As a school student, I have wondered while studying mass defect the following mysterious problem

My assumption

  1. Just like a car's mass is constituted by each part of it(i.e total mass of car will be equal to mass of body+engine etc..), I assume that the mass of nucleus is the sum total of the mass of the particles the nucleus contains, i.e mass of nucleus =mass of protons +mass of neutrons

  2. I assume all the protons, neutrons are exactly the same, they have (each kind) exactly same mass

  3. I assume the charge of proton is distributed uniformly.


A quote from Wikipedia: http://en.wikipedia.org/wiki/Binding_energy

It is observed experimentally that the mass of the nucleus is smaller than the number of nucleons each counted with a mass of 1 a.m.u.. This difference is called mass excess.

The mysterious problem I encounter

There is no change in the number of neutrons or protons in the nucleus of the atom. And my idea was as the mass of nucleus is the total mass of protons and neutrons, if the mass of nucleus is to change what I can think about the possibilities are

  1. Either the number of neutrons or number of protons should change
  2. In order to fit the 2nd assumption, some part of the mass of every neutron and every proton will go (probably as energy) so that all the protons are same and all the neutrons too are same.

The 1st possible explanation is obviously wrong as we don't see any change in the number.

The 2nd possible explanation is just 'like a reason for the sake of giving a reason' logically difficult to convince myself. If that were true there should have been many types of protons and different types of neutrons (both classified according to their mass), which again is un-intuitive.

The question

  • What's the possible explanation to the question from where the mass is being lost?
  • Either one of my assumption is wrong (but isn't my assumption just logical?) or there should be some other reason how the mass can vary (may be we should better define what is the mass of the nucleus). In that case, another question , If my assumption 1 is false What constitute the mass of a nucleus?
  • Isn't there something like a standard proton or a standard neutron (By standard I mean a fixed mass fixed charge etc)
  • By my third assumption, If the proton loses some mass shouldn't it lose some of it's charge. And suppose we forget E=mc^2 can't we say the difference in the potential energy of electron-proton (as it changes when the charge changes) is an explanation of how the nucleus gets binding energy.
  • 2
    $\begingroup$ Am I correct in rephrasing your question like this: if nucleons lose mass when they bind together (yes, they do), then, why doesn't that mean that there are many different types of protons and neutrons, classified by their mass? $\endgroup$ Apr 11, 2013 at 19:03
  • $\begingroup$ Possible duplicate: physics.stackexchange.com/q/47417/2451 $\endgroup$
    – Qmechanic
    Jun 11, 2013 at 1:00

3 Answers 3


A nucleon in nuclear context is simply not the same as one in a free context. Not in mass nor in form factor. These corrections are not known in complete detail but there are parameterizations of them that are used in nuclear and particle physics experiments. In my disertation project we used a parameterization due to de Forest, which is a popular but now somewhat dated model.

  • $\begingroup$ Interesting!. Then what is the possible reason from where the nucleus gets binding energy?. $\endgroup$
    – user23045
    Apr 12, 2013 at 17:27
  • 1
    $\begingroup$ The two effects---changed nature of the nucleon and binding of the nucleus---are both facets of the same physics, which is mostly that of the residual strong nuclear force. $\endgroup$ Apr 12, 2013 at 17:36

That's because the mass of an object is the same as the energy the object possesses at rest. According to $E=mc^2$ e.g. a compressed spring has more mass than an uncompressed one, a charged battery has more mass than an uncharged battery, etc. Mass and (rest) energy are not just equivalent, they are the same thing. Energy bends space time which causes gravity. So every concentration of energy (e.g. matter) will possess gravity. In fact more than 98% of the mass of an atom comes from the binding energy of the quarks that make up the protons and neutrons. A simpler example - if you take two magnets and stick them together, the combination of the two will have a lower mass than the sum of the two. There is a mass defect, just like when sticking together protons and neutrons. However in case of the magnets that mass defect is very tiny. Difficult to measure. But you can calculate it. It's the energy released when the magnets snap together devided by $c^2$

  • 2
    $\begingroup$ Interesting!. But not the answer to the original question. If the mass is lost there should be some change in proton's neutrons etc. But what kind of changes are happening to protons, doesn't there exist a standard proton or neutron?. $\endgroup$
    – user23045
    Apr 12, 2013 at 12:48
  • $\begingroup$ "if you take two magnets and stick them together, the combination of the two will have a lower mass than the sum of the two". I can't just believe this . And what do you mean by the energy released by the magnets?. Can't it be of other nature ?. $\endgroup$
    – user23045
    Apr 12, 2013 at 17:23
  • $\begingroup$ The protons and neutrons do not change. What changes is their fields. Protons have an electric field and both, neutrons and protons also have a field due to the nuclear force. Fields have energy and therefore mass. If you reduce the energy content in those fields you reduce the mass. The particles don't have to change to do that. The same thing happens with magnets. The total energy contained in the magnetic field gets reduced so it's mass reduces. $\endgroup$
    – Tesseract
    Apr 12, 2013 at 20:55
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    $\begingroup$ SpiderPig, the nucleons do change. What is important here is that nucleons are not fundamental particles: they're composite. We can measure the form-factor of individual protons in a nuclear context and it is different from the form factor of a free proton. Now that is an effect that can be reasonably defined as changes in the residual strong field, but it is also proper to to understand it in terms of changes in the particles themselves. $\endgroup$ Apr 13, 2013 at 0:24

Well the protons and neutrons just lose a small amount of energy because that is the lower energy state. They lose their energy and release that as gamma radiation. Some of the protons and neutrons mass is converted to energy. Well a standard proton or neutron would be one that is not in a nucleus and is far away from any object. Also the proton or neutron has to be stationary(in real life it is impossible for the proton or neutron to be stationary due to Heisenberg's uncertainty principle)- that is the ideal proton or neutron. The proton or neutron here as a rough mass of 938 MEV.The proton does not lose its charge because unlike in classical physics the charge is a fundamental property of these particles. It is independent of its mass.


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