A proton a deuteron and an `alpha` - particle having the same kinetic energy are moving in circular trajectories in a constant magnetic of the trajectories of these particle, then

Options

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

Answer

B

Explanation

Radius of circular path followed by a charged particle in a uniform magnetic field (B) is given
`r=(mv)/(qB)=p/(qB)=(sqrt(2mK))/(qB)`
For electron `r_(e)=(sqrt(2m_(e)K))/(eB)`, for proton `r_(p)=(sqrt(2m_(p)K))/(eB)`
For a particle `r_(alpha)=(sqrt(2m_(alpha)K))/(2eB)=(sqrt(2(4m_(p)K)))/(2eB)=(sqrt(2m_(p)K))/(eB), ` As `m_(p)gtm_(e),` so `r_(alpha)=r_(p)gtr_(e)`