Q7 of 47 Page 1

A deuteron and an alpha particle having same momentum are in turn allowed to pass through a magnetic field, acting normal to the direction of motion of the particles. Calculate the ratio of the radii of the circular paths described by them.

Deuteron(+e,2mp)


-particle(+2e,4mp)


Deuteron has charge of +e and mass 2mp where mp is the mass of proton.


-particlehas charge of +2e and mass 4mp.


We know that force on a charged particle due to magnetic field is given by



where, q=charge


v=velocity


B=magnetic field


v and B are perpendicular in this case



Since here because


..........(1)


We can observe the trajectory is circular due to centrifugal force


Fc whose magnitude is given by


...........(2)


Equating 1 and 2



Rearranging we get,



Since momentum p=mv



Now,


For-particle


where q=2e


so,


For Deuteron


where q=e


so,


Now according to question,




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