Question

An electron rotates in a circle around a nucleus having positive charge Ze. Correct relation between total energy (E) of electron to its potential energy (U) is:

• A. E = 2U
• B. 2E = 3U
• C. E = U
• D. 2E = U

Answer 1

Answer: (D)

2E = U

Answer 2

The electrostatic force between the electron and nucleus is given by:

$F = \frac{K(Ze)(e)}{r^2} = \frac{mv^2}{r}$

Kinetic energy (KE) of the electron is:

$\text{KE} = \frac{1}{2}mv^2 = \frac{1}{2} \frac{K(Ze)(e)}{r}$

Potential energy (PE) is given by:

$\text{PE} = -\frac{K(Ze)(e)}{r}$

Total energy (TE) is:

$\text{TE} = \text{KE} + \text{PE} = \frac{K(Ze)(e)}{2r} + \left( -\frac{K(Ze)(e)}{r} \right) = -\frac{K(Ze)(e)}{2r}$

Thus, the relationship between total energy and potential energy is:

$2 \times \text{TE} = \text{PE}$

Therefore, $2E = U$, which corresponds to Option (4).