Question

The force acting on the electron in hydrogen atom (Bohr's theory) is related to the principal quantum number n as

• A. \(n^4\)
• B. \(n^{-4}\)
• C. \(n^2\)
• D. \(n^{-2}\)

Hint:

Force is k e^2 / r^2 and r is proportional to n squared.

Answer 1

The Correct Option is B

Step 1: Use centripetal force:
$F = \dfrac{mv^2}{r}$ with $v\propto\dfrac1n$ and $r\propto n^2$.

Step 2: Combine:
$F\propto\dfrac{1/n^2}{n^2} = \dfrac1{n^4}$.

Step 3: Result:
$F\propto n^{-4}$, option (B).

Final Answer:
The force is proportional to n^-4. \[ \boxed{\text{(B) }n^{-4}} \]