# Love = Negative Energy

Perhaps due to a lack of details regarding his or their martyrdom, the Catholic Church pulled Saint Valentine from its liturgical veneration in 1969. Since that time, the holiday has expanded world-wide to areas that have never heard of early Roman martyrs. What a descent. From ecstatic religious devotion to a crude worshipping at the altars of sex and money. The now unholy day is coming up soon, and I thought that the following exchange would be appropriate for the occasion:

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I am sorry for bothering you with this question.

But my high school students are asking this questions and I am not able to answer. Could you help me?

You wrote in Physics forum.

“When energy is released, it means that the binding is increased. The number of nucleons in gamma decay (emission of a photon, if I recall) stays constant. Therefore, the binding energy per nucleon increases.”

I am not able to find any textbooks or website explaining this. Could you indicate where I can find it so that I can explain iit.

Regards,
xxx

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No bother at all. It helps to remember things to be asked easy questions.

Any problems you have are likely a matter of the definition of the words. Try this wikipedia entry:
Binding_energy

Carl

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The exam question is this.

A freshly-prepared sample of cobalt-64 decays by the emission of gamma-ray photons. The decay may be represented by the nuclear equation energy. (This should be Co to Co + energy )

After this decay, the binding energy per nucleon has

A. increased in magnitude because energy has been emitted from the nucleus.

B. decreased in magnitude because energy has been emitted from the nucleus.

C. stayed constant because the number of nucleons in the nucleus is unchanged.

D. stayed constant because the proton number is unchanged.

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The question is that if energy is emitted, the total energy is lower. Then why the binding energy is increasing?

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I can’t explain it better than Wikipedia.

Oh, maybe I can. You are confused only because the sign seems that it should be wrong. Let me put it in human terms.

Think of binding energy as “love”. Particles stay together because they are in love. The amount of love is called the binding energy.

When a pair emits a gamma ray, that is like a problem that was hurting their relationship. It goes away. The result is that they fall deeper in love. Their binding energy increases.

Nothing could be more natural.

Here’s another way of looking at it. The way your intuition would prefer to take care of it, the binding energy should be negative because positive energy was taken away by the gamma ray. This makes complete sense, but so does the other way of looking at it.

You can either write down the answer that you think is correct (and have trouble talking with physicists) or you can agree that binding energy is a positive amount (that contributes negatively to the mass of the bound state as the Wikipedia article makes clear), but your instructor will mark your test wrong. Later, when you write a text book, you can correct this error. But for now, try to not be a nail that sticks up too much.

Carl

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Thank you very much.

I will contemplate on it.

Filed under heresy, History, physics

### 5 responses to “Love = Negative Energy”

1. nige cook

That multiple choice question is a fascinating way of looking at nuclear binding energy, and I like your answer. I hadn’t thought about this before, despite having been interested in nuclear physics since 14 it clarifies my understanding.

When nucleons emit energy, they falls to a lower energy level, so the nucleus approach get closer together. At closer distances, the strong force which binds nucleons into the nucleus is stronger, so the energy binding the nucleons gets bigger. The binding energy is the energy you need to supply to release the particles, not what you can release.

It’s like the emission of quanta from electrons. Once the energy is gone, the electron has fallen to its ground state, and then it can’t emit more energy. You need to supply energy from outside the sustem to make the electron gain energy and escape. Stability increases after energy is lost because it stops further energy from being lost.

Binding energy is the potential energy of the field attracting say an electron to a nucleus. If the electron loses energy by emitting a photon, then it falls closer to the nucleus where the electrostatic potential energy is actually higher than it was before, because the potential energy is inversely proportional to distance of electron from nucleus (hence, the smaller the distance of the electron from the nucleus, the bigger the electrostatic binding energy): http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elepe.html

The strong nuclear attractive Yukawa force between nucleons, mediated by pions, is pretty similar in its general form to the Coulomb force, except for an exponential attenuation which occurs in addition to the inverse of distance (for potential energy) or inverse square law (for force or acceleration), making the force short-ranged.

So when a nucleon which is in a high energy state falls back to a lower energy state by emitting a gamma ray, the same general process happens as occurs in the emission of a photon by an electron. The nucleon loses its excitation energy, falls towards the ground state, and thus gets slightly closer to the middle of the nucleus, gaining some potential energy or “binding energy”.

It’s counter-intuitive at first that binding energy increases when a gamma ray is released. However, it’s just one of those things.

If I drop an apple, the apple releases sound waves when it hits the floor, and at the same time it gains gravitational potential energy because it moves slightly closer to the Earth’s core, where the apple has more binding energy (the closer a mass is the the Earth’s centre, the more energy you need to carry it away from the Earth). Hence, potential energy is not the same as binding energy. Potential energy is at a maximum when two attracting particles are far apart, when there is a maximum amount of kinetic energy to be gained by releasing them. Binding energy is at a maximum when two particles are as close as possible together (i.e. in the ground state), because the Coulomb or Yukawa force which does the binding gets bigger the closer the particles are.

So really, the overall energy available in the nucleus decreases when a gamma ray is emitted. The increase in binding energy is not available or releasable energy, but just what you need to supply to break up the nucleus.

Nickel and iron nuclei have the highest binding energy, which means you can’t get any energy out of them: http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/nucbin.html

The graph of binding energy on that page shows that iron has about 8.7 MeV/nucleon of binding energy. Uranium-235 only has about 7.5 MeV/nucleon.

So the more nuclear binding energy a nucleus has, the more stable it is. The less nuclear binding energy, the more unstable it is in general, and the more likely the nucleus is to undergo nuclear fission or nuclear fusion. In other words, the potential for getting energy out of a nucleus is not proportional to its binding energy.

Having a maximum binding energy actually prevents either fusion or fission from occurring in principle. In the process of both fusion of light elements and fission of heavy ones, an increase in binding energy occurs as well in addition to the release of nuclear energy.

I think this is very interesting because of the analogy between electron structure and photon emission and nuclear shell structure and gamma ray emission. It’s well known that the line spectra of gamma rays emitted by nuclei are analogous in some ways to the line spectra of photons emitted by electrons, unlike beta particles which have a continuous spectra up to a limit or alpha particles which tunnel out of the nucleus. Moreover, just as stable chemical elements occur with “magic numbers” of electrons which correspond to filled, closed outer shells (e.g, helium), the same kind of thing occurs with the number of nucleons in the nucleus. From the stability of nuclei and from the details of the gamma ray line spectra, good nuclear shell models have been worked out.

Physics becomes interesting when questions of that sort are asked, because the person then wants an answer and is curious to find out something.

In the nuclear shell structure model, the most stable nuclei are those with 2, 8, 20, 50 or 82 protons or 2, 8, 20, 50, 82 or 126 neutrons, or both.

This is analogous to the numbers of electrons in closed shells around the atom, 2, 8, 18, 32 and 50 electrons. So there is some evidence for a shell structure in nuclei.

In the case of electrons, the numbers 2, 8, 18, 32, and 50 come from the different combinations of 4 different quantum numbers: n, l, m and s. The Pauli exclusion principle says that each electron in an individual atom has a unique set of the four quantum numbers. The number s can only have two different values (it represents spin). Spinning charges like electrons have a magnetic moment, and if you drop magnets into a small box, then tend to be most stable when they pair up in parallel with the North pole of one pointing in the direction that the South pole of another is pointing. The fact that electrons have spin and thus are magnetic dipoles hence seems the reason why the electron spin is quantized into two values, i.e. the Zeeman effect.

n (shell number): 1, 2, 3, 4, …
s (spin number): +1/2 or -1/2
l (ellipticity number): n-1, n-2, n-3, …
m (magnetic number)= l , l-1, l-2, … 0, -(l-2), -(l-), -l.

Applying the Pauli exclusion principle to these numbers, you find that for n=1 (hence l = 0 and m = 0) only 2 unique electron number sets exist, so the first shell can only accommodate 2 electrons. For n = 2, there are 8 combinations of quantum numbers, so 8 electrons fill the second shell, and so on for other values of n. These numbers of filled electron shells correspond with the number of elements in successive periods of the periodic table, explaining the basics of chemistry.

So presumably the nuclear shell structure comes about because the nucleons have a set of quantum numbers which give rise by the exclusion principle to the “magic numbers” of neutrons and of protons in stable (non-radioactive) nuclei.

Because nucleons thus seem to have quantum numbers, it would seem possible that the virtual particles in the vacuum around a fundamental particle which provide mass (some kind of Higgs field effect) may undergo a similar process. This may link up to the problem of fundamental particle masses. Excluding the electron, virtually all other particle masses are closely quantized to near integer multiples of

{electron mass, 0.511 MeV}*n(N+1)/(2*{alpha})

= 35n(N+1) MeV

where n = number of apparent fundamental particles per observable particle (n=1 for leptons, n = 2 for mesons i.e. quark doublets, and n=3 for baryons i.e. quark triplets), and N is an integer which seems to be related to how many massive bosons in the vacuum (Higgs-like quanta) become associated with the particle. N appears to take “magic numbers” of 2, 8 and 50, if the formula above is correct. I’ve still a lot more work to do on this, mainly because I’ve found that my composite write up contains different ideas I’ve had on the subject in spare moments over a period of years which don’t yet all fit together seemlessly. I will take account of your work on particle masses when I straighten out the details.

2. nige cook

Sorry, my sentence above saying that an apple gains gravitational potential energy when it falls to the floor is wrong. The apple loses gravitational potential energy in falling, gaining kinetic energy. The apple also gains gravitational binding energy, not potential energy, because it gets closer to the Earth and the gravitational field gets stronger at smaller distances, which binds it. I’d better get some sleep now before I make more errors.

3. nige cook

Sorry again, the first sentence of the second para to the first comment should read:

“When nucleons emit energy, they fall to a lower energy level, so they get closer together.”

It’s 1.25 am and my brain isn’t functioning.

By the way, I’ve just about given up on my idea that the correct symmetry of the universe is SU(2) x SU(3), because it seems too difficult to make SU(2) account for weak hypercharge, weak isospin charge, electric charge and gravity.

I thought it would work out by changing the Higgs field so that some massless versions of the 3 weak gauge bosons exist at low energy and cause electromagnetism, weak hypercharge and gravity.

However, since the physical model I’m working on uses the two electrically charged but massless SU(2) gauge bosons for electromagnetism, that leaves only the electrically neutral massless SU(2) gauge boson to perform both the role of weak hypercharge and gravity. That doesn’t work out, because the gravitational charges (masses) are evidently going to be different to the weak hypercharge which is only a factor of two different between an electron and a neutrino. Clearly, an electron is immensely more massive than a neutrino. So the SU(2) x SU(3) model must be wrong.

The only possibility left seems to be similar to the Standard Model U(1) x SU(2) x SU(3), but with differences from the Standard Model. U(1) would model gravitational charge (mass) and spin-1 (push) gravitons. The massless neutral SU(2) gauge boson in the model I’m working on would then mediate weak hypercharge only, instead of mediating gravitation as well.

4. William

“From ecstatic religious devotion to a crude worshipping at the altars of sex and money.”
In other words, exactly what the original Lupercalia was like.

5. carlbrannen

Nigel, yes, the “closer together” analogy is exactly what happens in gravitation. The stuff I’m working on for fundamental forces doesn’t have distance. Everything happens at a single point in spacetime. Which is why the particles you build from it are point particles.