Purchase Solution

Relativistic Kinetic Energy and Momentum

Not what you're looking for?

Ask Custom Question

An electron and a proton are each accelerated through a potential difference of 10.0 million volts.

a) What is the kinetic energy of the electron? What is the kinetic energy of the proton?
b) Calculate the momentum (MeV/c) of the proton using classical equations.
c) Calculate the momentum (MeV/c) of the proton using relativistic equations.
d) Calculate the momentum (MeV/c) of the electron using classical equations.
e) Calculate the momentum (MeV/c) of the electron using relativistic equations.
f) Why is there a difference?

Purchase this Solution

Solution Summary

We calculate the relativistic kinetic energy and momentum of a proton and an electron, each accelerated through 10 million volts.

Solution Preview

a) The kinetic energies of both the proton and the electron are 10.0 MeV since they each have a charge of +/-e.

b) The classical momentum P_c of the proton is given by

P_c = m_p v_p
= (m_p c^2)(v_p/c)/c
= (m_p c^2) beta_p/c
= 938 Mev/c * beta_p.

Now since gamma_p = 1/sqrt(1 - beta_p^2), we have

gamma_p^2 = 1/(1 - beta_p^2)
1/gamma_p^2 = 1 - beta_p^2
1 - 1/gamma_p^2 = beta_p^2


beta_p = sqrt(1 - 1/gamma_p^2).

We can compute gamma_p from the equation

K_p = (gamma_p - 1)(m_p c^2),


gamma_p = 1 ...

Purchase this Solution

Free BrainMass Quizzes
Basic Physics

This quiz will test your knowledge about basic Physics.

Intro to the Physics Waves

Some short-answer questions involving the basic vocabulary of string, sound, and water waves.

The Moon

Test your knowledge of moon phases and movement.

Introduction to Nanotechnology/Nanomaterials

This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.

Classical Mechanics

This quiz is designed to test and improve your knowledge on Classical Mechanics.