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JEE Main & Advanced Sample Paper JEE Main Sample Paper-25

  • question_answer
    An electron is moving in an orbit of a hydrogen atom form which there can be a maximum of six transition. An electron is moving in an orbit of another hydrogen atom from which there can be a maximum of three transition. The ratio of the velocities of the electron in these two orbits is :

    A)  \[\frac{1}{2}\]                                     

    B)  \[\frac{2}{1}\]

    C)  \[\frac{5}{4}\]                         

    D)  \[\frac{3}{4}\]

    Correct Answer: D

    Solution :

    Number of spectrical lines obtained due to transition of electrons from n^ orbit to lower orbit is given by \[N=\frac{n(n-1)}{2}\] Case-I: \[6=\frac{{{n}_{1}}({{n}_{1}}-1)}{2}\,\Rightarrow \,{{n}_{1}}=3\] Case-II: \[3=\frac{{{n}_{2}}({{n}_{2}}-1)}{2}\Rightarrow {{n}_{2}}=3\] Velocity of electron in hydrogen atom in nth orbit \[{{v}_{n}}\propto \,\frac{1}{n}\Rightarrow \,\frac{{{v}_{n}}}{{{v}_{n}}}=\frac{{{n}_{2}}}{{{n}_{1}}}\,\Rightarrow \,\frac{{{v}_{6}}}{{{v}_{3}}}\,=\frac{3}{4}\]


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