In a thread that is now closed Polycarp wrote:
This got me wondering as to what it is about these two isotopes that makes them fissionable?
Technically, any nuclide except H-1 is fissionable – if you get something impacting it just right with enough force, it can be split. However, “fissionable” in the usage I was applying means that it can be easily induced to fission in a chain reaction.
Essentially U-235 and Pu-239 (and a few other isotopes) are hung together in a relatively precarious fashion, so that an impact from a neutron will cause them to fission with the production of additional neutrons that will continue the process.
It would take a much better physicist than I to explain just why this is so, when it isn’t true for Pb-208 or Th-232 or U-238.
Actually, I was under the impression that several isotopes of the transuranics (Americium and Californium come to mind) were fissionable (in the sense of supporting an exothermal fission chain reaction), some of them even having much lower critical masses than the traditional bomb isotopes. But the higher-number transuranics are very difficult to produce in bulk (that is to say, even more difficult than U[sup]235[/sup] or Pu[sup]239[/sup]), which is why we don’t see any weapons made from them.
May very well be true, Chronos; however, transuranics are not found in nature.
Is there such a thing as a cobalt bomb?
The protons in the nucleus want to repel each other, but the strong nuclear force prevents that. A nucleus made entirely of protons would not be able to hold together, because there isn’t enough strong force to counteract the repulsive positve charge. Neutrons generate the strong force, without having any charge. Therefore their net effect is entirely attractive.
If a nucleus does not have enough neutrons, it will be unstable, which is why U-238 is stable,and U-235 is not. The number of protons is the same, but the U-238 has three more neutrons to generate attractive force.
Only U-235 and U-234 of the “naturally occurring” isotopes are fissionable – and U-234 is so rare as to be effectively out of the picture. (It’s produced by alpha decay of U-238 followed by two beta decays, and itself breaks down “rapidly” on a geologic time scale, so that its equilibrium status is in the parts-per-ten-thousand.)
We’re assuming by “exists in nature” here that we’re speaking of “in measurable quantities in the earth’s crust” – we know that Californium exists in supernovae, but that’s hardly useful. There are no doubt minuscule quantities of Pu-239 in nature from the occasional atom of U-238 that absorbs a neutron, but it’s not considered to “exist in nature” in any practical sense – think of it as equivalent to the fact that a tree will probably absorb a microgram of mercury from the ambient mercury as a trace element in the environment, but it would be ridiculous to process a thousand trees to get a milligram of mercury.
What about U-233? I know it is fissionable.
Yes. It’s essentially a regular atomic bomb with a cobalt tamper surrounding the fissile material. The stable cobalt is transmuted into radioactive cobalt-60 with a half-life of about 5.26 years. It is a gamma-ray emitter, and thus is extremly deadly. A cobalt bomb has never actually been built and tested, but nuclear theorists are certain it would work.
The classic definition of “fissionable” is that the isotope, upon capture of a neutron, will split. There are a number of unstable isotopes that meet the definition but they are so short lived, they are of no practical importance. The reason the three famous isotopes, U-233, U-235, and Pu-239 are important is that they are relatively stable and can be fissioned by neutrons of almost all energy levels. The reason U-235 is so much more interesting is that U-233 and Pu-239 don’t occur in nature in any appreciable quantity.
Interestingly, U-238 and Thorium-232 are also fissionable, but only by fast neutrons (very high energy). In a “Fast Breeder Reactor”, Thorium-232 and Uranium-238 both produce power by sustaining a critical reaction with fast neutrons but also produce U-233 and Pu-239, additional fuel, from the capture of slow (thermal) neutrons.
Why are some isotopes more fissionable than others. There are a number of factors, but you have to start with Binding Energy. When you look at binding energy per nucleon (protons and neutrons) of an atom plotted as a function of Atomic Weight, you find that very heavy elements, when split into two smaller elements will release energy. Therefore, they have a natural tendency to split.
Counteracting this energy balance is the stability of the atomic structure. However, atomic structures which have complete or almost complete “shells” of neutrons or protons (analogous to the noble gases complete shells of electrons) are more stable. Certain atoms like Oxygen, Carbon, Lead, Tin, etc. are extremely stable due to this nucleus structure.
As atomic numbers become larger, proton repulsive forces become larger by a second order relationship. As a result, a higher ratio of neutrons to protons is necessary to counteract these forces. However, this results in less complete shells and less stability of the nucleus. As a result, Lead (atomic number 82) is the heaviest “super stable” element and Bismuth (atomic number 83 is the heaviest element that has a stable (non-radioactive) isotope. All the heavier isotopes are radioactive to some extent even though half lives may be quite long.
Finally, why U-235 and Pu-239 and U-238 and Pu-240? The shell structure again results in less stability for the “odd numbered” isotopes as compared to the “even numbered” isotopes". It’s just the way the forces balance since adding a neutron counteracts the proton repulsion.
The classic definition of “fissionable” is that the isotope, upon capture of a neutron, will split. There are a number of unstable isotopes that meet the definition but they are so short lived, they are of no practical importance. The reason the three famous isotopes, U-233, U-235, and Pu-239 are important is that they are relatively stable and can be fissioned by neutrons of almost all energy levels. The reason U-235 is so much more interesting is that U-233 and Pu-239 don’t occur in nature in any appreciable quantity.
Interestingly, U-238 and Thorium-232 are also fissionable, but only by fast neutrons (very high energy). In a “Fast Breeder Reactor”, Thorium-232 and Uranium-238 both produce power by sustaining a critical reaction with fast neutrons but also produce U-233 and Pu-239, additional fuel, from the capture of slow (thermal) neutrons.
Why are some isotopes more fissionable than others. There are a number of factors, but you have to start with Binding Energy. When you look at binding energy per nucleon (protons and neutrons) of an atom plotted as a function of Atomic Weight, you find that very heavy elements, when split into two smaller elements will release energy. Therefore, they have a natural tendency to split.
Counteracting this energy balance is the stability of the atomic structure. However, atomic structures which have complete or almost complete “shells” of neutrons or protons (analogous to the noble gases complete shells of electrons) are more stable. Certain atoms like Oxygen, Carbon, Lead, Tin, etc. are extremely stable due to this nucleus structure.
As atomic numbers become larger, proton repulsive forces become larger by a second order relationship. As a result, a higher ratio of neutrons to protons is necessary to counteract these forces. However, this results in less complete shells and less stability of the nucleus. As a result, Lead (atomic number 82) is the heaviest “super stable” element and Bismuth (atomic number 83 is the heaviest element that has a stable (non-radioactive) isotope. All the heavier isotopes are radioactive to some extent even though half lives may be quite long.
Finally, why U-235 and Pu-239 and not U-238 and Pu-240? The shell structure again results in less stability for the “odd numbered” isotopes as compared to the “even numbered” isotopes". It’s just the way the forces balance since adding a neutron counteracts the proton repulsion.
Fascinating! I’ve never heard of proton and neutron shells. Are they equivalent to electon shells?
I have a question: if neutrons add to the stability of a neucleus, how come heavy atoms are broken down by the addition of a neutron in a fission reation?
Sorry about my previous double post. Internet connection is acting up.
I hesitate to say anything is “equivalent” in the world of subatomic physics but, for our purposes, I think it’s safe to say the shells are “analogous”.
Relative to stability, if you plot isotope nucleus composition on a graph where the x axis is the number of protons and y axis is the number of neutrons you will get a band of actual values. It starts off at 45 degrees but then takes a higher slope as the number of neutrons begins to exceed the number of protons. Outside this band (too many or not enough neutrons) and isotopes do not exist or are increasingly unstable. Not enough neutrons results in too much proton repulsion but I’m not 100% sure about too many. I think it disrupts the acceptable shell structures.
Maybe we’ve got a true nuclear physicist who can elaborate.
In his book Understanding Physics Isaac Asimov has a good section on nuclear stability that is accessible to the layman.