Q4. Reactor Theory: A homogeneous fuel-moderator mixture with the following properties is available to make a critical reactor.
δ = 0.00189 cm
d = 0.00142 cm
D = 0.84 cm
v = 2.06
p = 1600 kg/m³
The possible reactor shapes considered are:
i) Cube of sides a x a x a
ii) Finite cylinder with diameter = height
iii) Sphere of radius R
By using the criticality condition and proper geometric buckling for each reactor shape, determine the shape and dimensions of the reactor that would require the minimum amount of the fuel-moderator mixture. How many kg of this fuel-moderator mixture would be required for criticality?