Moderating a Neutron In a nuclear reactor, neutrons released...

Moderating a Neutron In a nuclear reactor, neutrons released by nuclear fission must be slowed down before they can trigger additional reactions in other nuclei. To see what sort of material is most effective in slowing (or moderating) a neutron, calculate the ratio of a neutron's final kinetic energy to its initial kinetic energy, Kf/Ki, for a head-on elastic collision with each of the following stationary target particles. (Note: The mass of a neutron is m = 1.009 u, where the atomic mass unit, u, is defined as follows: 1 u = 1.66 x 10^-27 kg. ) Part A An electron (M = 5.49 × 10^-4 u) . Express your answer using four significant figures. Kf / Ki = Part B A proton (M = 1.007 u) . Express your answer using one significant figure. Kf / Ki = Part C The nucleus of a lead atom (M = 207.2 u) . Express your answer using four significant figures.

Transcript

00:01 All right, so before you is a pretty horrific looking series of algebraic equations, but i'm going to explain how they relate to this problem.

00:09 So we want to evaluate the ratio of the final kinetic energy of a neutron to its initial kinetic energy.

00:15 So that's this expression right here.

00:19 And we're going to do so by noting that for an elastic collision, kinetic energy, the total kinetic energy is conserved and the total momentum is concerned.

00:27 So the total kinetic energy is equal to just...

00:30 Just the initial kinetic energy of the neutron, because initially all these target particles are at rest.

00:36 Anywhere you see a t -subscript in some of these equations, that means target, so it's just a particle that is being hit with the neutron.

00:45 So what we have is this first statement that says the initial kinetic energy of the neutron is equal to the final kinetic energy of the system.

00:54 So this is the final kinetic energy of the neutron plus the kinetic energy of the target particle.

00:59 Now we don't know v -prime, we don't know v -t, so this alone doesn't tell you a whole lot.

01:06 But we do know that the momentum conservation also applies.

01:10 So the initial momentum, which is just the momentum of the neutron, is equal to the final momentum of the neutron.

01:16 That's the mv prime plus the momentum of the target particle.

01:19 Now, since this is equal to mv, if i square this and divide by 2m, that is going to be the initial kinetic energy of the system.

01:32 And so i can equate that then with this final kinetic energy of the system right here and do lots and lots and lots of simplifications and cancellations and things like that.

01:44 And ultimately what we arrive at is an expression right here for the ratio of the kinetic energy of a particle of the neutron to its final or ratio of the final kinetic energy to the initial kinetic energy.

02:02 All right, so it's one minus the mass of the target particle divided by the mass of the neutron...

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