Assertion By increasing the accelerationg voltage in coolidge tube wavelength of characteristic X-rays does not change.
Reason Cut-off wavelength is inversely proportional to the acceleration voltage

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.

Answer

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

### Step 1: Understand the Assertion
The assertion states that by increasing the accelerating voltage in a Coolidge tube, the wavelength of characteristic X-rays does not change.

**Explanation**: Characteristic X-rays are produced when electrons collide with a target material and cause inner-shell electrons to be ejected. The energy difference between the shells results in the emission of X-rays with specific wavelengths. This process is independent of the accelerating voltage because the characteristic X-ray wavelengths are determined by the atomic structure of the target material, not the energy of the incoming electrons.

### Step 2: Understand the Reason
The reason states that the cut-off wavelength is inversely proportional to the accelerating voltage.

**Explanation**: The cut-off wavelength (λ_cut-off) is indeed related to the maximum energy of the electrons, which is determined by the accelerating voltage (V). The relationship is given by the equation:
\[ \lambda_{cut-off} = \frac{hc}{eV} \]
where \( h \) is Planck's constant, \( c \) is the speed of light, and \( e \) is the charge of an electron. This shows that as the accelerating voltage increases, the cut-off wavelength decreases, confirming that they are inversely proportional.

### Step 3: Conclusion
Now, we can conclude:
- The assertion is true: Increasing the accelerating voltage does not change the wavelength of characteristic X-rays.
- The reason is also true: The cut-off wavelength is inversely proportional to the accelerating voltage.
- However, the reason does not explain the assertion because the characteristic X-ray wavelengths are not affected by the accelerating voltage.

### Final Answer
Both the assertion and the reason are true, but the reason is not the correct explanation for the assertion.

---