potential V]

λ = h/√(2qVm)

=> λ ∝ 1/V

=> λ ∝ V^-1

The value of n is -1 as debroglie wavelength is inversely proportional to the potential.