# During fusion, how does mass turn into energy?

This is my (flawed) understanding of how fusion basically works:

Let's assume that a fusion reaction has a net gain in energy.

First, there is an input amount of kinetic energy to get the two light nuclei close enough to overcome the Coulomb barrier, so that the attractive strong nuclear force becomes greater than the electrostatic repulsion.

Then, the potential energy from the strong nuclear force causes the two nuclei to 'fall into' each other by converting the potential energy into kinetic energy (doing work). They then fuse into one nuclei.

The residual output kinetic energy is then the 'released energy' from the process and is, in this case, greater than the input energy. The reason why the output energy is greater than the input, is because the gain of energy from the strong force interaction is greater than the energy required to overcome the Coulomb barrier.

For heavier nuclei, the Coulomb barrier is too strong, so that the input energy is greater than the output energy from the strong force interaction.

My question:

In my explanation, I didn't mention the probably most defining feature of fusion, which is the conversion of mass into energy (and energy into mass).

I don't understand why it is necessary for mass to be converted into energy. Where exactly in the process does it happen, and how exactly does it happen?

Every time I read something about it, they just mention $$E=mc^2,$$ or $$Q=-\Delta mc^2,$$ but that doesn't explain where and why it is necessary for the process to happen. It just describes how you can calculate the energy lost or gained from the fusion over all. Doesn't the strong nuclear force just by virtue of proximity make all the kinetic energy?

Update 1:

I saw this video that explains it:

Though I understood virtually nothing, I guess my flawed understanding basically lies in the fact that I haven't studied quantum mechanics. The strong force and the nuclear force look pretty complicated.

Update 2:

The answer by RC_23 opened my eyes to the fact that conversion from mass to energy and energy to mass are processes that happen everywhere. The only reason why it is so specifically associated with nuclear reactions, is because the mass changes that happen in them are generally quite significant, which makes them useful to humanity, because it means that we can harness energy from them. And also, because it's interesting to explain how stars are powered.

But all of this just reaffirms how awesome $$E = mc^2$$ is, because many processes can actually be explained by it.

Here are some everyday examples given by this Wikipedia article https://en.wikipedia.org/wiki/Mass–energy_equivalence:

"A spring's mass increases whenever it is put into compression or tension. Its mass increase arises from the increased potential energy stored within it, which is bound in the stretched chemical (electron) bonds linking the atoms within the spring."

"Raising the temperature of an object (increasing its thermal energy) increases its mass. For example, consider the world's primary mass standard for the kilogram, made of platinum and iridum. If its temperature is allowed to change by 1 °C, its mass changes by 1.5 picograms."

"A spinning ball has greater mass than when it is not spinning. Its increase of mass is exactly the equivalent of the mass of energy of rotation, which is itself the sum of the kinetic energies of all the moving parts of the ball. For example, the Earth itself is more massive due to its rotation, than it would be with no rotation."

https://www.wtamu.edu/~cbaird/sq/2013/10/21/why-is-mass-conserved-in-chemical-reactions/

I'm baffled that I never knew this.

Mass gets converted into energy vice versa in fusion reactions too, it's just that it requires some quite advanced knowledge about quantum mechanics to explain how exactly it works.

• In a nutshell, your "strong nuclear interaction's potential energy" argument is too qualitative to get the most salient physical fact that the masses of the products are smaller than the masses of the reactants, with the difference converted into energy. It can be made to work, despite the fact that we currently cannot compute so. There are also many minor misconceptions. Commented Nov 24, 2023 at 16:26
• Related question: How is the speed of nucleons in the nucleus measured? That question was triggered by a popular science article that opens with the statement: "Researchers [...] have demonstrated that a quarter of the nucleons in a dense nucleus exceed 25 percent of the speed of light". A nucleus is a bound state. Kinetic energies of the constituents of a bound state correlate with how deep the potential well is. Kinetic energy (of necleons) has corresponding inertial mass Commented Nov 24, 2023 at 16:32
• As mass is already (rest) energy, no conversion is involved. Commented Nov 25, 2023 at 5:48
• You may enjoy this answer, physics.stackexchange.com/a/652569/123208 where I estimate that the thermal energy of the Earth's core contributes ~210 billion tonnes to the Earth's mass. Commented Nov 25, 2023 at 9:57
• That really puts it into perspective! Commented Nov 25, 2023 at 10:56

Your explanation vis a vis the strong force and the Coulomb barrier is spot-on conceptually, and you've discovered that there is no reason to invoke "mass energy conversion." Indeed, I think mass energy conversion started as a pop science way of explaining atomic energy to the layperson by journalists, and is a very poor choice for modeling anything at a scientific level. Energy and energy levels are what you should focus on; the only meaningful conversion that is happening is potential to kinetic energy.

It is true that any confined energy has a corresponding mass, $$m = E/c^2$$, and that consequently any energy change in a system will result in a corresponding mass change. But this is a superfluous detail. Nuclear reactions result in a mass difference between the reactants and products; but so do chemical reactions; so does a 90°C pot of water cooling to 20°C; so does a meteor falling from space to the ground.

The real reason fission and fusion reactions are more powerful than chemical reactions is simply that the difference in energy levels between different nuclear states is much greater than the difference in energy levels between electron states (which drive chemical reactions). But there is no qualitative difference, when it comes to mass-energy conversion.

This video may be helpful, and this Q/A discussion.

• For fusion specifically, correct? Because I thought there was actual mass-energy conversions somewhere else, like kugelblitzes and really exotic things like that. Commented Nov 24, 2023 at 21:13
• @DKNguyen An electron and a positron — both of which are particles with mass — can annihilate to two photons — neither of which has mass. Mass-energy can convert to other kinds of energy, and vice-versa. This is not particularly exotic. (Note, however, that the outgoing system of two photons has the same invariant mass as the incoming system, despite its constituents being massless.) Commented Nov 24, 2023 at 23:15
• @EdwardChen It's a quantitative difference. For instance, when a free proton and free electron bind to form hydrogen, the mass decreases by 13 eV. But that is a part-per-billion correction to the atomic mass of hydrogen, so we don't usually talk about it. The mass correction associated with mechanical stress, as in your comment, is orders of magnitude smaller still.
– rob
Commented Nov 24, 2023 at 23:51
• @EdwardChen, it is good to understand what mass really is. Mass is a property that energy exhibits when it is confined. The Photon in a Box thought experiment is very illuminating. Free photons have zero mass. But if you put a massless photon in a massless box, that system will exhibit mass (i.e. inertia). youtu.be/gSKzgpt4HBU. Commented Nov 25, 2023 at 0:34
• @DKNguyen a kugelblitz is the (hypothetical, but probably possible) scenario where a large quantity of light aimed at a central point forms a black hole. The light itself viewed in isolation is massless. But, if you draw a large sphere around the light as it is converging, the interior of that sphere has the same mass before and after the black hole forms. Mass is a property energy can have, and not a separate thing that can convert to energy. Being a property is why saying "this region of space has X kg of mass" can be true completely irrespective of the type of energy in the region. Commented Nov 25, 2023 at 17:17

There is no reason to call mass-energy conversion as merely as popular science

### Experimental measurements of masses:

 Proton mass = 1.67262192369e-27 #kg
Neutron rest mass=1.67492749804e-27 # kg
Rest mass alpha particle=6.6446573357e-27 #kg


Over the last 60-70 years, we have spent a lot of time making these numbers as accurate as possible. They are so accurate that we can use them as basic units in many cases. Alpha particles, also called alpha rays or alpha radiation, consist of two protons and two neutrons:

 mass_of_individual_particles = 2 *(Proton_mass + Neutron_rest_mass)
diff = mass_of_individual_particles - Rest_mass_alpha_particle


So it takes less energy to bind the nucleons when fusion happens and excess energy is released. But this process needs us to overcome to coulomb barrier. This is why fusion only happens in extreme conditions and has been a challenge for mankind to achieve controlled fusion in the laboratory in an energy positive way.

Yes, this analog can be extended to other reactions and dynamics where kinetic energy is converted to potential energy. But the above case is so easy to demonstrate.

• My answer was not supposed to imply that mass-energy conversion is fictitious, or only a pop sci concept. But to call it the reason for nuclear reactions releasing energy I do Call a pop sci concept, and a misleading one. The "reason" apart from mere observational fact, is that there exist nuclear states with lower potential energy, and as you understand very well, that change in potential E is released as kinetic E of the products. Commented Apr 5 at 3:37