An alpha particle and a proton enters in crossed magnetic field with same kinetic energy. find the ratio of their radii. 

Asked by shaileshbhagat82816 | 14th Jun, 2019, 12:29: PM

Expert Answer:

when a charged particle of kinetic energy E, charge q and  mass m  enters magnetic field B
and its direction of motion is perpendicular to that of magnetic field,
 
then we have,   begin mathsize 14px style R space equals space fraction numerator square root of 2 m E end root over denominator B space q end fraction space equals space fraction numerator square root of 2 E end root over denominator B end fraction cross times fraction numerator square root of m over denominator q end fraction end style ....................(1)
where R is radius of circular path.
 
Hence if an alpha particle and a proton  enter with same kinetic energy in crossed magnetic field, then we have
 
begin mathsize 14px style R subscript alpha over R subscript p space equals space fraction numerator begin display style bevelled fraction numerator square root of 4 m end root over denominator 2 q end fraction end style over denominator begin display style bevelled fraction numerator square root of m over denominator q end fraction end style end fraction space equals space 1 end style   ..............................(2)
Hence radius of circular path is same for alpha particle and proton,
because mass of alpha particle 4 times of mass of proton and charge of alpha particle is twice of charge of proton

Answered by Thiyagarajan K | 14th Jun, 2019, 01:51: PM

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