In X-ray spectrum wavelength `lamda` of line `K_(alpha)` depends on atomic number Z as

Options

A. `lambda propZ^(2)`
B. `lambdaprop(Z-1)^(2)`
C. `lambdaprop(1)/((Z-1))`
D. `lambdaprop(1)/((Z-1)^(2))`

Explanation

To find the relationship between the wavelength \( \lambda \) of the K-alpha line in the X-ray spectrum and the atomic number \( Z \), we start with the known formula:

1. **Start with the formula for K-alpha wavelength**:
\[ \frac{1}{\lambda} = \frac{3}{4}(Z - 1)^2 \]

2. **Rearranging the formula**:
To express \( \lambda \) in terms of \( Z \), we can take the reciprocal of both sides:
\[ \lambda = \frac{4}{3(Z - 1)^2} \]

3. **Identifying the relationship**:
From the rearranged formula, we can see that \( \lambda \) is inversely proportional to \( (Z - 1)^2 \):
\[ \lambda \propto \frac{1}{(Z - 1)^2} \]

4. **Final conclusion**:
Therefore, the correct relationship that describes how the wavelength \( \lambda \) of the K-alpha line depends on the atomic number \( Z \) is:
\[ \lambda \propto \frac{1}{(Z - 1)^2} \]

Thus, the answer is that the wavelength \( \lambda \) of the K-alpha line is directly proportional to \( \frac{1}{(Z - 1)^2} \).