Moseley's law for characteristic X-rays is `sqrt v = a(Z-b)`. In this,

Options

A. both a and b are independent of the material
B. a is independent but b depends on the material
C. b is independent but a depends on the material
D. both a and b depend on the material

Answer

To solve the question regarding Moseley's law for characteristic X-rays, we need to analyze the equation given and the options provided.

### Step-by-Step Solution:

1. **Understanding Moseley's Law**:
Moseley's law is given by the equation:
\[ \sqrt{v} = a(Z - b) \]
where:
- \( v \) is the frequency of the emitted X-rays,
- \( Z \) is the atomic number of the element,
- \( a \) and \( b \) are constants.

2. **Identifying Constants**:
- The constant \( a \) is related to the energy levels of the electrons in the atom and is generally considered to be a characteristic of the type of X-ray transition occurring.
- The constant \( b \) is associated with the shielding effect of inner electrons and can vary depending on the material.

3. **Analyzing the Options**:
- **Option 1**: Both \( A \) and \( B \) are independent of the material.
- **Option 2**: \( A \) is independent but \( B \) depends on the material.
- **Option 3**: \( B \) is independent but \( A \) depends on the material.
- **Option 4**: Both \( A \) and \( B \) depend on the material.

4. **Evaluating Each Option**:
- **Option 1** is correct because \( a \) (or \( A \)) is a constant for a given type of transition and does not depend on the material, while \( b \) (or \( B \)) can vary slightly but is generally treated as a constant for a given element.
- **Option 2** is incorrect because \( a \) does not depend on the material.
- **Option 3** is incorrect because \( b \) does not depend on the material in the context of this law.
- **Option 4** is incorrect because both constants are not dependent on the material.

5. **Conclusion**:
The correct answer is **Option 1**: both \( A \) and \( B \) are independent of the material.