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In a nuclear reaction 235 U undergoes fission liberating 200 MeV of energy. The reactor has a 10% efficiency and produces 1000 MW power. If the reactor is to function for 10 years, find the total mass of uranium required.

In a nuclear reaction 235U undergoes fission liberating 200 MeV of energy. The reactor has a 10% efficiency and produces 1000 MW power. If the reactor is to function for 10  years, find the total mass of uranium required. 

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
6 years ago
Hello Student,
Please find the answer to your question
The formula for η of power will be
η = P­out / Pin
∴ Pin = Pout / η = 1000 x 106 / 0.1 = 1010 W
Energy required for this power is given by
E = p x t
= 1010 x 86, 400 x 365 x 10
= 3. 1536 x 1018 J
200 x 1.6 x 10-13 J of energy is released by 1 fission
∴ 3.1536 x 1018 J of energy is released by
3.1536 x 1018 / 200 x 1.6 x 10-13 fission
= 0.9855 x 1029 fission
= 0.985 x 1029 of U235 atoms.
6.023 x 1023 atoms of Uranium has
235 x 0.9855 x 1029 / 6.023 x 1023 g = 38451 kg
Thanks
Navjot Kalra
askIITians Faculty

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