Assertio Wavelength of charachteristic X-rays is given by
`(1)/(lambda)prop((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))`
in trasnition from ` n_(2) to n_(1)` . In the abvoe relation proportionality constant is series dependent. For different series (K-series, L-series, etc. ) value of this constant will be different.
Reason For L-series value of this constant is less than the value for K-series

Options

A. If both Assertion and Reason ar true and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are true but Reason is not correct explanation of Assertion
C. If Assertion is true by Reason is false.
D. If Assertion is false but Reason is true.

Explanation

To solve the assertion-reason question regarding the wavelength of characteristic X-rays and the proportionality constant for different series, we can break down the problem into a series of logical steps.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that the wavelength of characteristic X-rays is given by the formula:
\[ \frac{1}{\lambda} \propto \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]
This means that the reciprocal of the wavelength (\( \frac{1}{\lambda} \)) is proportional to the difference in the reciprocals of the squares of the principal quantum numbers involved in the transition.

**Hint**: Recall that \( n_1 \) and \( n_2 \) represent the principal quantum numbers of the energy levels involved in the transition.

2. **Proportionality Constant**:
The assertion also mentions that the proportionality constant is series dependent. This means that for different series (like K-series, L-series), the value of this constant will differ.

**Hint**: Think about how the atomic structure and energy levels change for different series and how that affects the proportionality constant.

3. **Analyzing the Reason**:
The reason states that for the L-series, the value of this constant is less than that for the K-series. To verify this, we need to look at the values of the proportionality constant for both series.

- For the K-series, the proportionality constant \( B \) is typically taken as \( 1 \).
- For the L-series, the value of \( B \) is approximately \( 7.4 \).

**Hint**: Compare the numerical values of the proportionality constants for K and L series to determine which is greater.

4. **Conclusion**:
Since the value of \( B \) for the L-series (7.4) is greater than that for the K-series (1), the reason provided is incorrect. Therefore, we conclude that:
- The assertion is true.
- The reason is false.

**Final Answer**: The correct option is that the assertion is true, but the reason is false.