Moderating a Neutron In a nuclear reactor, neutrons released by nuclear fission

Question

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=1.009u, where the atomic mass unit, u, is defined as follows: 1u=1.66×1027kg.)

(Part A)

An electron (M=5.49×104u).

(((Express your answer using ((four)) significant figures)))

(Part B)

A proton (M=1.007u).

(((Express your answer using ((one)) significant figure)))

(Part C)

The nucleus of a lead atom (M=207.2u).

(((Express your answer using ((four)) significant figures)))

Explanation / Answer

Let v1 be the initial speed of the neutron

From elastic collision we have the velocity after the collision (of the incoming particle) is

v2 = (ma - mb)/(ma + mb)*v1

Now K = 1/2*m*v^2

Since the mass of the neutron doesn't change then Kf/Ki = v2^2/v1^2

= ((ma - mb)/(ma + mb)/ma)^2

So Kf/Ki(proton) = ((1.009-1.007)/(1.009+1.007))^2 = 9.84x10^-7


and Kf/Ki(lead) = ((1.009-207.2)/(1.009+207.2))^2 = 0.981

b) So the proton is more effective in reducing the K of the neutron               

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