# How does the shape of radioactive material effect its critical mass?

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?

Why hasn't at least one stored nuclear weapons undergone a reaction(not necessarily an explosion but a sustained reaction)? -I know that the fissile material used in atomic weapons are kept in pieces or at a lower density so they aren't at critical mass, but shouldn't this have happened by chance to at least 1 part of the core to at least one weapon?

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.

• Critical mass is lowest for spheres. – Pieter Feb 17 '19 at 9:48
• this might have an answer for you, but you have to go through it as it is a photo osti.gov/servlets/purl/5040422 – anna v Feb 17 '19 at 19:25