A proton, a deuteron and an q-particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If `r_(p),r_(d)andr_(alpha)` ro denote respectively the radii of the trajectories of these particles then

Options

A. `r_(alpha) = r_(d) gt r_(p)`
B. `r_(alpha) = r_(d) = r_(p)`
C. `r_(alpha) lt r_(d) lt r_(p)`
D. `r_(alpha) = r_(p) gt r_(d)`

Answer

D

Explanation

Radius of the curcular path of a charged particles a magnetic field id given by
`:.(r_(A))/(r_(B))=(sin90^(@))/(sin30^(@))=2orr_(A)=r_(B)orr_(B) < r_(A)" " ( because "kinetic energy",K=(1)/(2)mv^(2))`
For the same value of K and B `:.rprop(sqrtm)/(q)`
`:.r_(p):r_r_(alpha)=(sqrtm_(p))/(qp):(sqrtm_(d))/(qd):(sqrtm_(alpha))/(qalpha)`
`=(sqrtm)/(e):(sqrt2m)/(e):(sqrt4m)/(2e)=1:sqrt2:1`
`impliesr_(alpha)=r_(p) < r_(d)`