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BCECE Engineering BCECE Engineering Solved Paper-2012

  • question_answer
    If the ratio of radii of nuclei \[_{\text{13}}^{\text{27}}\text{Al}\]and \[_{\text{52}}^{\text{A}}\text{X}\]is 3 : 5, then the number of neutrons in the nuclei of X will be

    A)  13                         

    B)         52

    C)  100                       

    D)         73

    Correct Answer: D

    Solution :

    By using the relation, \[r\propto {{A}^{1/3}}\] \[\frac{{{r}_{1}}}{{{r}_{2}}}={{\left( \frac{{{A}_{1}}}{{{A}_{2}}} \right)}^{1/3}}\] \[\frac{3}{5}={{\left( \frac{27}{A} \right)}^{1/3}}\] \[\frac{27}{125}=\frac{27}{A}\] \[A=125\]           So, number of nuclei in atom                 \[X=A-52=125-52=73\]


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