If critical mass is defined by the amount of fissile material required to sustain nuclear fission. Assuming a subcritical mass object, and knowing radioactive materials can merely by chance break apart due to radioactive decay releasing neutrons in random directions causing only minor reactions because the object isn't at critical mass (not enough material in the right quantity, shape, pressure etc or without enough help from a neutron reflector) the majority of the neutrons will fly out of the object with no sustained reaction. Simply put the object is merely radioactive.

Given that (specifically calling to the importance of shape in critical mass), shouldn't there be a possibility, albeit very small, of a mass object that would be critical given it had a spherical shape but instead has a cylindrical shape(meaning its not at critical mass because of its current shape), of having a sustained reaction. I could understand if criticality was defined solely by temperature, enrichment or some other factors but shouldn't the size shape and density(especially since an object can't maintain a perfectly even density) cause a fairly large ambiguity in calculating the critical mass of an object.

My questions are: Firstly, are there any flaws in my current thinking/understanding?

If not how can you calculate critical mass accurately given such a large dependence on chance?

And how do you actually calculate the critical mass of an object?

If you could provide a lecture or some resource that shows how critical mass is calculated, it would greatly help my understanding.


the critical mass of a chunk of fissionable material is sensitively dependent on its shape. Any shape that is nonspherical will have a higher critical mass than that of a sphere of the same material. For example, in fission bomb design, it is a common technique to begin with a mass of plutonium which is oblate and subcritical and then use explosives to force it into a spherical shape, at which time it becomes critical.


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