Number of spectral lines falling Balmer series when electrons are de - excited from ` n^(th)` shell will be given as

Options

A. `(n-2) ` in UV
B. (n-2) in visible region
C. (n-3) in near IR
D. (n-3) in far IR

Answer

To determine the number of spectral lines in the Balmer series when electrons are de-excited from the \( n^{th} \) shell, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Balmer Series**:
The Balmer series corresponds to the transitions of electrons in a hydrogen atom where the final energy level (n1) is 2. The initial energy level (n2) can be any integer greater than 2 (i.e., n2 = 3, 4, 5, ...).

2. **Identifying the Range of n2**:
When electrons transition from the \( n^{th} \) shell, the possible values for n2 are from 3 up to n. Therefore, the values of n2 can be: 3, 4, 5, ..., n.

3. **Counting the Transitions**:
The total number of transitions (or spectral lines) that can occur is equal to the number of possible values for n2. This can be calculated as:
- The smallest value of n2 is 3.
- The largest value of n2 is n.
- Therefore, the number of possible values for n2 is given by \( n - 2 \) (because we count from 3 to n).

4. **Conclusion**:
Thus, the number of spectral lines in the Balmer series when electrons are de-excited from the \( n^{th} \) shell is \( n - 2 \).

### Final Answer:
The number of spectral lines in the Balmer series when electrons are de-excited from the \( n^{th} \) shell is \( n - 2 \).

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