in chemical terms, when the energy released from the reaction exceeds the activation energy and the reaction thus becomes self-perpetuating.

related: exothermic reacton

A chain reaction starts with something, the instigator, so to speak, which may be an object or a person, animal, etc. It is followed by a series of incidents, that form the chain, and usually ends with some big event, or it could phase out slowly.. it may never end. The main thing to remember is that it is a chain, and all things that happen in it are linked. Any way..

Here's a good example of a real-life chain reaction that just happened today, in my crazy life:

My sister was being a jerk. I was trying to prepare dinner (spaghetti, for those interested).. I told my sister to get lost because she was driving me crazy. She in turn threw cheese in my hair. This was funny to me, so I threw the cheese back at her, attempting to get it into her hair. She then did it again and in order to stop the cycle I got up to play-wrestle/fight with her, and she took off out the door. At that point, she realized that this would only lead to me locking her out, so she tried to come back in as I was closing the door. The whole thing came to a pretty sudden end when she shoved her hand through the glass in the door window. Oh lordy. Needless to say, this wasn't such a good thing. (Also of note, this is the second time she's shoved her hand through the same door.)

The initial incident in this case was my sister, and the final incident was the smashing of the window. The cycle will of course continue, because we'll both get in trouble for breaking it, etc., etc.

There is also a moral to that story:

Don't smash windows, it gets you in trouble.
In the nuclear field, a chain reaction is what occurs when you get a critical mass of some fissionable material, like uranium or plutonium.

If you are making a nuclear reactor, you get lots of heat, which makes lots of steam, which drives a turbine, which makes lots of megawatts of lovely electricity for the utility companies to charge an arm and a leg for.

If you are making a nuclear bomb, you get LOTS of heat and radiation, which makes lots of fire and burns and smoke and a really big mushroom cloud and a nasty pressure wave, which make lots and lots and lots of death and destruction and radiation sickness, and lots of cancer and mutations too, which means that in the end you lose an arm and a leg there as well.

The moral of the story? Stay away from chain reactions - they are bad for your limbs.
Diagram of a Chain Reaction


                                       |
                                       |
                                       |
                                       |
    (1)------------------------------> o

                                    . o o .
                                   . o_0_o . <-----------------------(2)
                                   . o 0 o .
                                    . o o .

                                       |
                                      \|/
                                       ~

                                 . o o. .o o .
    (3)-----------------------> . o_0_o"o_0_o .
                                . o 0 o~o 0 o .
                                 . o o.".o o .
                                       |
                                  /    |    \
                                |/_    |    _\|
                                ~~     |     ~~
                                       |
                           o o         |        o o
    (4)-----------------> o_0_o        |       o_0_o <---------------(5)
                          o~0~o        |       o~0~o
                           o o )       |      ( o o
                              /        o       \
                             /        (1)       \
                            /                    \
                           /                      \
                          /                        \
                         o (1)                  (1) o
                 . o o .            . o o .            . o o .
                . o_0_o .          . o_0_o .          . o_0_o .
                . o 0 o .  <-(2)-> . o 0 o . <-(2)->  . o 0 o .
                 . o o .            . o o .            . o o .

                  /                    |                    \
                |/_                   \|/                   _\|
                ~~                     ~                     ~~

      . o o. .o o .              . o o. .o o .              . o o. .o o .
     . o_0_o"o_0_o .            . o_0_o"o_0_o .            . o_0_o"o_0_o .
     . o 0 o~o 0 o . <--(3)-->  . o 0 o~o 0 o .  <--(3)--> . o 0 o~o 0 o .
      . o o.".o o .              . o o.".o o .              . o o.".o o .
        .   |   .                  .   |   .                  .   |   .
       /    |    \                /    |    \                /    |    \
       :    |    :                :    |    :                :    |    :
       :    |    :                :    |    :                :    |    :
      \:/   |   \:/              \:/   |   \:/              \:/   |   \:/
       ~    |    ~                ~    |    ~                ~    |    ~
  (4) o o   |   o o (5)      (4) o o   |   o o (5)      (4) o o   |   o o (5)
     o_0_o  |  o_0_o            o_0_o  |  o_0_o            o_0_o  |  o_0_o
     o~0~o  |  o~0~o            o~0~o  |  o~0~o            o~0~o  |  o~0~o
      o o ) | ( o o              o o ) | ( o o              o o ) | ( o o
         /  |  \                    /  |  \                    /  |  \
        /   |   \                  /   |   \                  /   |   \
       /    |    \                /    |    \                /    |    \
      /     |     \              /     |     \              /     |     \
     /      o      \            /      o      \            /      o      \
    /      (1)      \          /      (1)      \          /      (1)      \
   o                 o        o                 o        o                 o
  (1)               (1)      (1)               (1)      (1)               (1)
Diagram Outline
1 - Incoming Neutron
2 - Uranium-235
3 - Uranium-236
4 - Barium Atom
5 - Krypton Atom

There are things to be dealt with
but later

There are lances to forge
and checkbooks to balance
and mornings to break
and portholes to grease
and tides to release
and airships to ballast

There are shoes to resole
and souls to rest easy
and easy days thrown
at the feet of the weary

There are rings for engraving
and graves for repenting
and pent-up emotions

There are bottles of asp'rin
and pieces of marble
and delicate thimbles
and spoonfuls of sugar
and buckets of icewater

There are pores to be scrubbed
and scrubs to be bleached -
baskets of peaches
baskets of string
baskets of lobsters and other things

All to be filed and frozen and castrated
all to be sorted and dusted and bent
to be woven and crumpled and locked in a cupboard
in time

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