How Do You Calculate Alpha Particles' Impact and Behavior in a Current Problem?

[xerox2ooo]

Can anyone give some hints on this problem?
This is about current and resistance.

Problem: A steady beam of alpha particles (q= +2e) traveling with constant kinetic energy 20MeV carries a current of 0.25 micro ampere.
(a) If the beam is directed perpendicular to a plane surfece, how many alpha particlees strike the surface in 3.0s?
(b) At any instant, how many alpha particles are there in a given 20 cm length of the beam?
(c) Through what potential difference was it necessary to accelearte each alpha particle from rest to bring it to an energy of 20 MeV?

Thanks,

 

[Chen]

(a) Current is defined as the charge that flows through a cross section of the conductor in a given time frame:
$$I = \frac{dq}{dt}$$
So to find the number of charges that go through the cross section (or in our case, hit the perpendicular surface), just rearrange that equation:
$$dq = Idt = 0.25\mu A3s$$
Remember that each particle carries a charge of +2e so you need to divide the result by two to get the number of particles.

(c) The fact that the particles have 20 MeV of energy indicates the amount of energy that has gone into accelerating them. The energy that is given to a particle as it is accelerated by a potential difference is $$E = qV$$. You have the energy, you have the charge of each particle, you can find the potential difference.

Gotta think a bit about (b), be right back...

 

[Chen]

Ok, for (b) you can find the velocity of the particles, right? You know their energy, and the mass of each alpha particle is 4 times the mass of a proton (it has two protons and two neutrons). Once you have the velocity of the particles, you can find how much time it would take on of them to cover a distance of 20cm:
$$\Delta t = \frac{x}{v}$$
Now just plug that into the equation I used already above:
$$\Delta q = I\Delta t = I\frac{x}{v}$$
(Again, divide the result by two to get the number of particles)