A proton and an alpha particle both enters a region of uniform magnetic field B, moving at right angles to the field B. If the radius of circular orbits for both the particles is equal and the kinetic energy acquired by proton is `1 MeV`, the energy acquired by the alpha particles will be :

Options

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

Answer

A

Explanation

Radius in magnetic field
`R=(mv)/(qB)=(sqrt(2mE))/(qB)`
`E=(q^(2)B^(2)R^(2))/(2m)`
for proton
`E_(1)=(e^(2)xxB^(2)xxR^(2))/(2xxm_(p))`
for `alpha`-particle
`E_(2)=((2e)^(2)xxB^(2)xxR^(2))/(2xx4m_(P))`
`thereforeE_(1)=E_(2)`