Total number of spectral in UV region during transition from ` 5 ^(th)` excited state to `1^(St)` excited state

Options

A. 10
B. 3
C. 4
D. zero

Answer

To find the total number of spectral lines in the UV region during the transition from the 5th excited state to the 1st excited state, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Initial and Final States:**
- The electron is transitioning from the 5th excited state (n = 5) to the 1st excited state (n = 1).

2. **Understand the Concept of Transitions:**
- When an electron transitions from a higher energy level to a lower energy level, it can do so in multiple ways. Each unique transition corresponds to a spectral line.

3. **Use the Formula for Number of Transitions:**
- The formula to calculate the number of spectral lines (transitions) is given by:
\[ \text{Number of transitions} = \frac{n(n-1)}{2} \]
where \( n \) is the number of energy levels involved in the transition.

4. **Substitute the Value of n:**
- Here, \( n = 5 \) (since we are considering transitions from the 5th excited state down to the 1st).
- Plugging in the value:
\[ \text{Number of transitions} = \frac{5(5-1)}{2} = \frac{5 \times 4}{2} = \frac{20}{2} = 10 \]

5. **Conclusion:**
- Therefore, the total number of spectral lines in the UV region during the transition from the 5th excited state to the 1st excited state is **10**.