Find the number of spectral lines in Paschen series emitted by atomic H, when electron is excited from ground state to 7th energy level returns back .

Answer

To find the number of spectral lines in the Paschen series emitted by atomic hydrogen when an electron is excited from the ground state (n=1) to the 7th energy level (n=7) and then returns back, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Paschen Series:**
The Paschen series corresponds to transitions where the final energy level is n=3. Therefore, we need to consider transitions that end at n=3.

2. **Determine Possible Transitions:**
The electron can transition from higher energy levels (n=7, 6, 5, 4) down to n=3. We will consider all possible transitions from these levels:
- From n=7 to n=3
- From n=6 to n=3
- From n=5 to n=3
- From n=4 to n=3

3. **Count the Transitions:**
Each of these transitions will produce a spectral line:
- Transition from n=7 to n=3 → 1 line
- Transition from n=6 to n=3 → 1 line
- Transition from n=5 to n=3 → 1 line
- Transition from n=4 to n=3 → 1 line

4. **Total Number of Spectral Lines:**
Adding these up gives us:
- Total spectral lines = 1 (from n=7) + 1 (from n=6) + 1 (from n=5) + 1 (from n=4) = 4 spectral lines.

### Final Answer:
The total number of spectral lines emitted in the Paschen series when the electron transitions from the 7th energy level to the ground state is **4**.