Class Warfare Blog

June 26, 2019

The Mass Defect . . . For Physics Geeks Only

Filed under: Science — Steve Ruis @ 9:08 am
Tags: ,

I have wondered a great deal about how atomic nuclei get formed. We are still learning about this and modern theories differ from ones of just a few years ago. Here I am interested in a detail and just so you know the context, here is an example:

A carbon-12 atom is approximately 0.8% lighter than the individual component particles that were fused together make it up (6 protons and 6 neutrons and 6 electrons). The way carbon nuclei are formed is through the nuclear fusion of hydrogen into helium and then helium into carbon; the energy released is what powers most types of stars in both their normal and red giant phases, and the “lost mass” is where that energy comes from (E = mc2). This is how most types of “binding energy” work: the reason it’s harder to pull apart multiple things that are bound together is because they released energy when they were joined, and you have to put that amount of energy back in to free them again. My question involves what you actually get when you fuse them together. Is it like textbook diagrams, a bunch of round particles glued together or do they become something new?

In textbooks nuclei are often represented this way, because it is easy to draw, not because it is accurate. First, there is no color at this depth, not are there any hard edges, so all particles would be very fuzzy and rendered in grey, but that wouldn’t be pretty, now would it?

My simplistic interpretation was that the six fundamental particles in this example were “fused” (means “melted) together to make a new single particle, an atomic nucleus. The protons and neutrons themselves were no longer there, but whatever constituent particles that made them up (quarks and whatnot) were now combined in this new single particle.

There were some issues to be resolved, however. For one, the more particles that get fused together, the more the mass defect was. This made sense, but “how much more” did not. Here is a graph showing the mass defect (also called the nuclear binding energy) as a function of the number of nucleons (protons and neutrons) involved.

You can see from the graph that at first, as the number of nucleons being fused together increases, the mass defect per nucleon increases rapidly with it, but it inexplicably decreases between helium-4 and lithium-6. And then the increases get smaller and smaller as more nucleons become involved until it actually decreases from iron-56 onward, a clear example of “diminishing returns”!

My initial idea that some particle had to be spit out to account for the lost mass is blown out of the water with these facts. If a particle or particles, had to be spit out the loss in mass (aka binding energy) per nucleon involved would increase stepwise in a linear fashion.

In addition, if you repeat the reactions over and over, you get the same amount of energy produced. This regularity is hard to explain if the energy just comes from a pool of energy contained in the protons and neutrons, so we need to look at what these particles actually consist of.

The Insides of Protons
This is a topic that is still under development, but just recently physicists have calculated out where, according to theory, the mass of a proton is distributed. According to quantum chromodynamics theory, or QCD, the proton’s mass can be calculated (at 938 million electron volts) which agrees with measurements. But it turns out that only 9 percent of the proton’s mass comes from the masses of the constituent quarks. So where does the rest of the mass come from? According to the calculations, 32 percent comes from the energy of the quarks zipping around inside the proton! (E=mc2 again). Other occupants of the proton, massless particles called gluons that help hold the quarks together, contribute another 36 percent via their energy. The remaining 23 percent arises due to quantum effects that occur when quarks and gluons interact within the proton. Well this blows away all of our first intuitions regarding protons being little spherical bits of matter, hard bits. It seems that protons are mostly pools of mass-energy.

Presumable neutrons are much like this also, the masses of neutrons and protons being almost identical.

So . . .
So, my question is, during a fusion reaction, how does the process know when it has bled out “enough” energy to hold the constituent particles together? In addition, how does the reaction know when to stop? And, how do the particles know when to leak mass energy at all? (Realize these “reactions” happen at immensely high pressures and temperatures, conditions that usually result in energy being injected into particles, not prised out of them.) If there were some particle or particles spit out, taking mass and energy with them, a coherent process flows easily out of that, but this doesn’t appear to be the case. Quarks do not get spit out of fusing nuclei. It is hard to imagine the massless gluons carrying away much energy. In more mundane processes, chemical and/or ordinary physical ones (mechanical, etc.), the processes are controlled fairly simply. When a process needs energy to proceed, as the energy is added, nothing occurs until the right amount accumulates and then, Bam! it happens. If energy is being produced, attractions are broken and new stronger attractions made, the difference between them accounts for the energy involved. In the case of a dropped object, the attraction is gravity, the object falls from one elevation to another closer to the Earth and is stopped by an obstacle (e.g. the floor). The energy of movement the object displays is exactly accounted for by the change in attraction of the Earth for the object (the attraction got ever so slightly stronger, but the amount the object could fall due to that attraction got substantially less).

So, what the heck is going on in nuclear fusion reactions? Are the protons and neutrons still there, but being less massive versions of each? If so, then there are as many protons and neutron masses as there are nuclei (the masses of those particles would have to be variable according to the data in this scenario). Are there particles involved that we haven’t discovered yet? How does the reaction know when enough energy is released?

Damn, inquiring minds want to know.

Oh, and did you notice that my title with “For Physics Geeks Only” got some of you non-geeks to read this far? Pretty clever, eh?


  1. Yep. Caught me for sure. What can I say for myself? Well, I was a chemistry major at Cal Poly Pomona before the USMC and I got together and I still have a passing, often more like a slow drive by, with science. I may not understand it, mostly I don’t now days, but I still know it is bloody damn interesting. Oh, and science will be what we need to try and survive this global warming, none of the various religions will be of any use, but they never have been except for the top folks who live off the “offerings” given/strong armed from the followers of said religions.


    Comment by Walter Kronkat — June 26, 2019 @ 11:45 am | Reply

    • So we both were chemistry majors in schools not far apart (I was at SF State) and since we are of a certain age, it was at about the same time. Apparently, I was a better draft dodger, though.

      Actually, I didn’t dodge the draft. (Thought about it, though.) I had a fairly high draft lottery number and I opted to not resist the draft in its first year, because that pool contained 18-26 year olds and was huge. If I had waited a year, I would have been drafted for sure. (My number was like 206 and they stopped in the high 190’s.) I was sure, at the time, that if I were drafted and had seen combat, I would have done something stupid and not only gotten myself killed but a bunch of other guys, too. Worst case scenario was my stupidity would have gotten a bunch of kids killed and I survived and would have to live with that for the rest of my life. That bothered me more than anything else.

      On Wed, Jun 26, 2019 at 11:45 AM Class Warfare Blog wrote:



      Comment by Steve Ruis — June 26, 2019 @ 12:27 pm | Reply

  2. Loved this! And a thought occured to me as I read. Exclusion principle. Perhaps the nuclei is completely unaware of the protons, and the protons are entirely unaware of the quarks and gluons. They exist in perfect isolation to the other, bound only by an exclusion principle which is different at each level. What, then, is possible to one, say a nuclei (fision/fusion), is not possible to another, say a quark. In this sense, something can go complete nova, but it’s parts never know. The exclusion principle (the sort of quantum synaptic gap) is therefore an active agent in this whole study.

    Am I babbling?


    Comment by john zande — June 26, 2019 @ 12:13 pm | Reply

    • Yes, but it is fascinating. The exclusion principle is a limit on what we can measure simultaneously, We never anticipated that we would have physical uncertainty limits, we though they were just technological ones, that could be surmounted by better tech.

      This has been bother me for decades. I recently asked a physics guru on Quora this questions but I didn’t get an answer. I hesitate to send it to Sean Carroll, but I may end up doing just that.

      On Wed, Jun 26, 2019 at 12:13 PM Class Warfare Blog wrote:


      Liked by 1 person

      Comment by Steve Ruis — June 26, 2019 @ 12:30 pm | Reply

      • I like babbling. I like even more people who tell me I’m babbling.

        But, but, but I was thinking like the pauli exclusion principle: a third party keeping things apart.

        Still babbling?


        Comment by john zande — June 26, 2019 @ 12:34 pm | Reply

        • Yep, no third party … uh, we think. The mystery of quantum mechanics is that it works better (defined by precision of predictions) than any other theory known to us … and we still don’t know why. Effing strange it is and nobody knows way. (Nature is obtuse? nature is an asshole? I don’t know.)

          On Wed, Jun 26, 2019 at 12:34 PM Class Warfare Blog wrote:


          Liked by 2 people

          Comment by Steve Ruis — June 26, 2019 @ 12:37 pm | Reply

      • BTW, send it to Matthew Rave, Assoc Prof Physics. He’s a great bloke, and has a blog. Often answers my stupid questions.


        Comment by john zande — June 26, 2019 @ 12:37 pm | Reply

        • Thanks!

          On Wed, Jun 26, 2019 at 12:37 PM Class Warfare Blog wrote:



          Comment by Steve Ruis — June 26, 2019 @ 12:38 pm | Reply

          • Post your answer. I’d be interested to see what he says. He has a book, too: Why is there anything?


            Comment by john zande — June 26, 2019 @ 12:40 pm | Reply

            • Ah hah! Beat you to it. Went to his blog, asked my question, and then saw that you had recommended his book to someone else and bought it. All before reading this post! “Faster than a speeding bullet. More powerful than a locomotive. Able to leap tall buildings with a single bound.”

              On Wed, Jun 26, 2019 at 12:40 PM Class Warfare Blog wrote:


              Liked by 1 person

              Comment by Steve Ruis — June 26, 2019 @ 12:46 pm | Reply

              • It’s a fun read, socratic method.


                Comment by john zande — June 26, 2019 @ 1:25 pm | Reply

                • Well it was Einstein, was it not who said that the hard part is asking good questions.

                  On Wed, Jun 26, 2019 at 1:25 PM Class Warfare Blog wrote:


                  Liked by 1 person

                  Comment by Steve Ruis — June 26, 2019 @ 1:52 pm | Reply

        • Sent it … and ordered his book. Looks interesting! Thanks.

          On Wed, Jun 26, 2019 at 12:37 PM Class Warfare Blog wrote:


          Liked by 1 person

          Comment by Steve Ruis — June 26, 2019 @ 12:44 pm | Reply

  3. “how does the process know when it has bled out “enough” energy to hold the constituent particles together? … how does the reaction know when to stop? And, how do the particles know when to leak mass energy at all?”

    Particles don’t “know” anything. This is just blind physics.
    What difference does it make, anyway?
    Anyone, theist or atheist, who thinks that “purposes” exist anywhere but in our imaginations is sadly poorly informed.


    Comment by John Branyan — June 27, 2019 @ 3:24 pm | Reply

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