# Current from stream of particles

1. Feb 19, 2012

### jehan60188

1. The problem statement, all variables and given/known data
An α (Alpha) particle consists of two neutrons and two protons bound together into a single particle with a charge of +2e. We normally measure the kinetic energy of such particles in millions "electron volts" or MeV. (1 eV = 1.6 X 10-19J).

Assume a steady stream of α particles travels with a constant energy of 20 MeV and carries a current of 2 μA.

a) If the beam is directed perpendicular to a plane target, how many α's will strike this target in 5 seconds?
b) At any given instant, how many α's are in a 15 cm length of the beam?
c) Through what electrical potential diffence [sic] is it necessary to accelerate each α from rest to bring it to the energy of 20 MeV?

2. Relevant equations

v = ir
r = p*l/a
E = .5*mv^2

3. The attempt at a solution

I have the velocity of the particles.
But I don't know how many particles go through a point in 1 second.

if I can get a, b falls in to place.

but I have no idea how to start c

2. Feb 19, 2012

### jambaugh

That is what the current gives you. 1 Ampere = 1 Coulomb/second

3. Feb 19, 2012

### jehan60188

*facepalm* duh!

the current on the stream is 2 uA, so we have 2*10^-6 *1/(2e) := N1 particles going through a point
the unit is Particles/S
multiply that by 5, to get the number of particles passing through a point in 5 seconds

the velocity is about 30000000 m/s. so, it takes .15/3e7 seconds to cover 15 cm
in .15/3e7 seconds, there are (.15/3e6)*(N1) = 30287 particles going through a point

lastly, to bring a particle to V = U/q, so V = 20 MeV / (2eV) = 10000000

4. Feb 20, 2012

### jambaugh

Happens to me all the time ;)