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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 31

  • question_answer
    An \[\alpha \]-particle and a proton are fired through the same magnetic fields which is perpendicular to their velocity vectors. The \[\alpha \]-particle and proton move such that radius of curvature of their path is same, then \[\frac{{{\lambda }_{\alpha }}}{{{\lambda }_{\rho }}}=\]

    A) \[\frac{1}{2}\]  

    B)        \[\frac{2}{1}\]

    C) \[\frac{1}{4}\]              

    D)        \[\frac{4}{1}\]

    Correct Answer: A

    Solution :

    [a] radius of curvature in magnetic field \[r=\frac{mV}{qB}\]               ??...,(1) And \[\lambda =\frac{h}{mV}\]      ??....(2)             \[\therefore \] From (1) & (2) \[\frac{{{\lambda }_{\alpha }}}{{{\lambda }_{p}}}=\frac{{{q}_{p}}{{r}_{p}}}{{{q}_{\alpha }}{{r}_{\alpha }}}=\frac{1}{2}\]        


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