Question

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

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

Answer 1

Answer: (B)

Using Mosely's law for both cobalt and impurity $\sqrt{v}=K\left(Z-1\right)$
$\Rightarrow \sqrt{\frac{c}{\lambda }}=K\left(Z-1\right)$
$\Rightarrow \sqrt{\frac{c}{{\left(\lambda \right)}_{CO}}}=K\left(Z_{CO}-1\right)$ and $\sqrt{\frac{c}{{\left(\lambda \right)}_x}}=k\left(Z_x-1\right)$
$\sqrt{\frac{{\lambda }_{CO}}{{\lambda }_x}}=\frac{Z_x-1}{Z_{CO}-1}\Rightarrow Z_x=40$