KVPY Sample Paper KVPY Stream-SX Model Paper-21

  • question_answer
    A cobalt (atomic no. = 27) target is bombarded with electrons, and the wavelengths 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 \[{{K}_{a}}\] 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 \[\sqrt{\frac{c}{{{\lambda }_{x}}}}=K({{Z}_{x}}-1)\]\[\Rightarrow \sqrt{\frac{{{\lambda }_{co}}}{c}}=\frac{{{Z}_{x}}-1}{{{Z}_{co}}-1}={{Z}_{x}}=40\]

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