Question

The electron in hydrogen atom is initially in the second excited state. When it finally moves to ground state, the maximum number of spectral lines emitted are

• A. \(2\)
• B. \(3\)
• C. \(4\)
• D. \(5\)

Hint:

Second excited state means n = 3; lines = n(n-1)/2.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
The ground state is \(n = 1\), the first excited state is \(n = 2\), and the second excited state is \(n = 3\). An electron can come down in steps or directly.

Step 2: Count the lines
Possible transitions: \(3 \to 2\), \(2 \to 1\) and \(3 \to 1\).
\[ \frac{n(n - 1)}{2} = \frac{3 \times 2}{2} = 3 \]
So at most 3 spectral lines appear.

Final Answer:
A maximum of 3 lines are emitted, option (B). \[ \boxed{3} \]