Question 39.8: Linear Momentum of an Electron An electron, which has a mass......
Linear Momentum of an Electron
An electron, which has a mass of 9.11 \times 10^{-31} \mathrm{~kg}, moves with a speed of 0.750 c. Find the magnitude of its relativistic momentum and compare this value with the momentum calculated from the classical expression.
Conceptualize Imagine an electron moving with high speed. The electron carries momentum, but the magnitude of its momentum is not given by p=m u because the speed is relativistic.
Categorize We categorize this example as a substitution problem involving a relativistic equation.
Use Equation 39.19 with u=0.750 c to find the momentum:
\begin{aligned} p & =\frac{m_{e} u}{\sqrt{1-\frac{u^{2}}{c^{2}}}} \\ p & =\frac{\left(9.11 \times 10^{-31} \mathrm{~kg}\right)(0.750)\left(3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)}{\sqrt{1-\frac{(0.750 c)^{2}}{c^{2}}}} \\ & =3.10 \times 10^{-22} \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s} \end{aligned}
The classical expression (used incorrectly here) gives p_{\text {classical }}=m_{e} u=2.05 \times 10^{-22} \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}. Hence, the correct relativistic result is 50 \% greater than the classical result!