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A nuclear reactor contains nuclei that fission when bombarded by slow neutrons. The fission reaction produces fast neutrons which need to be moderated (i.e. slowed down) in collisions before they can cause further fissions. In this problem we consider a reactor which uses graphite (i.e. carbon) as moderator. Assume the neutron and carbon nuclear masses are 1.67 ¡Ñ 10¡V27 kg and 20.0 ¡Ñ 10¡V27 kg respectively. Consider a head-on collision between a neutron with speed 15 Mm/s and a stationary carbon nucleus.

(i) Calculate the speed of the neutron after the collision
(ii) Calculate the speed of the carbon nucleus after the collision

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