What is the minimum mass of a fissionable isotope in which a nuclear chain reaction can occur?

Answer 1

A critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction. The critical mass of a fissionable material depends upon its nuclear properties (e.g. the nuclear fission cross-section), its density, its shape, its enrichment, its temperature and its surroundings.

The minimum mass for a particular fissionable isotope will always be a sphere, as that is the shape which will lose the least neutrons for a given mass. The behavior of a sphere can be affected by its surroundings, if a neutron reflector is present this will reduce the amount needed. The easiest way to compare materials is to consider a bare sphere with no reflector. In this case Uranium 235 requires a mass of 52 kg and a sphere of diameter 17 cm. Plutonium 239 requires a mass of 10 kg and a sphere 9.9 cm diameter.

The Wikipedia article 'Critical Mass' gives a table of other isotopes, but the above two are of most practical interest

Answer 2

The minimum mass for a chain reaction is called the critical mass. The actual amount varies by isotope, but also by the shape of the mass, with a sphere having the least amount of material needed.

The critical masses of spheres of some isotopes are:

• californium-251 - 5 kg.
• plutonium-239 - 10 kg.
• uranium-233 - 15 kg.
• uranium-235 - 52 kg.
• protactinium-231 750 kg.

Since a controlled reaction requires a less dense mass of material, for example spread out among fuel rods, the mass used in a controlled reaction is greater than the amount used in an uncontrolled reaction.

A link to the Wikipedia article on critical mass is below.

Answer 3

Although two to three neutrons are produced for every nuclear fission, not all of these neutrons are available for continuing the fission reaction. If the conditions are such that the neutrons are lost at a faster rate than they are formed by fission, the chain reaction will not be self-sustaining.

Accordingly, at the point when the mass is enough that the chain reaction can become self-sustaining, this minimum mass is referred to as the critical mass.

This critical (or minimum) mass depends on several factors as the shape of the material, its composition and density, and the level of purity.