Answer to Question #124773 in Atomic and Nuclear Physics for Albert Eshun

Question

The position of a certain electron is determined at a certain time with an uncertainty of
10-10 m. Find the uncertainty in the electron's momentum. (2 marks)

Answer 1

According to the uncertainty principle, $\sigma_x\sigma_p \ge \dfrac{\hbar}{2}.$ Therefore, $\sigma_p \ge \dfrac{\hbar}{2} \cdot\dfrac{1}{\sigma_x} = \dfrac{1.05\cdot10^{-34}}{2}\cdot\dfrac{1}{10^{-10}} = 5.25\cdot10^{-25}\,\mathrm{kg\, m/s}.$