` 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

KEY CONCEPT: When the charged particles enter a magnetic field then a force acts on the particle which will act as a centripetal force . We know that when kinetic energy and magnetic field are equal then
` r prop (sqrt(m))/(q)`
` r_(H^(+)) prop (sqrt(1))/(1) , r_(He^(+)) prop(sqrt(4))/(1), r_(0^(++)) prop (sqrt(16))/(2)`
rArr ` r_(H^(+) prop 1 , r_(He^(+) prop 2, r_(0^++)) prop 2`
`He^(+) and O^(++)` will be deflected equally.
`H^(+) ` will be deflected the most since its radius is smallest.