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2.5 Use the de Broglie relation λ=h/p to find the wavelength of electrons with kinetic energy...

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.

Expert Solution

(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.

genius_generous answered 1 year ago

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