Question

The kinetic energy of the electron in an orbit of radius $r$ in hydrogen atom is proportional to ($e$ = electronic charge)

• A. $\dfrac{e^2}{2r^2}$
• B. $\dfrac{e^2}{r^2}$
• C. $\dfrac{e^2}{2r}$
• D. $\dfrac{e^2}{4r}$

Hint:

The Coulomb force supplies the centripetal force, which gives kinetic energy proportional to 1 over r.

Answer 1

The Correct Option is C

Step 1: Approach
Use the virial relation between kinetic and potential energy.

Step 2: Relation
The potential energy of the electron is $U=-\dfrac{e^2}{r}$ (Gaussian-style). For an inverse-square force in a circular orbit, $KE=-\dfrac U2$.

Step 3: Result
$KE=\dfrac{e^2}{2r}$, proportional to $e^2/r$. Option (C) has this form.

Final Answer:
The kinetic energy equals e squared over 2r, which varies as one over r, option (C). \[ \boxed{\frac{e^2}{2r}} \]