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BCECE Medical BCECE Medical Solved Papers-2009

  • question_answer
    An \[\alpha \]-particle and a deuteron projected with equal kinetic energies describe circular paths of radii \[{{r}_{1}}\] and \[{{r}_{2}}\] respectively in a uniform magnetic field. The ratio \[{{r}_{1}}/{{r}_{2}}\] is

    A)  1                

    B)  2

    C)  \[\frac{1}{\sqrt{2}}\]              

    D)  \[\sqrt{2}\]

    Correct Answer: D

    Solution :

    Given, \[{{K}_{\alpha }}={{K}_{d}}=K,\,{{q}_{\alpha }}=q={{q}_{d}},\,{{m}_{\alpha }}=2{{m}_{d}}\] For\[\alpha \]-particles \[{{r}_{1}}=\frac{\sqrt{2{{m}_{1}}K}}{Bq}\] For deuteron \[{{r}_{2}}=\frac{\sqrt{2{{m}_{2}}K}}{Bq}\] \[\therefore \] \[\frac{{{r}_{1}}}{_{2}}=\sqrt{2}\] \[\left( \because {{m}_{2}}=\frac{{{m}_{1}}}{2} \right)\]


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