I understand that too short a half-life and flash point, becomes kind of meaningless, if the element generates too much heat, so this only applies to longer half-lives.

Also, as I understand it, flash point is a process of neutrons and the density of the atomic nucleuses in the material, so adding more of the radioactive element can lead to a critical reaction (also here).

What I don't understand is, how the reaction starts? Alpha and Beta decay doesn't release neutrons, so where do the neutrons come from initially to create the flash point? I also understand, that some radioactive elements, like Uranium 235, because U-236 reasonably stable, U-235 doesn't have a critical mass.

If the alpha particles, electrons or positrons or gamma rays, trigger the initial splitting of some of the radioactive nuclei, then there should be a clear relation between half-life and critical mass, but looking at the chart, there doesn't seem to be.

Critical mass of sphere

I understand the relation between critical mass and density. That makes sense, but I don't understand where the neutrons come from to trigger the critical mass reaction in the first place.

Is it that some radioactive elements undergo natural splitting (also see here), as opposed to the more common radioactive decay? That's the only explanation I can think of.

An answer, partially in layman's terms would be appreciated. I have no plans to build a bomb, only to understand the basics of the physics. :-)

EDIT - I meant to say Uranium 238 doesn't reach critical mass as a sphere. This question has been so edited, I'm honestly not sure what to do with it.

Comment: I was only trying to figure out what causes the neutron chain reaction in a bare sphere of radioactive elements and why it seems to have no relation to the decay rate.

Interestingly, the answer that was turned into a comment by @Fred.Zwarts was my favorite response so far, because it mentioned spontaneous fission and neutron emission, which makes sense.

I was just trying to understand the cause or trigger of how critical mass is met when the pure isotope is put in too large a sphere, or stacked as too many bricks.

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    $\begingroup$ Does this answer your question: arpansa.gov.au/understanding-radiation/what-is-radiation/… ? $\endgroup$ Commented Mar 25 at 9:01
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    $\begingroup$ Did you read the "flash point" article to which you linked? It says nothing about nuclear physics. $\endgroup$ Commented Mar 25 at 9:47
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    $\begingroup$ @Brendan Please don't vandalise questions by editing in irrelevant links. $\endgroup$
    – PM 2Ring
    Commented Mar 25 at 9:58
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    $\begingroup$ "so where do the neutrons come from initially to create the flash point?" They could be stray particles from outside the system such as cosmic rays or natural background radiation, that start an avalanche of chain reactions. Please clarify exactly what you mean by "flash point", perhaps with a link that IS relevant. $\endgroup$
    – KDP
    Commented Mar 25 at 18:13
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    $\begingroup$ Yes, what does "flash point" mean in this context? I have heard it used for fusion processes, but I don't remember ever hearing it used for fission. $\endgroup$ Commented Mar 25 at 18:41

2 Answers 2



It seems that *I* didn't initially read the article that *I* linked to either. But now I have read it, and I have updated my answer, below, to reflect what I learned.

I don't understand where the neutrons come from to trigger the [chain] reaction in the first place

If you want to build a nuclear reactor, you can rely on spontaneous fission, which is mentioned in the "critical mass" article to which you linked.

Modern nuclear weapons, on the other hand, must rely on other means to produce a burst of neutrons in exactly the right microsecond. One way they do that is by placing a capsule of mixed deuterium and tritium gas at the very center of the nuclear fuel. Tthe tritium is compressed and heated by the implosion shock wave the fission of the first approximately 1% of the plutonium fuel. The heavy hydrogen undergoes fusion, and yields enough neutrons at just the right moment to reliably initiate accelerate the chain reaction so that most of the plutonium fuel can be "burned" before the imploded core disassembles itself.


Without the fusion "boost," it's difficult to confine the exploding core for long enough for more than about 20% of it to be used.

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    $\begingroup$ Well, deuterium + tritium, which fuses much more easily than T-T. $\endgroup$
    – Jon Custer
    Commented Mar 25 at 20:18

A chain reaction requires fissile material

Fissile material is material that can undergo nuclear fission when struck by a neutron of low energy. A self-sustaining thermal chain reaction can only be achieved with fissile material.

Fissile elements have a high atomic number $\rm{Z}$ (number of protons). The electrostatic repulsion between the protons makes heavy nuclides unstable. The light stable nuclides have approximately equal numbers of protons and neutrons, but as $\rm{Z}$ increases the neutron / proton ratio increases, which spreads the protons out, reducing the repulsion. However, the nuclear force (the residual strong force), which binds nucleons together, drops off quickly over distance, so it primarily binds nucleons to their immediate neighbours. In contrast, the electrostatic force is long-range, so each proton in the nucleus "feels" the repulsion from all the other protons. In the heaviest elements adding more neutrons isn't sufficient to overcome the repulsion, and so the element is unstable.

The primary decay mode of these heavy elements is alpha particle emission. This reduces the mass of the nucleus, so it reduces the required neutron / proton ratio. An alpha particle consists of two protons and two neutrons, so emitting an alpha particle increases the nucleus's neutron / proton ratio.

A nucleus could increase the neutron / proton ratio by emitting a positron (beta+ decay), but that requires the weak interaction to convert a proton to a neutron, which operates on a slower timescale than the strong interaction, so it has a much lower probability. Also, the (rest) mass of a neutron is greater than that of a proton, so positron emission doesn't help much with the mass problem.

Another option is spontaneous fission (SF), where the nucleus splits into two smaller nuclei. Those smaller nuclei have much lower $\rm{Z}$ than the original nucleus, and so they require a lower neutron / proton ratio. Thus spontaneous fission also releases a number of neutrons.

The details of what types of decay occur, and their probabilities, and the energies of the decay products, are governed by the nuclear shell structure.

The relationship between the various decay modes is given by their branching ratios:

the branching fraction (or branching ratio) for a decay is the fraction of particles which decay by an individual decay mode.

Generally, the branching ratio of a given nuclide decaying by SF tends to be much smaller than the branching ratio of it decaying by alpha emission, and so the overall half-life of the nuclide tends to be dominated by its alpha emission rate.

Here's a table extracted from Wikipedia, originally from Fundamentals of Nuclear Science and Engineering by Shultis, J. Kenneth; Faw, Richard E. (2008).

Spontaneous fission rates

$$\begin{array}{|l|c|c|} \hline \text{Nuclide} & \text{Half-life} & \text{Fission rate}\\ \text{} & \text{(yrs)} & \text{(% of decays)}\\ \hline {}^{235}\rm{U} & 7.04·10^8 & 2.0·10^{-7}\\ {}^{238}\rm{U} & 4.47·10^9 & 5.4·10^{-5}\\ {}^{239}\rm{Pu} & 24100 & 4.4·10^{-10}\\ {}^{240}\rm{Pu} & 6569 & 5.0·10^{-6}\\ {}^{250}\rm{Cm} & 8300 & {\sim}74\\ {}^{252}\rm{Cf} & 2.6468 & 3.09\\ \hline \end{array}$$

We see that the branching ratios for SF tend to be very small, and cover a wide range of magnitudes.

From that table, it may seem that ${}^{238}\rm{U}$ would be a better nuclear fuel than ${}^{235}\rm{U}$. However, ${}^{238}\rm{U}$ is not fissile because it requires high energy neutrons to induce it to fission, but the neutrons it emits when it fissions have low energy.

A fission reactor (or weapon) usually doesn't rely on SF of the fuel to achieve criticality. The branching ratio is just too low. Some early reactors did rely on SF (and cosmic rays) to get started, but modern fission devices use an additional neutron source

A startup neutron source is a neutron source used for stable and reliable initiation of nuclear chain reaction in nuclear reactors, when they are loaded with fresh nuclear fuel, whose neutron flux from spontaneous fission is insufficient for a reliable startup, or after prolonged shutdown periods. Neutron sources ensure a constant minimal population of neutrons in the reactor core, sufficient for a smooth startup. Without them, the reactor could suffer fast power excursions during startup from state with too few self-generated neutrons (new core or after extended shutdown).


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