Assertion(A): Wavelength of limiting line of lyman series is less less than wavelength of limiting line of Balmer series.
Reason(R): Rydberg constant value is same for all elements

Options

A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of (A)
C. (A) is true but (R) is false
D. (A) is false but (R) is true

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

**Step 1: Understand the Lyman and Balmer Series**
- The Lyman series corresponds to electronic transitions in hydrogen where the electron falls to the n=1 energy level from higher levels (n=2, 3, ...).
- The Balmer series corresponds to transitions where the electron falls to the n=2 level from higher levels (n=3, 4, ...).

**Step 2: Determine the Limiting Lines**
- The limiting line for the Lyman series occurs when the electron transitions from n=∞ to n=1.
- The limiting line for the Balmer series occurs when the electron transitions from n=∞ to n=2.

**Step 3: Use the Rydberg Formula**
- The Rydberg formula for the wavelength (λ) of the emitted light is given by:
\[ \frac{1}{\lambda} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]
where \( R_H \) is the Rydberg constant.

**Step 4: Calculate the Wavelength for Lyman Series**
- For the Lyman series (n1=1, n2=∞):
\[ \frac{1}{\lambda_L} = R_H \left( \frac{1}{1^2} - \frac{1}{\infty^2} \right) = R_H \cdot 1 = R_H \]
Thus, \( \lambda_L = \frac{1}{R_H} \).

**Step 5: Calculate the Wavelength for Balmer Series**
- For the Balmer series (n1=2, n2=∞):
\[ \frac{1}{\lambda_B} = R_H \left( \frac{1}{2^2} - \frac{1}{\infty^2} \right) = R_H \cdot \frac{1}{4} \]
Thus, \( \lambda_B = \frac{4}{R_H} \).

**Step 6: Compare the Wavelengths**
- Now we compare \( \lambda_L \) and \( \lambda_B \):
\[ \lambda_L = \frac{1}{R_H} \quad \text{and} \quad \lambda_B = \frac{4}{R_H} \]
- Since \( \frac{1}{R_H} < \frac{4}{R_H} \), we conclude that \( \lambda_L < \lambda_B \). Therefore, the assertion is true.

**Step 7: Analyze the Reason**
- The reason states that the Rydberg constant value is the same for all elements. This is incorrect because the Rydberg constant varies with the atomic number (Z) of the element. The formula for the Rydberg constant is:
\[ R = R_H Z^2 \]
Hence, the reason is false.

### Conclusion:
- Assertion (A) is true: The wavelength of the limiting line of the Lyman series is less than that of the Balmer series.
- Reason (R) is false: The Rydberg constant is not the same for all elements.

### Final Answer:
The answer is: Assertion is true, Reason is false (A is true, R is false).

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