Atoms & Nuclei

JEE Main level, single correct, medium

208 of 239

Question 208 of 239

Imagine that a reactor converts all the given mass into energy and that it operates at a power level of 109Watt{10}^{9}Watt . The mass of the fuel consumed perhourperhour, in the reactor, will be:
(velocity of light, cc is 3×108ms−13\times {10}^{8}m{s}^{-1})

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Answer: (C) 4×10−2g4\times {10}^{-2}g

Power of reactor, P=EΔt=Δmc2ΔtP=\dfrac{E}{\Delta t}=\dfrac{\Delta m{c}^{2}}{\Delta t}(From mass-energy equivalence equation)
Given in the problem power level =109Watt={10}^{9}Watt .

∆m∆t=Pc2=109(3×108)2\dfrac{∆m}{∆t}=\dfrac{P}{{c}^{2}}=\dfrac{{10}^{9}}{{\left(3\times {10}^{8}\right)}^{2}}

⇒∆m∆t=10−79kgs−1\Rightarrow \dfrac{∆m}{∆t}=\dfrac{{10}^{-7}}{9}kg{s}^{-1}

The mass of fuel consumed perhourperhour=10−79×(1000g)(3600h−1)=4×10−2gh−1=\dfrac{{10}^{-7}}{9}\times \left(1000g\right)\left(3600{h}^{-1}\right)=4\times {10}^{-2}g{h}^{-1}.

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