A: If the accelerating potential in an X- ray machine is decreased, the minimum value of the wavelength of the emitted X -rays gets increased.
R: The minimum value of wavelength of the emitted X-rays is inversely proportional to the accelerating potential.

Options

A. If both Assertion & Reason are true and the reason is the correct explantion of the assertion , then mark (1)
B. if both Assertion & Reason are true but the reason is not the correct explantion of the assertion , then mark (2)
C. If Assertion is true statement but Reason is false, then mark (3)
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that if the accelerating potential in an X-ray machine is decreased, the minimum value of the wavelength of the emitted X-rays increases.

2. **Understanding the Reason (R)**:
- The reason states that the minimum value of the wavelength of the emitted X-rays is inversely proportional to the accelerating potential.

3. **Relation Between Wavelength and Accelerating Potential**:
- The energy of the electrons accelerated through a potential \( V \) is given by \( E = eV \), where \( e \) is the charge of the electron.
- When these electrons strike the anode, they produce X-rays. The maximum energy of the emitted X-rays corresponds to the energy of the electrons, which can be expressed as:
\[ E = \frac{hc}{\lambda_{\text{min}}} \]
where \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda_{\text{min}} \) is the minimum wavelength of the emitted X-rays.

4. **Deriving the Relationship**:
- Setting the two expressions for energy equal gives:
\[ eV = \frac{hc}{\lambda_{\text{min}}} \]
- Rearranging this equation to find \( \lambda_{\text{min}} \):
\[ \lambda_{\text{min}} = \frac{hc}{eV} \]
- From this equation, it is clear that \( \lambda_{\text{min}} \) is inversely proportional to the accelerating potential \( V \):
\[ \lambda_{\text{min}} \propto \frac{1}{V} \]

5. **Analyzing the Assertion**:
- If the accelerating potential \( V \) decreases, then \( \lambda_{\text{min}} \) must increase, confirming the assertion.

6. **Conclusion**:
- Both the assertion (A) and the reason (R) are correct. The assertion is true because a decrease in accelerating potential leads to an increase in minimum wavelength, and the reason is true as it correctly describes the relationship between wavelength and accelerating potential.

### Final Answer:
Both the assertion (A) and the reason (R) are correct.

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