Question

For a particular experiment at the SLAC National Accelerator Laboratory, electrons are each accelerated to an energy of exactly 50 GeV. Note: You may assume that the rest mass of an electron is exactly 0.5 MeV/c^2 for this problem.
Required:
a. What is the velocity of each electron?
b.The accelerator is 3km long. At the velocity in (a), how much time, as measured by the moving electrons, does it take the electrons to travel the length of the accelerator.
c. How long does the accelerator look from the perspective of the electrons?

Answer 1

Answer:

a) 0.99999 e

b) 1*10^-5 s

c) 3*10^-2 m

Explanation:

Given data:

Electron energy : 50 GeV

assuming the rest mass of an electron = 0.5 MeV/c^2

A) Determine the velocity of each electron

velocity of each electron ( v ) ≈ 0.999 e

B) How much time does it take the electrons to travel the length of the accelerator given that the accelerator = 3km long

Lo = 3 * 10^3 m

T = (3 * 10^3 )/ (0.999 * 3 * 10^8)

   = 1 * 10 ^-5

C) How long does the accelerator look form the perspective of the electrons

L = Lo / r  = Lo $\sqrt{1 - \frac{r^2}{v^2} }$

hence L = 3 * 10^-2 m