Question

A proton deuteron and an alpha particle are accelerated by same potential enter in uniform magnetic field perpendicularly. What is the ratio of radii of circular path respectively

Answer 1

Answer:THE ANSWER TO THIS QUESTION IS 1:√2:√2 FOR RADIUS OF PROTON : DUETERON : ALPHA PARTICLE

Explanation:

In order to solve this question

particle                           mass                   charge

proton                            m                           +e

deuteron                       2m                          +e

alpha particle                4m                          +2e

Now force due to magnetic field=Bqv

where B=magnetic field

            q=charge

            v=velocity in the field

this is balanced by centripetal force in the field =mv^2/r

where r=radius

Bqv=mv^2/r

r=mv/Bq

therefore r∝mv/q(as B is same)→1

now for finding v using the fact that they are accelerated through the same field

Vq=0.5mv^2 (Energy balance the energy under same potential is converted to kinetic)

As V is same v∝√(q/m)

from 1 r∝(m×√(q/m))/q⇒r∝√(m/q)

therefore r1:r2:r3=1:√2:√2