Question

EXAMPLE 8.11 MODERATING FISSION NEUTRONS IN A NUCLEAR REACTOR LUTION The fission of uranium nuclei in a nuclear reactor produces high- speed neutrons. Before such neutrons can efficiently cause addi- tional fissions, they must be slowed down by collisions with nuclei in the moderator of the reactor. The first nuclear reactor (built in 1942 at the University of Chicago) used carbon (graphite) as the moderator. Suppose a neutron (mass 1.0 u) traveling at 26 X 10' m/s undergoes a head-on elastic collision with a carbon nucleus (mass 12 u) initially at rest. Neglecting external forces during the collision, find the velocities after the collision. (1 u is e atomic mass unit, equal to 1.66 X 10kg.) 8.26 Our sketch for this problem. Vn2x = 2.6x 10 m/s Before no- © en mm = 1.0 u me = 12u After After con ©**-? EXECUTE: You can do the arithmetic. (Hint: There's no reason to

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Answer 1

Onix = 2.6x107 ms Before no @ Mnalou Me = 12u After Vnzx22 2x2 lu = 1.66 x 10-27 kg. elastic and kinetic collision, momentum conserved. energy is Using momentum conservation, My Voix & me xo = Onzxt me vc 2x 12mm Ucar - mr m = mndnin 12 Ucar - Unax = Unix - w Using kindergy conservation, I'm into = I'm den & verme den a n + 12 vex - (2) Since anos = 12 Nean - Wein So, die eine = ( 12 Verx - Um + 12 V 2x othing - 144 vir ou + vystok - 24 Negli orta + 12 V. 2x 156 vier - 24 Vega Venice = 0 12 Vax (130n - 2 dine] =0

Vear - 2 un 13 2x2.6 x 107 -0.4x10 m/s 13 So, vean & o or oux 10 m/s 2 - 12 Vo2 - Van for vero non – 2.6*10 m/s for voru ar 10, Unax = (12x014 – 2.6) x 10 m/s Nimam = 2.2 x107 mis
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