Question

For an electron passing through potential difference V, show that its
wavelength is; 

λ = 12.26/√V A°.

Answer 1

The wavelength of an electron with kinetic energy E is given by
λ = h/√2mE ............................ (1)

On the other hand, the kinetic energy of an electron passing through potential difference'V' is,
1/2 mv²  = eV

Hence, E=eV Thus, replacing E with eV in equation (1), we get,
λ =h √2meV ............................ (2)

Substituting values of,
h = 6.63 x 10³⁴ kg-m/s
m = 9. 7 x 10³¹ kg
e = 1.6 x 10¹⁹coulomb

in equation (2), we get,
λ= 1.226 x 10^-19/√V metre
λ = 72.26 /√V A°