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

The kinetic energy would also be increased by 138 times.

Step-by-step explanation:

Rest mass of an electron

`mc^2= 9.11* 10^(-31)* (3* 10^8)^2\\\Rightarrow mc^2=8.199* 10^(-14)`

Convert to MeV

`8.199* 10^(-14)* 6.242* 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.