In Mosley's equation , `sqrtv = a(Z-b)` which was derived from the observations made during the bombardment of the metal target with X - rays

Options

A. a is independent but b depends on the metal
B. Both a and b are independent of the metal
C. Both a and b depends on the metal
D. b is independent but a depends on the metal

Answer

To solve the question regarding Mosley's equation, we need to analyze the equation and the constants involved. The equation given is:

\[ \sqrt{v} = a(Z - b) \]

where:
- \( v \) is the frequency of the emitted X-rays,
- \( Z \) is the atomic number of the target material,
- \( a \) and \( b \) are constants.

### Step-by-Step Solution:

1. **Understanding the Equation**:
- The equation relates the frequency of X-rays emitted from a metal target to its atomic number.
- The term \( \sqrt{v} \) indicates that the frequency is proportional to a linear function of the atomic number \( Z \).

2. **Identifying the Constants**:
- In the equation, \( a \) and \( b \) are constants.
- \( a \) is a proportionality constant that scales the relationship between frequency and the atomic number.
- \( b \) is a constant that shifts the atomic number in the equation.

3. **Analyzing the Dependence on Material**:
- The question asks about the dependence of \( a \) and \( b \) on the material.
- Since \( a \) and \( b \) are constants, we need to determine if they vary with different materials.

4. **Evaluating \( a \) and \( b \)**:
- The constant \( a \) is derived from experimental observations and is generally considered to be a universal constant for a given type of radiation.
- The constant \( b \) is related to the specific properties of the materials being bombarded and can vary based on the material's atomic structure.

5. **Conclusion**:
- From the analysis, we can conclude that:
- \( a \) is independent of the material.
- \( b \) depends on the material.
- Therefore, the correct option is that \( a \) is independent, but \( b \) depends on the material.

### Final Answer:
- **Both \( a \) is independent of the material, while \( b \) depends on the material.**