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In a nuclear reactor an element X decays to a radio active element Y at a constant rate $10^{15}$ atoms per sec. Each decay releases $100 M e V$ energy. Half life of Y equals T and decays to a stable product Z. Each decay of Y releases $50 M e V .$ All energy released inside the reactor is used to produce electricity at an efficiency of 25%. Calculate electrical power in kW generated in the reactor in steady state.

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Detailed Solution

At steady state energy released per sec

$= η \times r (E_{1} + E_{2}) η = 25 % r = 10^{15} E_{1} = 100 \times 10^{6} \times 1.6 \times 10^{- 19} = 1.6 \times 10^{- 11} J E_{2} = 50 \times 10^{6} \times 1.6 \times 10^{- 19} = 0.8 \times 10^{- 11} J$

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