Current from stream of particles

[jehan60188]

Homework Statement

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?

Homework Equations

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

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 into place.

but I have no idea how to start c

 

[jambaugh]

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

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

 

[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

 

[jambaugh]

*facepalm* duh!

Happens to me all the time ;)