Calculating total amount of energy in a fusion reaction

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Homework Help Overview

The discussion revolves around calculating the total amount of energy produced in a fusion reaction involving deuterium and tritium nuclei combining to form helium. The original poster presents calculations based on given masses and the equation E=mc².

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the appropriateness of the mass units used, with some suggesting that atomic mass units (u) should be employed instead of grams. There are also questions regarding the accuracy of the mass values substituted in the calculations.

Discussion Status

The conversation includes attempts to clarify the original poster's calculations and assumptions. Some participants express uncertainty about the mass units and the implications of using grams versus atomic mass units. There is acknowledgment of the potential for large energy yields in fusion reactions, particularly in the context of nuclear weapons.

Contextual Notes

Participants note the importance of using correct mass units and the implications of calculating energy yields from multiple grams of material rather than single nuclei. There is a reference to textbook examples that may have influenced the original poster's approach.

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Homework Statement


In the following fusion reaction, a deuterium nucleus (D) combines with a tritium nucleus (T) to form a helium nucleus (He-4). If the following masses of deuterium and tritium are used to produce energy, calculate the total amount of energy produced.
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Homework Equations


E = mc2

The Attempt at a Solution


Adding: D + T = 2.014102 + 3.016049 = 5.030151
Adding: He + n = 4.002602 + 1.008665 = 5.011267

Subtracting the two: 5.030151 - 5.011267 = 0.018884 g or 1.8884x10-5 kg

Using the equation to find the total amount of energy:
E = mc2 = (1.8884x10-5) x (3x108m/s)2 = 1.7x1012J

Can someone confirm for me if I got all the steps right and calculations?
 

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No, I think you substituted the wrong numbers for D, T, He and n. Two and five grams is too heavy for nuclei. The weight of deuterium nucleus is 2.014 atomic mass units.

You need the weights in grams or, ultimately, kilograms.

Weight in kilograms = weight in atomic mass units times 1.66 x ##10^{-27}## kg per atomic mass unit
 
I was studying nuclear fusion and fission, their differences and reactions, and calculating the energy. My textbook had similar examples and questions with suggested answers:
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So I was following this example, to calculate this question. Do you still think it is incorrect? I just want to make sure I am doing it properly.
 

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I am sorry. I misread the problem. I think the solution you posted initially was correct.

I mistakenly assumed that you were supposed to calculate the yield from a reaction involving single nuclei. Actually, the way you have stated the problem, you have several grams of material. In that case, the yield is huge. This is why hydrogen bombs, if ever used, would be so destructive.
 
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