In a nuclear reactor 253-U undergoes fission liberating 200 Mev of energy the reaction has 10% efficiency and produces - Physics - Nuclei

Question

In a nuclear reactor 253-U undergoes fission liberating 200 Mev of
energy the reaction has 10% efficiency and produces 1000 MW power
If the reactor has to work for 10 years, find the total mass of
uranium required

options :-
(a) 2 64 * 10 4 Kg
(b) 3 84 * â€‹ 10 4 Kg
(c) 4 75 * 10 4 Kg
(d) 5 21 10 4 Kg

Sayantan · Accepted Answer

Dear Student,

In 10 years we have 87600 hrs

Thus Total Energy= 1000 * 87600 MWh

Each unit of U-253 produces 10% of 200 Mev= 20 MeV =
~9×10-22 MWh

or No of Units of U-253 used =
87600×10009×10-22⇒9
7×1028  units

Mass of 1 unit of u-253= 253×1 67×10-27 kg

or, Total Mass used = ( mass of 1 unit X toatl no of units )

9 7×1028×253×1 6×10-27⇒3
94×104 Kgans(b)

Regards