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 $\sqrt{v}=K\left(Z - 1\right)$
$\Rightarrow \sqrt{\frac{c}{\lambda }}=K\left(Z - 1\right)$
$\Rightarrow \sqrt{\frac{c}{\left(\lambda \right)_{C O}}}=K\left(Z_{C O} - 1\right)$ and $\sqrt{\frac{c}{\left(\lambda \right)_{x}}}=k\left(Z_{x} - 1\right)$
$\sqrt{\frac{\lambda _{C O}}{\lambda _{x}}}=\frac{Z_{x} - 1}{Z_{C O} - 1}\Rightarrow Z_{x}=40$