Statement I: In an X-ray tube , if the energy with which an electron strickes the metal target increases , then the wavelength of the characteristic X-rays also changes.
Statement II : Wavelength of the characteristic X-rays depends only on the initial and final energy levels.

Options

A. Statement I is True , Statement II is True , Statement II is a correct explanation for Statement I.
B. Statement I is True , Statement II is True , Statement II is NOT a correct explanation for Statement I.
C. Statement I is True , Statement II is False.
D. Statement I is False , Statement II is True.

Explanation

To solve the given problem, we need to analyze both statements regarding X-ray production in an X-ray tube.

### Step 1: Analyze Statement I
**Statement I:** In an X-ray tube, if the energy with which an electron strikes the metal target increases, then the wavelength of the characteristic X-rays also changes.

- **Explanation:** Characteristic X-rays are produced when an electron transitions between specific energy levels in an atom. The energy of the emitted X-ray photon is determined by the difference in energy between these levels, not by the energy of the incoming electron. Therefore, even if the energy of the incoming electron increases, it does not affect the energy levels of the electrons in the target material. Hence, the wavelength of the characteristic X-rays remains unchanged.

### Step 2: Analyze Statement II
**Statement II:** Wavelength of the characteristic X-rays depends only on the initial and final energy levels.

- **Explanation:** This statement is correct. The wavelength of characteristic X-rays is given by the formula:

\[ E = E_{n1} - E_{n2} \]

where \(E\) is the energy of the emitted X-ray, \(E_{n1}\) is the energy of the initial level, and \(E_{n2}\) is the energy of the final level. The wavelength \(\lambda\) can be calculated using the relation:

\[ \lambda = \frac{hc}{E} \]

This shows that the wavelength depends solely on the energy difference between the two levels, confirming that it is independent of the incoming electron's energy.

### Step 3: Conclusion
- **Statement I is false** because the wavelength of characteristic X-rays does not change with the energy of the incoming electrons.
- **Statement II is true** because the wavelength is determined only by the energy levels involved in the transition.

### Final Answer
Based on the analysis:
- Statement I: False
- Statement II: True

Thus, the correct answer is **D: Statement I is false and Statement II is true.**

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