Assertion. In Lyman series of H-spectra, the maximum wavelength of lines is 121.56 nm
Reason. Wavelength is maximum when the transition is from the very next level

Options

A. If both assertion and reason are true, and reason is the true explanation of the assertion
B. If both assertion and reason are true, but reason is not the true explanation of the assertion
C. If assertion is true, but reason is false
D. If both assertion and reason are false

Explanation

To solve the question regarding the Lyman series of the hydrogen spectrum, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Lyman Series**:
- The Lyman series corresponds to electronic transitions in hydrogen where an electron falls from a higher energy level (n ≥ 2) to the first energy level (n = 1).
- The maximum wavelength in the Lyman series occurs when the transition is from the second energy level (n = 2) to the first energy level (n = 1).

2. **Formula for Wavelength**:
- The formula to calculate the wavelength (λ) of the emitted light during these transitions is given by the Rydberg formula:
\[ \frac{1}{\lambda} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]
- Here, \( R_H \) is the Rydberg constant for hydrogen, approximately \( 1.097 \times 10^7 \, \text{m}^{-1} \), \( n_1 \) is the lower energy level (1 for Lyman series), and \( n_2 \) is the higher energy level (2, 3, 4, ...).

3. **Calculating Maximum Wavelength**:
- For the maximum wavelength, we set \( n_2 = 2 \) and \( n_1 = 1 \):
\[ \frac{1}{\lambda} = R_H \left( \frac{1}{1^2} - \frac{1}{2^2} \right) \]
\[ \frac{1}{\lambda} = R_H \left( 1 - \frac{1}{4} \right) = R_H \left( \frac{3}{4} \right) \]
- Substituting the value of \( R_H \):
\[ \frac{1}{\lambda} = 1.097 \times 10^7 \times \frac{3}{4} \]
\[ \lambda = \frac{4}{3 \times 1.097 \times 10^7} \approx 121.56 \, \text{nm} \]

4. **Evaluating the Assertion**:
- The assertion states that the maximum wavelength of lines in the Lyman series is 121.56 nm, which we have calculated and confirmed to be correct.

5. **Evaluating the Reason**:
- The reason states that the wavelength is maximum when the transition is from the very next level (n = 2 to n = 1). This is also correct, as the maximum wavelength corresponds to the smallest energy difference, which occurs in this transition.

6. **Conclusion**:
- Both the assertion and the reason are true, and the reason correctly explains the assertion.

### Final Answer:
Both the assertion and the reason are true, and the reason is the correct explanation for the assertion.

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