Physics - Modern Physics Question with Solution | TestHub

The reactor produces 1000 MW power or 109J/s. The reactor is to function for 10 yr. Therefore, total energy which the reactor will supply in 10 yr is

E = (power) (time)

= (10⁹J/s) (10 x 365 x 24 x 3600s)

= 3. 1536 x 10¹⁷J

But since the efficiency of the reactor is only 10%, therefore actual energy needed is 10 times of it or 3. 1536 x${10}^{18}$J. One uranium atom liberates 200 MeV of energy or 200 x 1. 6 x${10}^{-13}$J or 3. 2 x${10}^{-11}$J of energy. So, number of uranium atoms needed are

$\genfrac{}{}{0.1ex}{}{3.1536\times 10^{18}}{3.2\times 10^{-11}}=0.9855\times 10^{29}$

or number of kg - moles of uranium needed are

$n=\genfrac{}{}{0.1ex}{}{0.9855\times 10^{29}}{6.02\times 10^{26}}=163.7$

Hence, total mass of uranium required is

m = (n)M

or = (163. 7) (235) kg

or m = 38470 kg

or m = 38470 kg