The mass of a carbon nucleus is approximately 12 times the mass of a neutron. 

(a) Use the results of Problem 128 to show that after N head-on collisions of a neutron with carbon nuclei at rest, the energy of the neutron is approximately 0.716^NE₀, where E₀ is its original energy. Neutrons emitted in the fission of a uranium nucleus have an energy of about 2 MeV. For such a neutron to cause the fission of another uranium nucleus in a reactor, its energy must be reduced to about 0.02 eV. 

(b) How many head-on collisions are needed to reduce the energy of a neutron from 2 MeV to 0.02 eV, assuming elastic head-on collisions with stationary carbon nuclei?

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K (m M)2 m/ M)2