Chapter 39, Problem 1OQ

(i)

To determine

The upper limit for the speed of an electron.

Answer to Problem 1OQ

Option (a) yes, the speed of light $c$.

Explanation of Solution

Unlike momentum and energy, speed has an upper limit that is the speed of light, $c=2.99\times {10}^8\text{m}/\text{s}$.

Therefore, the upper limit for the speed of an electron is $c$.

(ii)

To determine

Whether the magnitude of an electron’s momentum has an upper limit.

Answer to Problem 1OQ

Option (c) no

Explanation of Solution

The upper limit for speed is $c$ and when an electron reaches that limit, the factor $\gamma$ tends to infinity. The formula for momentum is $p=\gamma mv$. By substituting the $\gamma =\infty$, the momentum of electron also tends to infinity.

Therefore, the magnitude of an electron’s momentum has no upper limit.

(iii)

To determine

Whether the kinetic energy of electron has an upper limit.

Answer to Problem 1OQ

Option (d) no

Explanation of Solution

The upper limit for speed is $c$ and when an electron reaches that limit, the factor $\gamma$ tends to infinity. The formula for kinetic energy is $K=\left(\gamma -1\right)m{c}^2$. By substituting the $\gamma =\infty$, the kinetic energy of electron also tends to infinity.

Therefore, the kinetic energy of electron has no upper limit.