The term
shake in
weaponeering refers to the smallest 'useful unit' of time that occurs during
fission. It is not directly derived from a particular process; rather, it represents a rough average of the time required for a single 'generation' of fission. Not only is this time averaged across multiple neutron emission/capture cycles, it is also averaged across various fissile materials. The time of a fission 'generation' is related to both the velocity of the neutrons emitted within the material as well as to the density of that material, which relates to what is referred to as the
mean free path. This is the mean distance, usually expressed in
centimeters, which each neutron will travel within the critical mass before being captured by an atom, resulting in a new fission generation. Averaging the most common fissile materials' values gives a result of approximately 13cm; a 1
MeV neutron traverses this distance in just around 10 nanoseconds - which is the basis of the shake.
The speed of this reaction, and the process of fission, becomes clear if you work the math outwards from here. It takes roughly 2*10^24 atoms splitting to release 20 kt of energy, or the amount of energy released by a small atomic bomb. Since fission generations increase in size exponentially (1 neutron results in 2 neutrons emitted which results in 4 neutrons emitted and so forth - the term for this is k, a coefficient which indicates the number of neutrons which not only are produced per available neutron, but are restricted to those that do not escape or undergo capture by a non-fissioning atom. In a weapon, k tends to be around 2) the total number of atoms that have undergone fission at any point can be expressed as 2^(n-1) where n is the number of generations that have occurred. Therefore, solving for n, we get (I hope, my maths are horrible):
2*10^24 = 2^(n-1)
log 2 (2*10^24) = n-1
log 2 (2*10^24) +1 = n
/me struggles with scientific calculators, then Google, and finds that oh hurray, Carey Sublette already did this math! According to him:
81.7 = n
..or less than 82 fission generations are required to split all the atoms necessary to release 20 kilotons of energy. Even if we were to assume a purely mechanical and linear process (it isn't; generations overlap in time in the 'real world' meaning the actual number will be smaller) that's still only 82 shakes, or 820 billionths of a second. It gets worse; since the energy release is exponential, that means that the most recent 4-5 generations have produced (at any point) 99 percent of the total energy released thus far! That means that realistically, 99 percent of the actual energy release of a 20 kt atomic bomb happens in less than 5 shakes, or 50 billionths of a second.
So the shake is extremely important when designing, describing, or predicting the outcome of atomic fission, whether the low-k 'critical' type such as is found in nuclear reactors, or the high-k 'supercritical' type found in nuclear explosions.