A proton and a deuteron both having the same kinetic energy, enter perpendicularly into a uniform magnetic field `B`. For motion of proton and deuteron on circular path or radius `R_(p)` and `R_(d)` respectively, the correct statement is

Options

A. `R_(d)=sqrt2R_(p)`
B. `R_(d)=R_(p)//sqrt2`
C. `R_(d)=R_(p)`
D. `R_(d)=2R_(p)`

Answer

A

Explanation

`(mv^(2))/(R)=qvB.` For proton `R_(p)=(mv)/(qB)=sqrt(2m_(p)E)/(qB)`
and for deuteron `R_(d)=(sqrt(2m_(d)E))/(qB)`
`implies (R_(d))/(R_(p))=sqrt(m_(d)/(m_(p)))=sqrt(2) impliesR_(d)=sqrt(2)R_(p)`