Question

What is the momentum of a photon having the same total energy as an electron with a kinetic energy of 100 keV?

Answer 1

The momentum of the photon is 1.707 x 10⁻²² kg.m/s

Step-by-step explanation:

Given;

kinetic of electron, K.E = 100 keV = 100,000 eV = 100,000 x 1.6 x 10⁻¹⁹ J = 1.6 x 10⁻¹⁴ J

Kinetic energy is given as;

K.E = ¹/₂mv²

where;

v is speed of the electron

`K.E = (1)/(2)mv^2\\\\mv^2 = 2K.E \\\\v^2 = (2K.E)/(m) \\\\v = \sqrt{(2K.E)/(m)} \\\\but \ momentum ,P = mv\\\\(v)m = (\sqrt{(2K.E)/(m)})m\\\\P_(photon) = (\sqrt{(2K.E)/(m_e)})m_e\\\\P_(photon) = (\sqrt{(2* 1.6* 10^(-14))/(9.11*10^(-31))})(9.11* 10^(-31))\\\\P_(photon) = 1.707 * 10^(-22) \ kg.m/s`

Therefore, the momentum of the photon is 1.707 x 10⁻²² kg.m/s