Question

A, proton, a deuteron and α-an particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If rp, rd and denote respectively the radii of trajectories of these particles, then

(a) rα = rp < rd

(b) rα > rd > rp

(c) rα = rd > rp

(d) rp = rd = rα

Answer 1

The correct option (a) rα = rp < rd

Explanation:

We r = [√(2Ekm)/9B]

Where Ek is kinetic energy,

m is mass

q is charge.

Here B is same & KE is also Equal

∴ r ∝ (√m/q)

If mp, qp : mass and charge on proton then

For deuteron, md = 2mp and qd = qp

For ∝ particle, mα = 4mp and qα = 2qp

∵ rp : rd : rα = (√mp/qp) : [√(2mp)/(qp)] : [√(4mp)/(2qp)]

rp : rd : rα = (√mp/qp) = [(√2 ∙ √mp)/(qp)] = [(√mp) / (qp)]

∴ hence rp = rα

and rd > rp and rd > rα

i.e. rp = rα < rd