The momentum of an electron is 1.75 times larger than the value computed non-relativistically. What is the speed of the electron

Speed of the electron is 2.46 x 10^8 m/s

Explanation:

momentum of the electron before relativistic effect =

where is the rest mass of the electron

V is the velocity of the electron.

under relativistic effect, the mass increases.

under relativistic effect, the new mass M will be

M =

where

c  is the speed of light = 3 x 10^8 m/s

V is the speed with which the electron travels.

The new momentum will therefore be

==>

It is stated that the relativistic momentum is 1.75 times the non-relativistic momentum. Equating, we have

1.75 =

the equation reduces to

1.75 =

square both sides of the equation, we have

3.0625 = 1/

3.0625 - 3.0625 = 1

2.0625 = 3.0625

= 0.67

β = 0.819

substitute for  

V/c = 0.819

V = c x 0.819

V = 3 x 10^8 x 0.819 = 2.46 x 10^8 m/s