Question

3. An electron of rest energy 0.511 MeV (another way to say this is me- = 0.511 MeV/c^2 has a total energy of 5 MeV. Find its momentum in units of MeV/c. [Note: 1 eV 1.602 x10^-19 J]

Please show all work and be neat thank you.

Answer 1

apply the formula for relativistic momentum P = gamma mV

also relativistic energy KE = gamma mc^2 = 0.511 MeV

Total energy of a particle = γ*m_0*c^2

where m_0 is rest mass and γ =1/sqrt(1 - (v^2/c^2)), where v is the veolcity.

Rest energy of an object is m_0c^2.

Hence we have the equation

m_0c^2/sqrt(1 - (v^2/c^2)) = 0.511

1/sqrt(1 - (v^2/c^2)) = 0.511

sqrt(1 - v^2/c^)2 = 0.511

v^2/c^2 = 1-0.2611

V^2 = 0.7389 C^2

V = 0.859 C

so

Momentum P = mv

P = 9.11 e-31 * 0.859 * 3e8

P = 2.34 e -22 kgm/s

P = 2.34 e -22* 3e8/1.6 e-13

P = 0.438 MeV/c