Chemiluminescence
Chemiluminescence is the emission of light as a part of the product from a chemical reaction.  It is known that when a chemical reation creates light, heat is also produced.  Light and heat go hand in hand.  However some reactions can produce light without heat.  These are called chemiluminescent reactions.  Chemiluminescence is generated by electromagnetic radiation (radiation shown in EM spectrum).  It can be produced as ultraviolet, visible, or infrared, but is primarily emitted as visible light.  It is shown as light from released energy by a chemical reaction.  In this reaction, from the reactants A and B, with intermediate X, you get A + B -> X -> products + light.  We receive light in these reactions due to the decay of the excited state (X) moving to a lower energy level.  Generally?, one photon of light is given off for each molecule of reactant.  An example of light emitted by chemiluminescence is a light stick.  Chemiluminescent reactions that take place within living organisms are called bioluminescent reactions.
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Bioluminescence
Bioluminescence is the emission of light as produced by a chemical reaction in an organism.  It is the occurence of certain living organisms to produce light.  This phenomenon is created when two chemicals react.  One, called the luciferin, which produces the light. And one, called the luciferase, which catalyzes the reaction.  Within the luciferin, a certain protein is oxidised (oxidation is the loss of an electron from an atom or molecule) from an enzyme, also known as the luciferase.  This chemical reaction can be either an intracellular or external process.  When the molecule (luciferin and luciferase) is added to a certain ion, the combination causes light to be produced. (see right).  Bioluminescence can be found in organisms such as fireflies.
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Bioluminescent mushroom
Image from http://www.mcb.harvard.edu/hastings/Images/bioluminescence.html
Example of Bioluminescence- Antarctic Krill
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