Calculating total amount of energy in a fusion reaction

In summary, the problem states that if two masses of deuterium and tritium are used to create energy, the result is 5.030151 grams. The problem also asks for the energy in grams. After multiplying the masses by 1.66, the result is 1.7x1012 Joules.
  • #1
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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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  • #3
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
 
  • #4
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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  • #5
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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FAQ: Calculating total amount of energy in a fusion reaction

What is a fusion reaction?

A fusion reaction is a process where two or more atomic nuclei combine to form a heavier nucleus, releasing a large amount of energy in the process.

How is the total energy in a fusion reaction calculated?

The total amount of energy in a fusion reaction is calculated by using the famous equation E=mc², where E is the energy released, m is the mass difference between the initial and final nuclei, and c is the speed of light.

What factors affect the total energy released in a fusion reaction?

The total energy released in a fusion reaction is affected by the mass of the nuclei involved, the speed at which they collide, and the conditions of the environment in which the reaction takes place.

What is the difference between the total energy and net energy in a fusion reaction?

The total energy in a fusion reaction refers to the overall amount of energy released, while the net energy takes into account any energy lost during the reaction, such as through radiation or other forms of energy transfer.

Can the total energy in a fusion reaction be controlled?

Yes, the total energy in a fusion reaction can be controlled by adjusting the conditions of the reaction, such as the temperature and pressure, to achieve the desired amount of energy release.

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