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Q.

A U²³⁵ nuclear reactor generates energy at rate of 3.70 × 10⁷J/s. Each fission liberates 185 MeV useful energy. If the reactor has to operate for 144 × 10⁴ s, then the mass of the fuel needed is
(Assume Avogadro's number = 6 × 10²³ mol^–1, 1eV = 1.6 × 10^–19J)

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a

1.31 kg

b

70.5 kg

c

13.1 kg

d

0.705 kg

answer is B.

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Detailed Solution

$\begin{array}{l} P = \frac{NE}{t}; N = \frac{Pt}{E}; \frac{m}{M} = \frac{N}{N_{A}}; m = \frac{MN}{N_{A}} \\ m = \frac{M}{N_{A}} \times \frac{Pt}{E} \\ m = \frac{235 \times 3 .7 \times 10^{7} \times 144 \times 10^{4}}{6 .023 \times 10^{23} \times 185 \times 1 .6 \times 10^{- 13}} \\ m = 0 .702 kg \end{array}$

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A U235 nuclear reactor generates energy at rate of 3.70 × 107J/s. Each fission liberates 185 MeV useful energy. If the reactor has to operate for 144 × 104 s, then the mass of the fuel needed is(Assume Avogadro's number = 6 × 1023 mol–1, 1eV = 1.6 × 10–19J)