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 find 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 1: Understand the Balmer Series
The Balmer series corresponds to electronic transitions in hydrogen 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, ... up to n).

### Step 2: Determine the Range of n2
For an electron de-exciting from the \( n^{th} \) shell, the possible values of n2 are from 3 to n. Therefore, the possible values of n2 are:
- n2 = 3
- n2 = 4
- n2 = 5
- ...
- n2 = n

### Step 3: Count the Possible Transitions
The number of transitions from n2 to n1 (where n1 = 2) can be calculated as follows:
- The first transition is from n2 = 3 to n1 = 2.
- The second transition is from n2 = 4 to n1 = 2.
- This continues up to n2 = n.

Thus, the number of possible values for n2 is:
\[ n - 2 \]
This is because n2 can take values from 3 to n, which gives us (n - 2) possible transitions.

### Step 4: Calculate the Number of Spectral Lines
Each transition corresponds to one spectral line. Therefore, the total number of spectral lines in the Balmer series when electrons are de-excited from the \( n^{th} \) shell is:
\[ \text{Number of spectral lines} = n - 2 \]

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

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