Question

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

• A. \(\frac{e^2}{2r^2}\)
• B. \(\frac{e^2}{r}\)
• C. \(\frac{e^2}{2r}\)
• D. \(\frac{e^2}{r^2}\)

Hint:

Set the Coulomb force equal to the centripetal force.

Answer 1

The Correct Option is C

Step 1: Use total energy
Potential energy is $-\frac{ke^2}{r}$ and total energy is $-\frac{ke^2}{2r}$. Since $E=U+K$, $K=E-U=\frac{ke^2}{2r}$. Option (C).

Final Answer:
Option (C). \[ \boxed{\text{(C)}} \]