Canadian nuclear reactors use heavy water moderators in which elastic collisions

Question

Canadian nuclear reactors use heavy water moderators in which elastic collisions occur between the neutrons and deuterons of mass 2.0 u. Part A What is the speed of a neutron, expressed as a fraction of its original speed, after a head-on, elastic collision with a deuteron which is initially at rest? Part B What is its kinetic energy, expressed as a fraction of its original kinetic energy? PartC How many such successive collisions will reduce the speed of a neutron to 1/1.77 times 10^5 of its original value?

Explanation / Answer

a) speed of neutron = (2u - 1u) / (2u + 1u)

= 1/3 = 0.333

b) Kinetic energy is directly propotional to square of velocity

KE = (0.3332) = 0.111 = 1/9

c)After N collisions, velocity is reduced by

(1/3)N = 1/ 177000

N = ln (177000) / ln 3

N = 10.99 = 11

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