Proton , deuton and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton , deuteron and alpha particle are respectively `r_(p), r_(d) and r_(alpha)`. Which one of the following relation is correct?

Options

A. `r_(alpha)=r_(p)=r_(d)`
B. `r_(alpha)=r_(p)ltr_(d)`
C. `r_(alpha)gtr_(d)gtr_(p)`
D. `r_(alpha)=r_(d)gtr_(p)`

Answer

B

Explanation

For charged particle in magnetic field, radius
`r=(mv)/(qB)=(sqrt(2km))/(qB)[ "as" mv =pimpliesK=1/2 mv^(2)=(m^(2)v^(2))/(2m)=p^(2)//2mp=sqrt(2Km)]`
`implies r prop (sqrt(m))/q` or `m_(d)=2m_(p)` and `q_(d)=q_(p), m_(alpha)=4m_(p)`
And `q_(alpha)=2q_(p)impliesr_(p):r_(d):r_(alpha)=(sqrt(m_(p)))/(qp):(sqrt(2m_(p)))/(qP): (sqrt(4m_(p)))/(2q_(p)): 1:sqrt(2):1impliesr_(alpha)=r_(p)ltr_(d)`