Question

2.5 Use the de Broglie relation λ=h/p to find the wavelength of electrons with kinetic energy equal to 550 eV. Indicate if relativistic or classical calculations are required.

2.3 Determine the energy of an electron and a photon if each has momentum equal to 1.071 x 10-21 kgm/s. Provide answer with 4 significant figures.ual to 550 eV. Indicate if relativistic or classical calculations are required.

Answer 1

(2.5)

The rest mass energy of electron is 511 keV (kilo electron volts). Since the kinetic energy (550 eV= 0.550 keV) is much lesser than the rest mass energy of the electron, the electron is non-relativistic.

Non-relativistic kinetic energy is given by

The momentum is

The de Broglie wavelength of the electrons is

Substituting , , we get

(2.3)

The energy and momentum of a particle are related as

For photon m=0

Substituting values

The energy will be in joules, to convert it into electron-volts we divide it be the electronic charge e

For electron m=9.109x10^-31kg, the energy of electron is given by

Substituting , we get

Converting it into electron-volts by dividing with electronic charge

The total energy is greater than the rest mass energy (511 keV =0.511 MeV), so we cannot use non-relativistic calculation.