Number of spectral lines in Balmer series when an electron retrurn from `7 ^(th )` orbit to` 1 ^(st)` orbit of hydrogen atom are

Options

A. 5
B. 6
C. 21
D. 15

Answer

To determine the number of spectral lines in the Balmer series when an electron transitions from the 7th orbit to the 1st orbit of a hydrogen atom, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Balmer Series**:
The Balmer series corresponds to electronic transitions where the final energy level (n1) is 2. The initial energy level (n2) can be any integer greater than 2 (n2 = 3, 4, 5, ...).

2. **Determine the Transition**:
In this case, the electron is transitioning from the 7th orbit (n2 = 7) to the 1st orbit (n1 = 1). However, since we are looking for the spectral lines in the Balmer series, we need to consider transitions that end at n1 = 2.

3. **Calculate the Number of Spectral Lines**:
The formula to calculate the number of spectral lines (N) produced during a transition from an initial level (n2) to a final level (n1) is given by:
\[ N = n2 - n1 \]
For the Balmer series, since n1 is fixed at 2, we have:
\[ N = n2 - n1 = 7 - 2 = 5 \]

4. **Conclusion**:
Therefore, the number of spectral lines in the Balmer series when an electron transitions from the 7th orbit to the 1st orbit is 5.

### Final Answer:
The number of spectral lines in the Balmer series when an electron returns from the 7th orbit to the 1st orbit of a hydrogen atom is **5**.

---