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JEE Main & Advanced Physics EM Waves Question Bank Mock Test - Electromagnetic Waves and Dual Nature

  • 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 paths are equal to each other assuming the field induction vector \[\vec{B}\] 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 :

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


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