Question

Which expression results from adding the kinetic energy and electrostatic potential energy of the electron?

Options

• \[E=-\frac{e^2}{8\pi\epsilon_0r}-\frac{e^2}{4\pi\epsilon_0r}\]

• \[E=\frac{e^2}{8\pi\epsilon_0r}-\frac{e^2}{4\pi\epsilon_0r}\]

• \[E=\frac{e^2}{8\pi\epsilon_0r}+\frac{e^2}{4\pi\epsilon_0r}\]

• \[E=\frac{e^2}{4\pi\epsilon_0r}-\frac{e^2}{8\pi\epsilon_0r}\]

Answer 1

Substitute \[K=\frac{e^2}{8\pi\epsilon_0r}\] and \[U=-\frac{e^2}{4\pi\epsilon_0r}\] into \[E=K+U\]. The potential-energy term is subtracted because it is negative.