In a nuclear reaction 235 U undergoes fission libe

Question

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.

Navjyot Kalra · Accepted Answer

Hello Student,

Please find the answer to your question

The formula for η of power will be

η = P_out / P_in

∴ P_in = P_out / 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
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