JEE Main & Advanced Sample Paper JEE Main Sample Paper-5

  • question_answer
    The electron in a H-atom makes transition\[{{n}_{1}}\to {{n}_{2}}\]where, \[{{n}_{1}}\]and\[{{n}_{2}}\]are principal quantum numbers of two states. Assume the Bohr model to be valid. The time period of the electron in the initial state is eight times the final state. Then, the possible value of\[{{n}_{1}}\]and\[{{n}_{2}}\]are

    A)  \[{{n}_{1}}=4;{{n}_{2}}=1\]        

    B)  \[{{n}_{1}}=8,{{n}_{2}}=2\]

    C)  \[{{n}_{1}}=6,{{n}_{2}}=2\]                        

    D)  \[{{n}_{1}}=4,{{n}_{2}}=2\]

    Correct Answer: D

    Solution :

     Time period\[=\frac{\text{circumference}}{\text{velocity}}=\frac{2\pi r}{v}\] \[\therefore \]\[T\propto r/v\] Now, radius i.e., \[r\propto \frac{{{n}^{2}}}{Z}\]and velocity i.e., \[v\propto \frac{Z}{n}\] \[\therefore \]\[T\propto \frac{{{n}^{3}}}{{{z}^{2}}}\]for\[Z=1,T\propto {{n}^{3}}\] For given case\[{{T}_{1}}=8{{T}_{2}}\] \[\therefore \]\[{{n}_{1}}=2{{n}_{2}}\] So, option [d] satisfies the given condition.

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