Question

An electron is accelerated to a speed where its total energy is 138 times larger than its rest energy. How many times is the kinetic energy of the electron larger than its rest energy?

Answer 1

Answer:

The kinetic energy would also be increased by 138 times.

Explanation:

Rest mass of an electron

$mc^2= 9.11\times 10^{-31}\times (3\times 10^8)^2\\\Rightarrow mc^2=8.199\times 10^{-14}$

Convert to MeV

$8.199\times 10^{-14}\times 6.242\times 10^{12}=0.511 MeV$

Total energy of the electron = 138×mc²  =70.518 MeV

Kinetic energy of an electron

E = mc²

According to the question

E = 138×0.511 MeV = 70.518 MeV

So, the kinetic energy would also be increased by 138 times.