How many spectral line of balmer series present in visible region :

Options

A. 5
B. 4
C. 2
D. 3

Answer

To determine how many spectral lines of the Balmer series are present in the visible region, we can follow these steps:

### Step 1: Understand the Balmer Series
The Balmer series corresponds to electronic transitions in hydrogen where an electron falls from a higher energy level (n2) to the second energy level (n1 = 2). The possible values for n2 are 3, 4, 5, 6, and so on.

### Step 2: Identify the Transitions
The transitions that correspond to the Balmer series are:
- n2 = 3 to n1 = 2
- n2 = 4 to n1 = 2
- n2 = 5 to n1 = 2
- n2 = 6 to n1 = 2

### Step 3: Determine the Wavelengths
The wavelengths of the spectral lines can be calculated using the Rydberg formula for hydrogen:
\[ \frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]
where R is the Rydberg constant (approximately \(1.097 \times 10^7 \, \text{m}^{-1}\)).

### Step 4: Check Which Wavelengths Fall in the Visible Region
The visible region of the electromagnetic spectrum is approximately from 400 nm to 700 nm. We need to check the wavelengths for each of the transitions identified in Step 2:

1. **Transition from n2 = 3 to n1 = 2**:
- Wavelength calculation gives a value in the visible range.

2. **Transition from n2 = 4 to n1 = 2**:
- Wavelength calculation gives a value in the visible range.

3. **Transition from n2 = 5 to n1 = 2**:
- Wavelength calculation gives a value in the visible range.

4. **Transition from n2 = 6 to n1 = 2**:
- Wavelength calculation gives a value in the visible range.

### Step 5: Count the Visible Lines
From the transitions identified, we find that there are four transitions that result in spectral lines that fall within the visible range.

### Conclusion
Therefore, the total number of spectral lines of the Balmer series present in the visible region is **4**.

### Final Answer
**Option B: 4**

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