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Electricity and Magnetism

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Escape Velocity of an Electron

EANDM-FBRVGY

An electron sits a distance $r=0.1 \: \text{nm}$ away from a proton.

What minimum velocity must the electron have in order for it to escape the electrostatic attraction of the proton?

[Useful parameters: $m_e = 9.1 \times {10}^{-31} \: \text{kg}$, $\epsilon_0 = 8.85 \times {10}^{-12} \frac {\text{Nm}^2}{C}$, and $e=1.6 \times {10}^{-19} \: \text C$]

A

$ v = 2.94 \times {10}^{3} \: \cfrac {\text m}{\text s}$

B

$ v = 5.05 \times {10}^{12} \: \cfrac {\text m}{\text s}$

C

$ v = 7.3 \times {10}^{4} \:\cfrac {\text m}{\text s}$

D

$ v = 3.0 \times {10}^{8} \: \cfrac {\text m}{\text s}$

E

$ v = 2.25 \times {10}^{6} \: \cfrac {\text m}{\text s}$