` 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 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

(c) As `r=(mv)/(qB)` and `K=1/2mv^2`, `r=(sqrt(2mK))/(qB)`
i.e., `rpropsqrtm/q` [for same K and B]
`r_(H+)propsqrt1/1` and `r_(O^(2+))` are equal, So `He^+` and `O^(2+)` will be deflected equally.
(a) Since `(r_(H^+))/(r_(He^+))=(sqrt1//1)/(sqrt4//1)=1/2`,
`r_(H^+)=1/2He^+=1/2r_(O^(2+))`
`H^+` will be deflected most.