Consider the following two statements A and B and identify the correct choice in the given answer
A : The characteristic X-ray spectrum depends on the nature of the material of the target
B : The short wavelength limit of continuous X-ray spectrum varies inversely with the potential difference applied to the X-rays tube

Options

A. A is true and B is false
B. A is false and B are true
C. Both A and B are true
D. Both A and B are false

Answer

To solve the problem, we need to analyze the two statements A and B regarding X-rays.

### Step 1: Analyze Statement A
**Statement A:** "The characteristic X-ray spectrum depends on the nature of the material of the target."

- Characteristic X-rays are produced when high-energy electrons collide with a target material, causing inner-shell electrons to be ejected and outer-shell electrons to fill these vacancies. The energy difference between these shells corresponds to specific wavelengths of X-rays emitted.
- The specific wavelengths (or energies) of the emitted X-rays depend on the atomic structure of the target material, which is characterized by its atomic number (Z). Therefore, different materials will produce different characteristic X-ray spectra.

**Conclusion:** Statement A is **correct**.

### Step 2: Analyze Statement B
**Statement B:** "The short wavelength limit of the continuous X-ray spectrum varies inversely with the potential difference applied to the X-ray tube."

- The continuous X-ray spectrum is produced when high-energy electrons are decelerated upon hitting the target. The minimum wavelength (λ_min) of the continuous spectrum can be calculated using the formula:
\[ \lambda_{\text{min}} = \frac{hc}{eV} \]
where:
- \( h \) is Planck's constant,
- \( c \) is the speed of light,
- \( e \) is the charge of the electron,
- \( V \) is the potential difference.
- From this formula, we can see that λ_min is inversely proportional to the potential difference (V). As the potential difference increases, the minimum wavelength decreases, confirming that the statement is true.

**Conclusion:** Statement B is **correct**.

### Final Conclusion
Both statements A and B are true. Therefore, the correct answer is that both statements are true.

### Summary of the Solution
- **Statement A:** True (depends on the target material).
- **Statement B:** True (short wavelength limit varies inversely with potential difference).
- **Final Answer:** Both statements A and B are true.

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