A deuteron and a proton moving with equal kinetic energy enter into to a uniform magnetic field at right angle to the field. If r d and r p are the radii of their circular paths respectively, then the ratio r d r p will be x : 1 where x is _____ .

Step-by-step solution

As we know, radius of circular path followed by charged particle under perpendicular magnetic field is given by, R = m v q B and K E = 1 2 m v 2 Therefore, ⇒ R = 2 m K E q B Then, R ∝ m q ⇒ R d R p = m d m p × q p q d = 2 1 × 1 1 = 2 : 1 Thus, x = 2 .