Infrared radiation is obtained in an hydrogen atom when transition taks place from the state n=4 to n=2. Which transition will produce ultraviolet radiation?

Options

A. `3to2`
B. `4to3`
C. `5to4`
D. `2to1`

Answer

To determine which transition in a hydrogen atom produces ultraviolet radiation, we need to understand the relationship between the energy levels of the hydrogen atom and the type of radiation emitted during electron transitions between these levels.

### Step-by-Step Solution:

1. **Understanding Energy Levels**: In a hydrogen atom, electrons occupy discrete energy levels denoted by quantum numbers (n=1, n=2, n=3, etc.). The energy of these levels is given by the formula:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]
where \( E_n \) is the energy of the level and \( n \) is the principal quantum number.

2. **Transition from n=4 to n=2**: The problem states that a transition from n=4 to n=2 emits infrared radiation. This is because the energy difference between these two levels corresponds to the infrared region of the electromagnetic spectrum.

3. **Identifying Ultraviolet Radiation**: Ultraviolet radiation is produced when an electron transitions from a higher energy level to a lower energy level, specifically from n=2 to n=1. The transitions that typically produce ultraviolet radiation are:
- n=2 to n=1 (Lyman series)

4. **Evaluating the Options**: The given options for transitions are:
- (a) n=3 to n=2
- (b) n=4 to n=3
- (c) n=5 to n=4
- (d) n=2 to n=7

We need to identify which of these transitions results in ultraviolet radiation.

5. **Analyzing Each Option**:
- **Option (a)**: n=3 to n=2 - This transition emits visible light (Balmer series).
- **Option (b)**: n=4 to n=3 - This transition also emits visible light.
- **Option (c)**: n=5 to n=4 - This transition emits infrared radiation.
- **Option (d)**: n=2 to n=7 - This transition does not make sense as it goes to a higher level from a lower level.

6. **Conclusion**: The only transition that produces ultraviolet radiation is from n=2 to n=1. However, since this option is not provided in the list, we can conclude that the transition that is closest to producing ultraviolet radiation from the options given is not present. Therefore, we can state that the transition n=2 to n=1 is the correct answer for ultraviolet radiation.

### Final Answer:
The transition that produces ultraviolet radiation is from n=2 to n=1.