Calculating total amount of energy in a fusion reaction

Click For Summary
SUMMARY

The discussion focuses on calculating the total energy produced in a fusion reaction involving deuterium (D) and tritium (T) nuclei, resulting in helium-4 (He-4) and a neutron (n). The energy is calculated using Einstein's equation, E = mc², with the correct masses in atomic mass units (u). The final energy output calculated is approximately 1.7 x 1012 J, confirming the significant energy yield from fusion reactions. The conversation highlights the importance of using the correct units and understanding the scale of nuclear reactions.

PREREQUISITES
  • Understanding of Einstein's equation E = mc²
  • Knowledge of atomic mass units (u) and their conversion to kilograms
  • Familiarity with nuclear fusion processes and reactions
  • Basic skills in unit conversion and dimensional analysis
NEXT STEPS
  • Study the principles of nuclear fusion and fission
  • Learn about atomic mass unit conversions and their significance in nuclear physics
  • Explore advanced applications of E = mc² in different nuclear reactions
  • Investigate the implications of energy yield in fusion reactions for energy production
USEFUL FOR

Students studying nuclear physics, educators teaching fusion concepts, and researchers interested in energy production from fusion reactions.

Humbleness
Messages
31
Reaction score
1

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.
Untitled-1.jpg


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?
 

Attachments

  • Untitled-1.jpg
    Untitled-1.jpg
    10.8 KB · Views: 1,901
Physics news on Phys.org
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:
Untitled-2.jpg

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.
 

Attachments

  • Untitled-2.jpg
    Untitled-2.jpg
    36.1 KB · Views: 2,011
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.
 
  • Like
Likes   Reactions: Humbleness

Similar threads

Replies
1
Views
1K
Replies
3
Views
2K
  • · Replies 4 ·
Replies
4
Views
1K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 14 ·
Replies
14
Views
3K
Replies
11
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 3 ·
Replies
3
Views
4K