The maximum wavelength of Lyman series is

Options

A. `C/R`
B. `1/R^2`
C. `(4)/(3R)`
D. `(1)/(CR)`

Explanation

To find the maximum wavelength of the Lyman series, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Lyman Series**: The Lyman series corresponds to transitions of electrons in a hydrogen atom from higher energy levels (n_initial) to the lowest energy level (n_final = 1).

2. **Use the Rydberg Formula**: The formula for the wavelength (λ) in the Lyman series is given by:
\[ \frac{1}{\lambda} = R \left( \frac{1}{n_{final}^2} - \frac{1}{n_{initial}^2} \right) \]
where \( R \) is the Rydberg constant.

3. **Identify the Values**: For the Lyman series:
- \( n_{final} = 1 \)
- \( n_{initial} \) can be 2, 3, 4, ..., or infinity. To find the maximum wavelength, we need to consider the transition from the second energy level (n_initial = 2).

4. **Substitute the Values**: Plugging in the values into the formula for the maximum wavelength:
\[ \frac{1}{\lambda_{max}} = R \left( \frac{1}{1^2} - \frac{1}{2^2} \right) \]
This simplifies to:
\[ \frac{1}{\lambda_{max}} = R \left( 1 - \frac{1}{4} \right) = R \left( \frac{3}{4} \right) \]

5. **Rearranging for λ_max**:
\[ \lambda_{max} = \frac{4}{3R} \]

6. **Substitute the Rydberg Constant**: The Rydberg constant \( R \) is approximately \( 1.097 \times 10^7 \, \text{m}^{-1} \).
\[ \lambda_{max} = \frac{4}{3 \times 1.097 \times 10^7} \]

7. **Calculate λ_max**:
\[ \lambda_{max} = \frac{4}{3.291 \times 10^7} \approx 1.215 \times 10^{-7} \, \text{m} = 121.5 \, \text{nm} \]

### Final Answer:
The maximum wavelength of the Lyman series is approximately **121.5 nm**.