Question

The energy of an electron revolving in the nth orbit in Bohr model of hydrogen atom is proportional to:

• A. \(n^2\)
• B. \(n\)
• C. \(\frac{1}{n}\)
• D. \(\frac{1}{n^2}\)

Hint:

While Energy is proportional to \(1/n^2\), remember that the Radius of the orbit is proportional to \(n^2\) and Velocity is proportional to \(1/n\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
In the Bohr model, the total energy of an electron in a stationary orbit is the sum of its kinetic and potential energies. This energy is quantized and depends on the principal quantum number \(n\).

Step 2: Key Formula or Approach:
The energy of the \(n^{th}\) orbit is given by: \[ E_n = -\frac{me^4}{8\epsilon_0^2 h^2 n^2} \]

Step 3: Detailed Explanation:
The formula simplifies to \(E_n = -\frac{13.6}{n^2}\) eV for Hydrogen. From this expression, it is clear that: \[ E_n \propto \frac{1}{n^2} \] As \(n\) increases, the energy becomes less negative (increases), approaching zero at \(n = \infty\).

Step 4: Final Answer:
The energy is proportional to \(\frac{1}{n^2}\).