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In a nuclear reactor an element $\mathrm{X}$ decays to a radio active element $\mathrm{Y}$ at a constant rate $10^{15}$ atoms per sec. Each decay releases $100\, \, \mathrm{MeV}$ energy. Half life of $Y$ equals $T$ and decays to a stable product $Z$ . Each decay of $Y$ releases $50\, \, \mathrm{MeV}$ . All energy released inside the reactor is used to produce electricity at an efficiency of $25 \%$ . The electrical power in kw generated in the reactor in steady state is:
Option: 1
4

Option: 2
5

Option: 3
6

Option: 4
7

Answers (1)

best_answer

At steady state energy released per sec

$=\eta \times r\left(E_1+E_2\right)$

$\eta=25 \%$

$r=10^{15}$

$E_1=100 \times 10^6 \times 1.6 \times 10^{-19}=1.6 \times 10^{-11} \mathrm{~J}$

$E_2=50 \times 10^6 \times 1.6 \times 10^{-19}=0.8 \times 10^{-11} \mathrm{~J}$

$Energy \, \, released \, \, per\, \, sec$ $=0.25 \times 10^{15} \times\left(1.6 \times 10^{-11} \mathrm{~J}+0.8 \times 10^{-11}\right)=6 \mathrm{KW} \text {. }$

Posted by

HARSH KANKARIA

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