Question

an electron whose rest mass is 9.11 multiply 10^-31 is moving with 0.8 c where c is speed of light. find its kinetic energy

Answer 1

Given: The rest mass of the electron (m₀) = 9.11 × 10 ⁻³¹ kg

Velocity of the electron (v) = 0.8 c

Here, velocity of light (c) = 3.0 ×10⁸ m/s

Concept: Relation between relativistic mass (m) and rest mass (m₀) is given as

$m = \frac{m_{o}}{\sqrt{1 - (\frac{v}{c})^{2}}}\\ m = \frac{m_{o}}{0.6}$

Now, we shall find the kinetic energy (KE) of the electron.

$KE = \frac{1}{2} mv^{2} \\ KE = \frac{1}{2} \frac{m_{o}}{0.6} (0.8c)^{2}$

Or, KE = ( 8/15)m₀×c²

or, KE = ( 8/15)×(9.11 × 10 ⁻³¹ kg )×(3.0 ×10⁸ m/s)²

or, KE = 4.4 × 10 ⁻ ¹⁴J

Hence, the kinetic energy of the electron will be 4.4 × 10 ⁻ ¹⁴J

Answer 2

The rest mass of the electron (m₀) = 9.11 × 10 ⁻³¹ kg

Velocity of the electron (v) = 0.8 c

Here, velocity of light (c) = 3.0 ×10⁸ m/s

Concept: Relation between relativistic mass (m) and rest mass (m₀) is given as

$$\begin{lgathered}m = \frac{m_{o}}{\sqrt{1 - (\frac{v}{c})^{2}}}\\ m = \frac{m_{o}}{0.6}\end{lgathered}$$

Now, we shall find the kinetic energy (KE) of the electron.

$$\begin{lgathered}KE = \frac{1}{2} mv^{2} \\ KE = \frac{1}{2} \frac{m_{o}}{0.6} (0.8c)^{2}\end{lgathered}$$

Or, KE = ( 8/15)m₀×c²

or, KE = ( 8/15)×(9.11 × 10 ⁻³¹ kg )×(3.0 ×10⁸ m/s)²

or, KE = 4.4 × 10 ⁻ ¹⁴J

Hence, the kinetic energy of the electron will be 4.4 × 10 ⁻ ¹⁴J