Question

A certain particle of mass m has momentum of magnitude mc. What is $\beta$ ?

Solution

Verified

Answered 6 months ago

Step 1

1 of 2

$\textbf{(a)}$ In a relativistic limit the momentum for a particle is given by:

\begin{align} p=\gamma mv\end{align}

the Lorentz factor in terms of the speed parameter is given by:

\gamma=\dfrac{1}{\sqrt{1-\beta^2}}

substitute into (1) to get (note that $v=\beta c$ ):

p=\dfrac{m\beta c}{\sqrt{1-\beta^2}}

for a particle with momentum of $p=mc$ , we get:

\dfrac{m\beta c}{\sqrt{1-\beta^2}}=mc

\beta=\sqrt{1-\beta^2}

\beta=\dfrac{1}{\sqrt{2}}=0.707

$\boxed{\beta=0.707}$

Create an account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

6th Edition•ISBN: 9780130606204 (3 more)Giancoli

4,384 solutions

8th Edition•ISBN: 9780471758013 (2 more)Halliday, Resnick, Walker

9,466 solutions

10th Edition•ISBN: 9781118230718 (5 more)David Halliday, Jearl Walker, Robert Resnick

8,949 solutions

11th Edition•ISBN: 9781119306856 (3 more)David Halliday, Jearl Walker, Robert Resnick

9,566 solutions