Assertion `(A) : K-` shell electron capture is detected by analyzing the wavelength of `X-` ray emitted.
Reason `(R):` The wavelength of the `X-` ray is characteristic of the daughter element and not the parent element.

Options

A. If both `(A)` and `(R)` are correct , and `(R)` is the correct explanation of `(A)`
B. If both `(A)` and `(R)` are correct, but (R) is not the correct explanation of `(A)`
C. If `(A)` is correct, but `(R)` is incorrect.
D. If `(A)` is incorrect, but `(R)` is correct.

Answer

To solve the question regarding the assertion and reason about K-shell electron capture and the emitted X-ray, we can break it down into clear steps.

### Step-by-Step Solution:

1. **Understanding Electron Capture**:
- Electron capture is a process where an electron from the innermost shell (K-shell) is captured by the nucleus. This process transforms a proton into a neutron, resulting in a change of the element.

2. **Emission of X-rays**:
- When an electron is captured from the K-shell, an electron from a higher energy level (like the L-shell) will transition down to fill the vacancy left by the captured electron. This transition releases energy in the form of X-rays.

3. **Analyzing the Wavelength of X-rays**:
- The wavelength of the emitted X-ray is characteristic of the energy difference between the two shells involved in the transition. Therefore, by analyzing the wavelength of the emitted X-ray, we can determine which shell the electron was captured from.

4. **Daughter Element Characteristics**:
- After electron capture, the original element (parent) transforms into a new element (daughter). The emitted X-ray is associated with the energy levels of the daughter element, not the parent element. Hence, the wavelength of the X-ray is characteristic of the daughter element.

5. **Evaluating Assertion and Reason**:
- The assertion states that K-shell electron capture can be detected by analyzing the wavelength of the emitted X-ray, which is true.
- The reason states that the wavelength of the X-ray is characteristic of the daughter element and not the parent element, which is also true.
- However, the reason does not directly explain the assertion. The assertion is about the detection method, while the reason discusses the characteristics of the emitted X-ray.

6. **Conclusion**:
- Both the assertion and reason are true, but the reason is not the explanation for the assertion. Therefore, the correct answer is that both statements are true, but the reason does not explain the assertion.