Question

Find the energy of third stationary orbit of Bohr's model of hydrogen atom if the energy of ground state is \(-E\) J

• A. \(-\frac{E}{2}\) J
• B. \(-\frac{E}{4}\) J
• C. \(-\frac{E}{9}\) J
• D. \(-\frac{E}{16}\) J

Hint:

In a hydrogen atom the orbit energy varies as 1/n squared.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The energy of an electron in the \(n^{th}\) Bohr orbit of hydrogen is inversely proportional to \(n^2\). The ground state is \(n=1\) and the third orbit is \(n=3\).

Step 2: Key Formula or Approach:
\[ E_n = -\frac{13.6}{n^2}\text{ eV} = \frac{E_1}{n^2} \]
Here \(E_1 = -E\) J is the ground state energy.

Step 3: Detailed Explanation:
For the third stationary orbit, \(n = 3\).
\[ E_3 = \frac{E_1}{3^2} = \frac{-E}{9} \]
Option (A) corresponds to \(n^2 = 2\), option (B) to \(n = 2\) (second orbit) and option (D) to \(n=4\) (fourth orbit). None of these is the third orbit.

Final Answer:
The energy of the third orbit is one ninth of the ground state energy, so option (C) is correct. \[ \boxed{-\frac{E}{9}\text{ J}} \]