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 problem, we will analyze the assertion (A) and the reason (R) given in the question regarding the relationship between the accelerating potential in an X-ray machine and the wavelength of emitted X-rays.

### Step-by-Step Solution:

1. **Understanding the Concept of X-ray Production**:
- X-rays are produced when high-speed electrons collide with a target material. The energy of the electrons is converted into X-ray photons during these collisions.

2. **Energy of Electrons**:
- The energy (E) of the electrons in an X-ray machine is given by the formula:
\[ E = eV \]
where \(e\) is the charge of the electron and \(V\) is the accelerating potential.

3. **Relationship Between Energy and Wavelength**:
- The energy of a photon is related to its wavelength (\(\lambda\)) by the equation:
\[ E = \frac{hc}{\lambda} \]
where \(h\) is Planck's constant and \(c\) is the speed of light.

4. **Finding Minimum Wavelength**:
- The minimum wavelength (\(\lambda_{min}\)) occurs when the energy of the photon is at its maximum, which corresponds to the maximum energy of the electrons:
\[ \lambda_{min} = \frac{hc}{E} \]
- Substituting the expression for energy:
\[ \lambda_{min} = \frac{hc}{eV} \]

5. **Effect of Decreasing the Accelerating Potential**:
- If the accelerating potential \(V\) is decreased, the energy \(E\) of the electrons also decreases. This leads to an increase in the minimum wavelength of the emitted X-rays:
\[ \lambda_{min} \propto \frac{1}{V} \]
- Thus, as \(V\) decreases, \(\lambda_{min}\) increases.

6. **Conclusion**:
- The assertion (A) is true: if the accelerating potential in an X-ray machine is decreased, the minimum value of the wavelength of the emitted X-rays gets increased.
- The reason (R) is also true: the minimum value of wavelength of the emitted X-rays is inversely proportional to the accelerating potential.

### Final Statement:
Both the assertion (A) and the reason (R) are true, and R correctly explains A.

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