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JEE Main & Advanced Physics Nuclear Physics And Radioactivity Question Bank Graphical Questions

  • question_answer
    The figure shows a graph between \[\ln \left| \frac{{{A}_{n}}}{{{A}_{1}}} \right|\] and ln|n|, where \[{{A}_{n}}\] is the area enclosed by the nth orbit in a hydrogen like atom. The correct curve is

    A)            4

    B)            3

    C)            2

    D)            1

    Correct Answer: A

    Solution :

                       \[{{A}_{n}}=\pi r_{n}^{2}\]Þ \[\frac{{{A}_{n}}}{{{A}_{1}}}={{\left( \frac{{{r}_{n}}}{{{r}_{1}}} \right)}^{2}}={{\left( \frac{n}{1} \right)}^{4}}\]          \[(\because {{r}_{n}}\propto {{n}^{2}})\] Taking loge both the side  \[{{\log }_{e}}\frac{{{A}_{n}}}{{{A}_{1}}}=4\,{{\log }_{e}}(n)\] Comparing it with y = mx + c, graph (4) is correct.


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