The speed of a fast moving electron, having total energy of 2 MeV, is nearly:

Question

Question

This question was previously asked in

AAI ATC Junior Executive 2018 Official Paper (Shift 1)

Answer 1

Concept:

A relativistic particle is a particle that moves with a relativistic speed; that is, a speed comparable to the speed of light.

Here the speed is comparable to the light, hence we should follow the relativistic approach

In the relativistic approach, the total energy is given by:

E = rest energy + K.E

Where

Calculation:

Given particle is electron, the mass of electron is m = 9.11 × 10^-31 kg, c = 3 × 10⁸ m/s

1 eV = 1.602 × 10-19 J

E = 2 MeV = 2 × 10⁶ × 1.602 × 10^-19 J = 3.204 × 10^-13 J

Now from the above formula:

v = 0.97 c

If we take directly K.E = 0.5 mv²

Which is way more than the speed of light, so not possible.

Note: Mass of proton = 1.67 × 10^-27 kg, Mass of Neutron = 1.67 × 10^-27kg;