# Calculating Energy Released in Fusion: 21H + 31H -> 42He + 10n

• ProPatto16
In summary, the nuclear reaction 21H + 31H -> 42He + 10n is being studied for its potential as a source of fusion power. The energy released when two atoms fuse according to this reaction is 17.59 MeV. To calculate the energy released per mole of reactants, the atomic masses of 21H and 31H are not relevant. The energy per unit mole of reaction is just half of the total energy released.
ProPatto16

## Homework Statement

A nuclear reaction being studied for its potential as a source of fusion power is:

21H + 31H -> 42He + 10n

1) calculate energy in MeV released when two atoms fuse according to the reaction above.
2) calculate the energy in joules released per mole of reactants. (ie. one mole of H-2 and one mole of H-3)

## The Attempt at a Solution

1) the answer is 17.59 Mev
and i don't know how to go about 2)

i know combined they release that energy found in part 1)... but I am not sure how to divide that energy up between them. is it done on a ratio of 2:3 by atomic mass? or is it done by mass in kg? i just don't know the connection there...

Well if you know the masses of 21H and 31H, since they are both currently 1 mole, you can just add the atomic masses, which would be in the units kg/mol.

E=mc2

Last edited:
the mass of 21H is 2.014102 so E is just 2.014102c^2?
same for 31H.

ProPatto16 said:
the mass of 21H is 2.014102 so E is just 2.014102c^2?
same for 31H.

It is 2.014102u where u = 1.66053886 × 10-27 kg.

yeah, i used that conversion, just didnt clarify.

E of 21H = 3.01*10^-10J
E of 31H = 4.507*10^-10J

ProPatto16 said:
yeah, i used that conversion, just didnt clarify.

E of 21H = 3.01*10^-10J
E of 31H = 4.507*10^-10J

Sorry, I thought your question was asking something else. Just convert the value you got to Joules, then you only have 2 moles of reactants so, that the energy per unit mole of reaction is just Ereactant/2.

ohh... so the atomic masses and whatnot of the elements isn't even relevant? the energy is just half anf half?

ProPatto16 said:
ohh... so the atomic masses and whatnot of the elements isn't even relevant? the energy is just half anf half?

Well you are finding per mole of reactant and not something like per mole of H-2 which I think would work out to be different, but my reasoning of the problem could be wrong.

2) calculate the energy in joules released per mole of reactants. (ie. one mole of H-2 and one mole of H-3)

so its energy per H-3 and per H-2.

## 1. How is the energy released in fusion calculated?

The energy released in fusion is calculated using Einstein's famous equation, E=mc^2. This equation relates the amount of energy released (E) to the mass (m) that is converted into energy and the speed of light (c).

## 2. What is the fusion reaction formula for 21H + 31H -> 42He + 10n?

The fusion reaction formula for this reaction is 21H + 31H -> 42He + 10n. This equation represents the fusion of two hydrogen isotopes, deuterium (21H) and tritium (31H), to form a helium isotope (42He) and a neutron (10n).

## 3. How much energy is released in the fusion of 21H and 31H?

The fusion of 21H and 31H releases a total of 17.6 MeV (mega electron volts) of energy. This energy is a result of the difference in mass between the reactants and products, as well as the conversion of this mass into energy according to E=mc^2.

## 4. What factors affect the amount of energy released in fusion?

The amount of energy released in fusion is affected by the isotopes involved in the reaction, the temperature and pressure of the reactants, and the efficiency of the fusion process. Generally, reactions involving lighter isotopes such as hydrogen or helium release more energy than reactions involving heavier elements.

## 5. What is the potential of fusion as an energy source?

Fusion has the potential to be a nearly limitless source of clean energy. The fusion of hydrogen isotopes, which are abundant in seawater, releases large amounts of energy without producing harmful byproducts. However, the technology to harness fusion energy in a controlled and sustainable manner is still under development.

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