For the Paschen series thr values of `n_(1)` and `n_(2)` in the expression `Delta E = R_(H)c [(1)/(n_(1)^(2))-(1)/(n_(2)^(2))]` are

Options

A. `n_(1) = 1, n_(2) = 2, 3, 4`
B. `n_(1) = 2, n_(2) = 3, 4, 5`
C. `n_(1) = 3, n_(2) = 4, 5, 6`
D. `n_(1) = 4, n_(2) = 5,6,7`

Answer

To solve the question regarding the Paschen series and the values of \( n_1 \) and \( n_2 \) in the expression

\[ \Delta E = R_H c \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right), \]

we need to understand the definition of the Paschen series in the context of hydrogen atom transitions.

### Step-by-Step Solution:

1. **Identify the Series**: The Paschen series corresponds to electronic transitions in a hydrogen atom where the electron falls to the third energy level (n=3).

2. **Determine \( n_1 \)**: In the Paschen series, the lower energy level (final state) is always \( n_1 = 3 \). This is because the transitions end at the third energy level.

3. **Determine \( n_2 \)**: The upper energy level (initial state) can be any level higher than \( n_1 \). Therefore, \( n_2 \) can take values of 4, 5, 6, etc.

4. **Conclusion**: For the Paschen series, the fixed value of \( n_1 \) is 3, and \( n_2 \) can be any integer greater than 3 (4, 5, 6, ...).

### Final Answer:
- \( n_1 = 3 \)
- \( n_2 \) can be 4, 5, 6, etc. (but typically, we refer to the first transition which is \( n_2 = 4 \)).