Question

The potential energy of the orbital electron in the ground state of hydrogen atom is -E. Its kinetic energy is

• A. E/4
• B. E/2
• C. 2E
• D. 4E

Answer 1

Answer: (B)

potential energy of electron in ground state of a hydrogen atom is given by,
$U=-\frac{k{e}^2}{r}=\frac{-e^2}{4\pi {\epsilon }_{0r}}=-E.....(i)$
kinetic energy of the orbital potential energy of electron in ground state of a hydrogen atom is given by,
$U=-\frac{k{e}^2}{r}=\frac{-e^2}{4\pi {\epsilon }_{0r}}=-E.....(i)$
kinetic energy of the orbital electron in the ground state of hydrogen atom is given by
$K=\frac{k{e}^2}{2r}=\frac{e^2}{8\pi {\epsilon }_{0}r}$
$=\frac{1}{2}\left[\frac{e^2}{4\pi {\epsilon }_{0}r}\right]=\frac{E}{2}$ [Using Eq(ii)]