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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2010

  • question_answer
    An electron is moving in an orbit of a hydrogen atom from 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 spectral lines obtained due to transition of electrons from nth orbit to lower orbit is,                 \[N=\frac{n(n-1)}{2}\] I case     \[6=\frac{{{n}_{1}}\,({{n}_{1}}-1)}{2}\] \[\Rightarrow \]               \[{{n}_{1}}=4\] II case   \[3=\frac{{{n}_{2}}({{n}_{2}}-1)}{2}\] \[\Rightarrow \]               \[{{n}_{2}}=3\] Velocity of electron in hydrogen atom in nth orbit                 \[{{v}_{n}}\propto \frac{1}{n}\]                 \[\frac{{{v}_{n}}}{v{{'}_{n}}}=\frac{{{n}_{2}}}{{{n}_{1}}}\] \[\Rightarrow \]               \[\frac{{{v}_{6}}}{{{v}_{3}}}=\frac{3}{4}\]


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