Question

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

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

Hint:

Since both total energy and angular momentum depend directly on the principal quantum number $n$, you can treat $n$ as a bridge variable. Squaring the momentum relation gives $L^2 \propto n^2$. Inverting this matches the energy relation ($\frac{1}{n^2}$), leading directly to $E \propto L^{-2}$.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
Find the proportionality relationship between total energy E and orbital angular momentum L for an electron in a Bohr orbit.

Step 2: Key Formula or Approach:
In Bohr's model, E ∝ 1/n² and L = nh/2π ∝ n. Substitute n ∝ L into energy relation.

Step 3: Detailed Explanation:
E ∝ 1/n² and n ∝ L → E ∝ 1/L², so E ∝ L⁻².

Step 4: Final Answer:
E ∝ L⁻², matching option (C).