Question

A cobalt target is bombarded with electrons and the wavelength of its characteristic spectrum are measured. A second fainter, characteristic spectrum is also found because of an impurity in the target. The wavelength of the $K_{\alpha }$ lines are 178.9 pm (cobalt) & 143.5 pm (impurity). If atomic number of impurity is 5x, then value of x is___

Answer 1

By Moseley's law:
$\sqrt{f}=a(Z-b)[\text{for}{K}_{\alpha };b=1]\sqrt{\frac{C}{\lambda }}=aZ-a$
$\therefore \sqrt{\frac{{\lambda }_{co}}{{\lambda }_{im}}}=\frac{Z_{im}-1}{Z_{co}-1}\Rightarrow \sqrt{\frac{178.9}{143.5}}=\frac{Z-1}{27-1}\Rightarrow Z=30$