# I Origin of mass converted to energy during nuclear fusion

1. Oct 12, 2017

### Cardinalmont

When two atoms undergo nuclear fusion, some of the mass is converted into energy, but where is this lost mass from? Atoms are composed of protons, neutrons, and electrons, but all three have all have set values for mass. What is the origin of this mass that is converted to energy?

2. Oct 12, 2017

### Orodruin

Staff Emeritus
It would be more appropriate to say that some of the mass is converted into other forms of energy as mass is better seen as a type of energy than as something different. The point is that atoms have a binding energy that needs to be subtracted from the masses of the constituents in order to obtain the mass of the atom. As a result, all atoms have masses that are smaller than the sum of the rest masses of the particles they consist of.

3. Oct 12, 2017

### Cardinalmont

Thank you for your response. It is still unclear to me where this mass is being removed from. Do the individual protons and neutrons in the combined atom have less mass than the individual protons and neutrons in the two atoms that are being fused?

4. Oct 12, 2017

### Orodruin

Staff Emeritus
No, but they exist in a bound state. The bound state contains less energy and therefore the system has less mass. Mass is essentially just a measure of how much energy a system has in its rest frame. For a bound state, it has the energy related to all the constituent masses minus the binding energy, which results in an energy that is smaller than the sum of the constituent masses.

5. Oct 12, 2017

### phyzguy

To follow up on Orodruin's comments, try taking the total mass of 2 protons, 2 neutrons and 2 electrons and compare it to the measured mass of a helium atom. The measured mass of the helium atom will be less than the sum of it's constituents, because it is a bound system. Note that this isn't a special property of atoms. If you could measure it, the measured mass of the Earth-Moon system would be less than the mass of the Earth plus the mass of the Moon if they were at infinite separation, because the Earth-Moon system is gravitationally bound.

6. Oct 12, 2017

### Staff: Mentor

We can't do it with the Earth-Moon system, but we can do it with Earth, which has a mass lower than the sum of all its particles as well. Lunar laser ranging achieves the necessary precision.

7. Oct 23, 2017

### ORF

Hello

The energy of fusion/fission comes from the bonding energy. For every system you have

M1 = sum ( parts1 ) + bonding(1);
M2 = sum ( parts1 ) + bonding(2)

In case of nuclei,
sum (parts ) = massProton * Z + massNeutron*(A-Z)
bonding() = mass-formula [1]

In case of fusion,
sum ( parts1 ) = sum ( parts2 ),

and the released energy comes from
M2 - M1 = bonding(2) - bonding(1)

the explanation for the differences in bonding energy:
--> in the case of fusion, the energy comes from the surface energy. the nuclear force is short-range; for light nuclei*, each nucleon can have more nucleons around. If there are more nucleons around, the surface energy increases and the bonding energy in greater, releasing energy
--> in the case of fission, from the Coulomb term.

Regards.
ORF
[1] https://en.wikipedia.org/wiki/Semi-empirical_mass_formula#The_liquid_drop_model_and_its_analysis
* A < 56 (Fe,Ni)

8. Nov 10, 2017

### Ken Ucarp

You said: Mass is essentially just a measure of how much energy a system has in its rest frame.
But isn't there some essential difference between mass and energy? I mean, I can't knock on a piece of energy but I think I can knock on a piece of mass. (Or maybe not! Maybe that's just how us laymen talk??)

9. Nov 10, 2017

### Orodruin

Staff Emeritus
You are confusing mass with matter.

10. Nov 10, 2017

### Ken Ucarp

So mass is a "quantitative property" of matter. Isn't there an essential difference between the quantitative property we call mass, and the quantitative property of matter we call energy? Or is energy not considered a qp? My question has to do with the difference between mass and energy. Don't focus on the side issue of knocking on something. I'm just always interested in how physicists talk of how mass is the same as energy. If that's the case, then why two terms? Or maybe in real life you guys don't use two terms. Mass then is just a little verbal device or shortcut for "measure of energy in a frame of rest".

11. Nov 10, 2017

### Orodruin

Staff Emeritus
Mass in relativity is just the energy of a system in the frame where it has zero momentum. Going to the non-relativistic limit, this can be identified with the inertial mass of Newtonian mechanics. This is the essence of the mass-energy equivalence.

12. Nov 17, 2017

### Mister T

Add up the masses of those protons, neutrons, and electrons and you don't get the mass of the atom.