Calculating total amount of energy in a fusion reaction

[Humbleness]

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.

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?

 

[haruspex]

Not sure about the quantities. The text refers to single atoms, but in that case the given masses should be in units of u (https://en.wikipedia.org/wiki/Unified_atomic_mass_unit), not g.

 

[Gene Naden]

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

 

[Humbleness]

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:

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.

 

[Gene Naden]

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.