JEE Main & Advanced Physics Photo Electric Effect, X- Rays & Matter Waves Question Bank X Rays

  • question_answer
    The wavelength of \[{{K}_{\alpha }}\] line for an element of atomic number 43 is l. Then the wavelength of \[{{K}_{\alpha }}\] line for an element of atomic number 29 is

    A)            \[\frac{43}{29}\lambda \]       

    B)            \[\frac{42}{28}\lambda \]

    C)            \[\frac{9}{4}\lambda \]    

    D)            \[\frac{4}{9}\lambda \]

    Correct Answer: C

    Solution :

                       \[\lambda \,\propto \frac{1}{{{(Z-1)}^{2}}}\]\[\Rightarrow \frac{{{\lambda }_{2}}}{{{\lambda }_{1}}}={{\left( \frac{{{Z}_{1}}-1}{{{Z}_{2}}-1} \right)}^{2}}\]            \[\Rightarrow \frac{{{\lambda }_{2}}}{\lambda }={{\left( \frac{43-1}{29-1} \right)}^{2}}={{\left( \frac{42}{28} \right)}^{2}}\] Þ  \[{{\lambda }_{2}}=\frac{9}{4}\lambda \].


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