Question

An electron and a photon each have a wavelength of 1.00 nm. Find

(a) their momenta,

(b) the energy of the photon, and

(c) the kinetic energy of electron.

Answer 1

(a) According to De Broglie hypothesis,
$p=\frac{h}{\lambda }$

$=\frac{6.62\ast {10}^{-34}}{1\ast {10}^{-9}}=6.62\ast {10}^{-25}kg-m/s$

The value remains the same irrespective of electron or photon.

(b) $\lambda =1nm$

$E=hc/\lambda e=1243.1eV=1.243keV$

(c) Momentum, $p=h/\lambda =6.63\times {10}^{-25}kgm/s$

K.E. of electron is $P^2/2m=2.415\times {10}^{-19}J=1.51eV$