A solid sphere of pure 235U (density 19.0g cm−3) has a radius of 6.0cm. Each fission of a 235U nucleus releases on the average ν=2.5 neutrons. Of all the neutrons produced inside the sphere, the probability that a neutron induces a fresh fission before either escaping or being absorbed non-productively is 0.90.
(i) Calculate the mass of the uranium sphere.
(ii) Taking the effective multiplication factor as k=νPf, where Pf is the probability given above, determine the value of k for this sphere.
(iii) On the basis of the value of k, state clearly whether the sphere is sub-critical, critical, or super-critical, and justify your answer.