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 Moseley's equation, we will break down the components and their significance step by step.

### Step 1: Understanding Moseley's Equation
Moseley's equation is given by:
\[ \sqrt{v} = a(Z - b) \]
where:
- \( v \) is the frequency of the emitted X-rays.
- \( Z \) is the atomic number of the target metal.
- \( a \) and \( b \) are constants.

### Step 2: Identifying the Constants
- The constant \( a \) is related to the series of X-rays being emitted (K series, L series, etc.).
- The constant \( b \) is known as the screening constant or shielding constant, which accounts for the effect of inner electrons on the outer electrons.

### Step 3: Values of Constants for Different Series
- For the K series:
\[ a = \sqrt{\frac{3R_c}{4}}, \quad b = 1 \]
- For the L series:
\[ a = \frac{5}{36}R_c, \quad b = 7.4 \]
where \( R_c \) is the Rydberg constant.

### Step 4: Independence of Constants
From the observations made, we can conclude that:
- The values of \( a \) and \( b \) are constants that do not depend on the specific metal being bombarded. They are derived from fundamental constants and the nature of the electron transitions involved.

### Step 5: Conclusion
Thus, the correct interpretation of the question is that both constants \( a \) and \( b \) are independent of the metal used in the bombardment process.

### Final Answer
The correct option is that both \( a \) and \( b \) are independent of the metal.

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