A proton and a deuteron both having the same kinetic energy enter perpendicularly in to uniform magnetic field B for motion of proton and deuteron on ciruclar path of radius `R_(p)` and `R_(d)` respectively the correct statement is

Options

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

Answer

A

Explanation

`(mv^(2))=qvB`
for proton `R_(p)=(mv)/(qB)=sqrt(2m_(p)E)/(qB)`
for deuteron `R_(d)=sqrt(2m_(d)E)/(qB)`
`rarr (R_(d))/(R_(p))=sqrt(m_(d))/(m_(p))=sqrt(2)`
`rarr R_(d)=sqrt(2R_(p)`