According to moselay.s law, the frequency `(vartheta)` of the `Kalpha` line and the atomic number (z) of the element have the relation (A and B) are constants

Options

A. `(vartheta)/((z-A))=B`
B. `(sqrtvartheta)/((z-A))=B`
C. `vartheta(Z-A)=B`
D. `vartheta(Z-A)^(2)=B`

Answer

To solve the problem based on Moseley's law regarding the frequency of the K-alpha line and the atomic number (Z) of an element, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Moseley's Law**:
Moseley's law states that the frequency (ν) of the K-alpha X-ray line emitted by an element is related to its atomic number (Z). The relationship can be expressed mathematically.

2. **Moseley's Law Formula**:
According to Moseley's law, the frequency of the K-alpha line can be given by the equation:
\[ \nu = k_1 (Z - k_2) \]
where \( k_1 \) and \( k_2 \) are constants.

3. **Rearranging the Equation**:
We can rearrange the equation to express it in a different form:
\[ \nu = k_1 Z - k_1 k_2 \]
This shows that frequency is a linear function of the atomic number.

4. **Identifying Constants**:
Here, we can identify \( k_1 \) as a constant that scales the atomic number, and \( k_2 \) as a constant that shifts the frequency.

5. **Expressing in Terms of Constants A and B**:
If we let \( k_1 = A \) and \( k_2 = B \), we can rewrite the equation as:
\[ \nu = A (Z - B) \]
This is the required relation according to the question.

6. **Conclusion**:
Thus, the relationship between the frequency of the K-alpha line and the atomic number can be summarized as:
\[ \nu = A (Z - B) \]
where \( A \) and \( B \) are constants.