Question

Assuming that about 200 MeV energy is released per fission of ₉₂U²³⁵ nuclei,
would be the mass of U²³⁵ consumed per day in the fission of reactor of power 1 MW
approximately?

a. 10 kg b. 100 kg c. 1 g d. 10⁻² g

Answer 1

1 eV = 1.602×10⁻¹⁹ J
Energy released from fission of 1 nucleus = 200 MeV
200 MeV = 200×10⁶×1.602×10⁻¹⁹ J = 3.204×10⁻¹¹ J

Energy released from 1 mole Uranium = 6.022×10²³×3.204×10⁻¹¹ J
                                                        = 1.929×10¹³ J
                                                        = 1.929×10⁷ MJ
Power = 1MW = 1 MJ per second
In  1 day, energy produced = 24×3600×1 MJ = 86400 MJ

1mole produces = 1.929×10⁷ MJ
86400 mJ will be produced = 86400/1.929×10⁷ = 0.004479 mole
mass of 1 mole Uranium = 235g
mass of 0.004479 mole Uranium = 235×0.004479 = 1.052 g ≈ 1g

So (c) is the correct option.