Please answer all parts Problem 9.39 Moderating a Neutron In a nuclear reactor,

Question

Please answer all parts Problem 9.39 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 ene 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 atormic m unit, u, is defined as follows. 1 u 166 x 10- kg.)

Explanation / Answer

let vi is the initial speed of the neutron.

and vf is the final speed of the neutron.

a) let m1 = 1.009 u

m2 = 5.49*10^-4* u

vf = (m1 - m2)*vi/(m1 + m2)

= (1.009 - 5.49*10^-4)*vi/(1.009 + 5.49*10^-4)

= 0.9989*vi

Kf/Ki = (1/2)*m1*vf^2/((1/2)*m1*vi^2)

= (vf/vi)^2

= 0.9989^2

= 0.9978

B) m2 = 1.007 u

vf = (m1 - m2)*vi/(m1 + m2)

= (1.009 - 1.007)*vi/(1.009 + 1.007)

= 0.000992*vi

Kf/Ki = (1/2)*m1*vf^2/((1/2)*m1*vi^2)

= (vf/vi)^2

= 0.000992^2

= 9.84*10^-7  

C)  

m2 = 207.u u

vf = (m1 - m2)*vi/(m1 + m2)

= (1.009 - 207.2)*vi/(1.009 + 207.2)

= -0.9903*vi

Kf/Ki = (1/2)*m1*vf^2/((1/2)*m1*vi^2)

= (vf/vi)^2

= 0.9903^2

= 0.981

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