KVPY Sample Paper KVPY Stream-SX Model Paper-18

A cobalt \[(\text{atomic}\,\,\text{no}\text{.}=27)\] 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 pm (cobalt) and 100.0 pm (impurity). Atomic number of the impurity is \[(take\,\,b=1)\]

A) 39

B) 40

C) 59

D) 60

Correct Answer: B

Solution :

Using Mosely'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 \[\sqrt{\frac{c}{{{\lambda }_{x}}}}=K\,({{Z}_{x}}-1)\]

\[\Rightarrow \] \[\sqrt{\frac{{{\lambda }_{co}}}{{{\lambda }_{x}}}}=\frac{{{Z}_{x}}-1}{{{Z}_{co}}-1}={{Z}_{x}}=40\]