Question

Find the mass, the kinetic energy and the momentum of an electron moving at 0.8c.

Answer 1

We know,
Rest mass of electron, m₀ = 9.1 × 10⁻³¹ kg
Velocity of electron, v = 0.8 c

(a) Mass of electron is given by

\[m = \frac{m_0}{\sqrt{1 - v^2 / c^2}}\]

\[\Rightarrow m = \frac{9 . 1 \times {10}^{- 31}}{\sqrt{1 - 0 . 64 c^2 / c^2}} = \frac{9 . 1 \times {10}^{- 31}}{0 . 6}\]

\[ \Rightarrow m = 15 . 16 \times {10}^{- 31} kg \approx 15 . 2 \times {10}^{- 31} kg\]

(b) Kinetic energy of electron = mc² − m₀c²

\[KE = \left( m - m_0 \right) c^2 \]
\[ = \left( 15 . 2 - 9 . 1 \right) \times {10}^{- 31} \times 9 \times {10}^{16} \]
\[ = 5 . 5 \times {10}^{- 14} J\]

(c) Momentum of electron, p = mv

\[p = 15 . 2 \times {10}^{- 31} \times 0 . 8 \times 3 \times {10}^8 \]
\[ = 3 . 65 \times {10}^{22}\text{ kgm/s}\]