A-bomb critical mass

When creating an atomic bomb out of Uranium 235 or plutonium, you must have a minimum mass to initiate fission. What is this critical mass, and how did scientists discover it? I mean, what physical parameters dictate this minimum mass?

IIRC it’s 5kg of U-235.

I don’t know how they figured it out but presumably not by trial and error.

Basically they did it with experiments and math.

They figured out the ‘efficiency’ of small chain reactions in uranium (what percentage of freed neutrons would go on to split more nuclei and free more neutrons). This told them how ‘many’ U nuclei would need to be split in order for the reaction to continue and explode.

Then using the density of uranium and cubic geometry they figured out how ‘big’ this many nuclei of U would be.

It was a tad more complicated than this, but this is the basic idea.

I’m sure someone has better details than I do - possibly from a more recent reading of Tom Clancy, but doesn’t density also play a part in initiating a sustainable chain reaction?

As I understand it, a critical mass will eventually explode all by itself, which is not ideal for storing weapons, so the bomb is made with a sub-critical mass, surrounded by shaped high explosives. When the explosive shield is detonated, the inward force compresses the core, increasing density considerably, and initiating a chain reaction. Boom.


Here’s a site that goes into a lot of detail about making all kinds of atomic weapons:


According to this, a typical critical mass for an unreflected sphere of U-235 is 52 kg. For Pu-239 in the alpha phase, it’s about 10 kg.

Elsewhere on the site, it does say that density has a very big effect on critical mass, which is important in implosion-type bombs, so that 5 kg may be enough for a plutonium bomb because plutonium can be compressed enough to lower the critical mass quite a bit. If you look around on that site, you’ll probably find all the details you need to understand the process.