Electron and proton of equal momentum enter a uniform magnetic field normal to the lines of force. If the radii of curvature of circular paths be `r_(e ) and r_(p)` respectively, then

Options

A. `(r_(e ))/(r_(p))= (1)/(1)`
B. `(r_(e ))/(r_(p)) = (m_(p))/(m_(e))`
C. `(r_(e))/(r_(p)) = sqrt(m_(p)//m_(e))`
D. `(r_(e))/(r_(p)) = sqrt(m_(e )//m_(p))`

Answer

A

Explanation

Radius of circular path travelled by electron `r_(e ) = (p_(e))/(Be)`, radius of circular path travelled by proton `r_(p) = (p_(m))/(Be)`
As the momentum of `p_(m) and p_(e )` are equal and magnitude of charge of electron and proton are equal along with same magnetic field `r_(p) = r_(e) or r_(p)//r_(e)= 1//1`