Silver fusion and fission

George Gamow’s One Two Three… Infinity (which I highly recommend) states but does not explain that silver cannot be made to undergo fission or fusion; that it represents the ultimate end state of such reactions. Is there a good explanation of why silver has this property or has the theory changed since publication - my edition is from 1971.

Silver, I see, can undergo beta decay into cadmium, but will there be a gradually increasing abundance of silver in the universe, making long-term investment plans iffy at best? ( :smiley: )

I thought it was iron that was the endpoint.

Though even iron can be made to fuse, just not in a self sustaining reaction (otherwise we’d never find any elements heavier the Fe in the universe).

Yeah, I’ve always heard that about iron, not silver. I’ve got a copy of the book, but I can’t find the passage you’re referring to easily; which section is it in?

I just flipped through my copy (1961 ed.) of the book, and in the Microcosmos section, Modern Alchemy, on page 168 we have this:

He of course goes on to explain that the nuclei hardly ever get close enough together for this to happen so people intentionally fuse or fission them. Notice that he says “approximately up to silver”… Maybe he wasn’t sure. I think he was working from a surface-tension model of the nucleus and I’m not so sure how it’s done these days.

What the hell, I hope that helps.

At the risk of running afoul of [sup]1[/sup]copyright issues, I’ll submit a response a similar question about Iron from 2001. Here is the response by our own mod bibliophage The following words are all his:

One model of the nucleus that is pretty easy to envision is called “the liquid drop model.” In an actual drop of water, water molecules in the middle of the drop are attracted to all the neighboring molecules. Molecules near the surface have no neighbors on the outside, so the net force on surface molecules is toward the center. This is surface tension, which tends to keep the water drop spherical. Something similar keeps the nucleus together, but it gets a big complicated.

In the nucleus, there are attractive forces (the strong nuclear force) between all the nucleons (protons and neutrons), but also repulsive forces (the electric force) between the protons. (Protons repel each other because they are all positively charged.)

The stability of the nucleus depends on a lot of different things, which are encapsulated in a formula called Weizäcker’s semiempirical formula [sup]2[/sup], which has four terms:

  1. The first term depends only on the number of nucleons. It takes into account the attractive force between all the nucleons, the strong nuclear force. This term is positive because it tends to make the nucleus stable. This term tends to make heavier nuclei more stable than light ones.
  2. The second term depends on the number of nucleons (to the 2/3 power. This term is negative.
  3. The third term depends on the number of protons (squared) and the number of nucleons (to the 1/3 power). It takes into account the electrical repulsion between the protons. (The reason it doesn’t depend solely on the number of protons is that with more neutrons, the protons are less closely packed and repel each other less.) This term is negative because it tends to make the nucleus less stable. This term tends to make nuclei with many neutrons more stable than those with few neutrons.
  4. The fourth and final term is the one most difficult to understand. It takes into account the “asymmetry energy.” Isotopes with equal numbers of neutrons and protons tend to be especially stable. For example, Carbon-12 is composed of exactly 6 protons and 6 neutrons, and is much more stable than any other nucleus composed of 12 nucleons.

The reason is that protons can’t all fit into the same energy state, and the neutrons can’t all fiti into the same neutron state. (Neutron energy states are separate from proton energy states.) When you add an extra proton (or neutron), it goes into a higher energy state than the rest. Imagine a hypothetical molecule with six protons and no neutrons (Carbon-6). The sixth proton goes into a very high energy state, but there are a lot of empty neutron energy states that have gone unfilled, an unstable combination.

So the fourth term tends to make nuclei more stable that have an equal number of protons and neutrons. This term is zero for “balanced,” negative for all others. The bigger the difference between the number of protons and neutrons, the more negative the number will be.

Iron-56 (with 26 protons and 30 neutrons) is as stable as it is because it represents a compromise between these four considerations. Carbon-12, for example, loses few points for #3, but also gets more points for #1 and #2. Uranium-238 gets more points for #1 and #2, but loses more points for #3 and #4. It’s true that Iron-56 is the most stable isotope, but there are a lot of isotopes with about 40-70 nucleons that are almost as stable.
[sup]1[/sup]The original thread seems to have been deleted. I printed a copy a long time ago, because the answer was too good to risk losing.

[sup]2[/sup] B = 15.753 A – 17.804 A[sup]2/3[/sup] – 0.7103 Z[sup]2[/sup]/A[sup]1/3[/sup] – 94.77(½A – Z)[sup]2[/sup]/A
Where B is the binding energy in MeV, Z is the number of protons, and A is the number of nucleons.

If my calculations are right, the formula would predict that the binding energy per nucleon. . .
For Carbon-12: 7.0 MeV
For Iron-56: 9.9 MeV
For U-238: 7.7 MeV

Iron is the lowest energy per nucleon, but it’s still quite possible that silver could not energetically-favorably split. Remember, fission doesn’t split off one proton at a time; the parent nucleus splits more or less in half. So the first exothermic fissionable element could plausibly be as much as twice as large as iron. And silver is, in fact, a bit less than twice iron.

Issac Asimov wrote an essay called “The Dead-End Middle” about iron-56 (which I also recommend). Iron-56 can be compelled, under supernova conditions, to fuse into heavier nuclei. Gamow, however, is quite specific about silver (chapter 7, section 2 in my copy):

I think we are missing the OP, and getting into if silver can release energy if fused/fisioned, and if it’s the lowest energy state. The OP stated that silver can not undergo fusion or fission at all. It seems like not a proton or neutron can be added or taken away, even if energy is input into the system to make it happen endothermically, as I read the OP.

I can’t see it happening, but I really have no idea. At the very least I’m pretty sure you can off a subatomic partial using a antiparticle, convert it to neutronium, colapse it into a singularity , so there are ways of getting rid of the stuff, but none of that is fusion or fission.

Actually one of the easiest ways to get rid silver is to leave it at curbside with a sign saying ‘FREE’