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JEE Main & Advanced Physics Photo Electric Effect, X- Rays & Matter Waves Question Bank Critical Thinking

  • question_answer
    The ratio of de-Broglie wavelength of a a-particle to that of a proton being subjected to the same magnetic field so that the radii of their path are equal to each other assuming the field induction vector \[\overrightarrow{B}\] is perpendicular to the velocity vectors of the a-particle and the proton is

    A)            1    

    B)            \[\frac{1}{4}\]

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

    D)            2

    Correct Answer: C

    Solution :

                       When a charged particle (charge q, mass m) enters perpendicularly in a magnetic field  than, radius of the path described by it \[r=\frac{mv}{qB}\Rightarrow mv=qBr\]. Also de-Broglie wavelength \[\lambda =\frac{h}{mv}\] Þ \[\lambda =\frac{h}{qBr}\]\[\Rightarrow \frac{{{\lambda }_{\alpha }}}{{{\lambda }_{p}}}=\frac{{{q}_{p}}{{r}_{p}}}{{{q}_{\alpha }}{{r}_{\alpha }}}=\frac{1}{2}\]


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