Question

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

• A. 3
• B. 4
• C. 5
• D. 6

Hint:

Always remember: the $n^{\text{th}}$ excited state means the actual energy level is $n + 1$. Once you have the correct $n$, just use the quick handshake formula $\frac{n(n-1)}{2}$ to get the number of lines instantly!

Answer 1

The Correct Option is D

Step 1: Identify the levels.
The third excited state is $n=4$, and the ground state is $n=1$.

Step 2: Use the line-count formula.
The number of possible spectral lines from level $n$ down to the ground is $\frac{n(n-1)}{2}$.

Step 3: Put in $n=4$.
\[ \frac{4\times3}{2}=6 \]
\[ \boxed{6} \]