`H^(+), He^(+)` and `O^(2+)` ions having same kinetic energy pass through a region of space filled with uniform magnetic field B directed perpendicular to the velocity of ions. The masses of the ions
`H^(+), He^(+)` and `O^(2+)` are respectively, in the ratio `1:4:16`. As a result

Options

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

Answer

A,C

Explanation

`{:(,H^(+),He^(+),O^(2+)),((q)/(m),(1)/(1),(1)/(4),(2)/(16)),((q)/(sqrtm),1,(1)/(2),(2)/(4)):}`
`R=(mv)/(qB)`
`=sqrt(2km)/(qB)`
`=sqrtm/q sqrt(2k)/B`
`R_(He^(+))=R_(O^(2+))`
`Rprop(1/q)/sqrtm`
`R_(H^(+)):R_(He^(+)):R_(O^(2+))=1:2:2`