In a hypothetical nuclear-fusion reactor, two deuterium nuclei combine or \"fuse

Question

In a hypothetical nuclear-fusion reactor, two deuterium nuclei combine or "fuse" to form one helium nucleus. The mass of a deuterium nucleus, expressed in atomic mass units (u), is 2.0136 u; that of a helium nucleus is 4.0015 u. (1u=1.661×1027kg).

Part A

How much energy is released when 1.0 kg of deuterium undergoes fusion?

Express your answer using two significant figures.

E=______________J

Part B

The annual consumption of electrical energy in the United States is on the order of 9.0×1018 J . How much deuterium must react to produce this much energy?

Express your answer using two significant figures.

m=_________________kg

Explanation / Answer

a) The fraction of the initial mass that becomes energy is

1-4.0015 u / ( 2*2.0136 u) = 6.382*10^-3

Energy release per kilogram is

E =mc^2 = 1 kg * 6.382*10^-3 *( 3*10^8)^2 = 5.74* 10^14 J answer

partb

9*10^18 / (5.74* 10^14 ) = 15679.44 kg

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