` 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

When the charged particles enter a magnetic field, then a
force acts on the particle which will acts as a centripetal force.
`q upsilonB=(m upsilon^2)/rimplies r=(m upsilon)/(qB)....(i) `
Now, `E=1/2m upsilon^2 implies upsilon=(sqrt(2E))/m....(ii)`
`:. r=m/(qB) sqrt((2E)/m)=(sqrt(2Em))/(qB)=(sqrt(2E))/Bxx(sqrtm)/q`
`implies rprop (sqrtm)/q`
`:. r_H^+ prop (sqrt1)/1, pr_(He^+) prop (sqrt4)/1, r_(O^+) prop (sqrt16)/2`
`implies r_(H^(+)) prop1, r_(He^(+))prop 2, r_(O^+)prop2`
`implies He^(+) and O^(+)` will be deflected
equally.
`H^(+)` will be deflected the most since its
radius is smallest.
`:.` (a),(c) are correct options.