Answer to Question #131344 in Atomic and Nuclear Physics for Robert

Question

In a certain chain reaction, each fission event releases on average two neutrons that go on to cause further fission after 0.1 seconds. How many nuclei would have been fissioned 1 second after an initial fission event?

Answer 1

After every 0.1 second the number of new nuclei doubles. Initially we have 1 nucleus, after 0.1 second we get two additional nuclei, after next 0.1 seconds we get 4=2² additional nuclei, and so on. After the tenth 0.1 second we get 2^{10 } additional nuclei. Therefore, the total number of nuclei will be

$1+2^1+2^2 +\ldots +2^{10} = \dfrac{2^{11}-1} {2-1} =2047$