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JEE Main & Advanced AIEEE Solved Paper-2012

  • question_answer
    Proton, Deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively \[{{r}_{p}},{{r}_{d}}\] and \[{{r}_{\alpha }}\]. Which one of the following relation is correct?   AIEEE  Solved  Paper-2012

    A) \[{{r}_{\alpha }}={{r}_{p}}={{r}_{d}}\]                       

    B) \[{{r}_{\alpha }}={{r}_{p}}<{{r}_{d}}\]

    C) \[{{r}_{\alpha }}>{{r}_{d}}>{{r}_{p}}\]                       

    D) \[{{r}_{\alpha }}={{r}_{d}}>{{r}_{p}}\]

    Correct Answer: B

    Solution :

                 \[r=\frac{\sqrt{2mE}}{3q}\]              \[r\propto \frac{\sqrt{m}}{q}\]              \[{{r}_{p}}=k\frac{\sqrt{m}}{q}\]              \[{{r}_{D}}=k\frac{\sqrt{2m}}{q}\]              \[{{r}_{\alpha }}=k\frac{\sqrt{4m}}{2q}=\frac{k\sqrt{m}}{q}\]              \[\therefore \,\,\,{{r}_{p}}={{r}_{\alpha }}<{{r}_{d}}\].


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