Question

If 'E' and 'L' denote the magnitude of total energy and angular momentum of revolving electron in \(n^{th}\) Bohr orbit then

• A. \(E\propto L\)
• B. \(E\propto L^{-1}\)
• C. \(E\propto L^{-2}\)
• D. \(E\propto L^2\)

Hint:

|E| goes as 1/n^2 and L goes as n.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In Bohr's model, the total energy in the \(n\)th orbit is \(E=-\dfrac{13.6}{n^2}\) eV, so its magnitude is \(|E|\propto\dfrac1{n^2}\). The angular momentum is \(L=\dfrac{nh}{2\pi}\), so \(L\propto n\).

Step 2: Combine:
Since \(n\propto L\), we get
\[ E\propto\frac1{n^2}\propto\frac1{L^2}=L^{-2} \]

Step 3: Choose:
Option (C).

Final Answer:
E is proportional to L to the power -2. \[ \boxed{E\propto L^{-2}} \]