Question

an alpha particle and a proton are accelerated through a same potential diffrence find the ratio (va/vp) of velocities acquired by two particles?​

Answer 1

Answer:

Let's recall a couple of important properties of proton and an alpha particle

mass of proton = 1u and mass of alpha particle=4u

charge on proton=e and charge on alpha particle=2e

now, for charged particle moving in a uniform potential field the following relation holds true

the kinetic energy acquired by then would be equal to the electric potential energy, thus

(1/2)mv2 = qV

or momentum

p = mv = (2qVm)1/2

here m and v are mass and velocity of the particle and q and V are the charge of the particle and the electric potential experienced.

so, for a proton the momentum will be

p1 = (2q1Vm1)1/2 = [2(e)V.(1u)]1/2

similarly for an alpha particle

p2 = (2q2Vm2)1/2 = [2.(2e)V.(4u)]1/2

so, the ratio will be

p1/p2 = [2(e)V.(1u)]1/2 / [2.(2e)V.(4u)]1/2

or

p1/p2 = √(1/8)

Answer 2

Answer:

mass of proton=1u and mass of alpha=particle=2e

charge of proton=e and charge of alpha particle=2e