The fission of uranium nuclei in a nuclear reactor produces high speed neutrons. Before a neutron can trigger additional fissions, it has to be slowed down by collisions with carbon nuclei in the moderator of the reactor. Suppose a neutron with mass of 1.0u travelling at 2.0x107m/s undergoes a head-on elastic collision with a carbon nucleus with mass of 12u initially at rest. Calculate the velocities of the neutron and carbon after the collision.
Let us write the conservation of momentum law:
Due to elastic collision, the energy is conserved, so
So we have a system of equations
We solve these equation by substituting into the second equation and get .