A proton carrying `1 MeV` kinetic energy is moving in a circular path of radius `R` in unifrom magentic field. What should be the energy of an `alpha-` particle to describe a circle of the same radius in the same field?

Options

A. `1 MeV`
B. `4 MeV`
C. `0.5 MeV`
D. `1.5 MeV`

Answer

A

Explanation

`R = (mv)/(q_(B)) = (sqrt(2mK))/(q_(B))`
`:' R_(alpha) = R_(p) :. (4m_(alpha) k_(a))/(q_(a)^(2) B^(2)) = (4m_(p) K_(p))/(q_(p)^(2) B^(2))`
`implies (4m_(p) k_(alpha))/(4e^(2)) = (m_(p) (1 MeGV))/(e^(2)) implies K_(alpha) = 1 MeV`