A shake is an informal unit of time equal to 10 nanoseconds, or 10−8 seconds. It has applications in nuclear physics, helping to conveniently express the timing of various events in a nuclear reaction, especially neutron reactions. The typical time required for one step in the chain reaction (i.e. the typical time for each neutron to cause a fission event, which releases more neutrons) is of the order of 1 shake, and the chain reaction is typically complete by 50 to 100 shakes.
This is also applicable to circuits. Since signal progression in IC chips is very rapid, on the order of nanoseconds, a shake is good measure of how quickly a signal can progress through an IC (integrated circuit).
Like many nuclear units, it is derived from top secret operations of the Manhattan Project during World War II. The word comes from the expression "two shakes of a lamb's tail", which indicates a very short time interval. For nuclear-bomb designers, 10 nanoseconds was a convenient specific interval to connect to this term.
It has been discussed at length that the oldest documented usage of the phrase "two shakes of a lamb's tail" can be found within the compiled works of Richard Harris Barham called The Ingoldsby Legends (1840), but likely existed in modern language long before then.
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