` H^(+), He^(+) and O^(++)` all having the same kinetic energy pass through a region in which there is a uniform magnetic field perpendicular to their velocity . The masses of ` H^(+), He^(+) and O^(2+)` are `1 amu, 4 amu and 16 amu` respectively . Then

Options

A. `H^(+)` will be deflected the most
B. `O^(2+)` will be deflected the most
C. `He^(+_` and O^(2+)` will be deflected equally.
D. All will be deflected equally

Answer

A, C

Explanation

`K=1/2 mv^(2) implies v=sqrt(2K//m), r=(mv)/(qB)=(sqrt(2mK))/(qB)`
`r_(H^+)=sqrt(2mK((eB), r_(He^+))=(sqrt(2(4m)K))/(eB))=2r_(H^+)`
`r_(O^(2+)) = (sqrt(2(16m)K))/(2eB)=2r_(H^+)`
Lasser the radius, more will be the deflection.