An electron is confined to a box with a dimension of 20 $\mu$m.If we have done our best to have the electron be at rest,within what range is its velocity likely to be found?
A)$\pm$0.2 m/s
B)$\pm$1.2 m/s
C)$\pm$5.8 m/s
D)$\pm$0.9 m/s

Question

Quizplus · Accepted Answer

The uncertainty in velocity of an electron in a 1D box is given by Δv = h/2mΔx, where h is the Planck's constant, m is the mass of the electron, and Δx is the size of the box. Plugging in the given values, we get Δv = (6.626x10^-34 J.s)/(2x9.109x10^-31 kg)x20x10^-6 m = 5.77x10^5 m/s. Therefore, the range of velocity likely to be found is F1F1F1S1±5.77x10^5 m/s, which is closest to F1F1F1S1±F1F1F105.8 m/s (option C).

An Electron Is Confined to a Box with a Dimension μ\muμ

An Electron Is Confined to a Box with a Dimension $\mu$