Which of the following transition is associated with coloured spectral line

Options

A. `n = 5` to `n = 3`
B. `n = 4` to `n = 2`
C. `n = 2` to `n = 1`
D. `n = 3` to `n = 1`

Explanation

To determine which transition is associated with a colored spectral line, we need to analyze the given transitions in the context of the Balmer series. The Balmer series corresponds to electronic transitions in hydrogen that result in the emission of light in the visible spectrum.

### Step-by-Step Solution:

1. **Understand the Balmer Series**:
The Balmer series consists of transitions where an electron falls from a higher energy level (n ≥ 3) to n = 2. The wavelengths of these transitions fall within the visible region of the electromagnetic spectrum.

2. **Identify the Relevant Transitions**:
- The transitions that are typically considered in the Balmer series are:
- n = 3 to n = 2
- n = 4 to n = 2
- n = 5 to n = 2
- n = 6 to n = 2
- These transitions will produce spectral lines that are colored and visible.

3. **Analyze the Given Transitions**:
- If the transitions provided in the question include any of the above transitions, they are associated with colored spectral lines.
- For example:
- Transition from n = 4 to n = 2 is part of the Balmer series and will produce a visible spectral line.
- Transition from n = 3 to n = 2 is also part of the Balmer series and will produce a visible spectral line.

4. **Calculate Wavelength (if necessary)**:
- The wavelength (λ) of the emitted light can be calculated using the Rydberg formula:
\[ \frac{1}{\lambda} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]
- Where \( R_H \) is the Rydberg constant (approximately \( 1.097 \times 10^7 \, \text{m}^{-1} \)), \( n_1 \) is the lower energy level (2 for Balmer series), and \( n_2 \) is the higher energy level.

5. **Determine the Wavelength Range**:
- The visible spectrum ranges from approximately 400 nm to 700 nm. If the calculated wavelength falls within this range, the transition is confirmed to produce a colored spectral line.

6. **Conclusion**:
- Based on the analysis, any transition from n ≥ 3 to n = 2 in the Balmer series will be associated with colored spectral lines.