Question

The kinetic energy of an electron is the same as that of a photon of wavelength 3100

a.U. What is the wave length of this electron

Answer 1

The wavelength of a 2 eV photon is given by:

l = h c / Eph = 6.625 x 10-34 x 3 x 108/(1.6 x 10-19 x 2) = 621 nm.

where the photon energy was multiplied with the electronic charge to convert the energy in Joule rather than electron Volt.

The kinetic energy of an electron is related to its momentum by:

T = p2/2m

from which we find the momentum, p:

p = (2mT)1/2 = (2 x 9.1 x 10-31 x 1.6 x 10-19 x 2)1/2 = 7.63 x 10-25 kg m/s.

The de Broglie wavelength of the electron is then obtained from:

l = h/p = 6.625 x 10-34 / 7.63 x 10-25 = 0.87 nm