Question

What is the relation between the orbital radius and the electron velocity?

Options

• \[r=\frac{e^2}{4\pi\epsilon_0mv^2}\]

• \[r=\frac{e^2}{8\pi\epsilon_0mv^2}\]

• \[r=\frac{e^2}{4\pi\epsilon_0mv}\]

• \[r=\frac{4\pi\epsilon_0mv^2}{e^2}\]

Answer 1

Equating the electrostatic and centripetal forces gives the radius–velocity relation. Solving that equality for the orbital radius yields \[r=\frac{e^2}{4\pi\epsilon_0mv^2}\].