Question

A cobalt (atomic no. $=27$) target is bombarded with electrons, and the wavelengths of its characteristic $X-$ray spectrum are measured. A second weak characteristic spectrum is also found, due to an impurity in the target. The wavelengths of the $K_{\alpha }$ lines are $225.0\text{pm}$ (cobalt) and $100.0\text{pm}$ (impurity). Atomic number of the impurity is (take $b=1$)

• A. $39$
• B. $40$
• C. $59$
• D. $60$

Answer 1

The correct option is B $40$

Using Moseley's law for both cobalt and impurity,
$\sqrt{f}=K(Z-1)$
$\Rightarrow \sqrt{\frac{c}{\lambda }}=K(Z-1)$
$\Rightarrow \sqrt{\frac{c}{{\lambda }_{co}}}=K(Z_{co}-1)$ and $\Rightarrow \sqrt{\frac{c}{{\lambda }_x}}=K(Z_x-1)$
$\Rightarrow \sqrt{\frac{{\lambda }_{co}}{{\lambda }_x}}=\frac{Z_x-1}{Z_{co}-1}\Rightarrow Z_x=40$