What is the process of determining a specific age of an object.

Carbon dating is usually used for the determination of the age or date of organic matter from the relative proportions of the carbon isotopes carbon-12 and carbon-14 that it contains. The ratio between them changes as radioactive carbon-14 decays and is not replaced by exchange with the atmosphere. Though other forms may be used. Remember to check yourself.
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Processes above and be sure to mention the movement of electrons and energy as the carbon atom moves from one reaction to another.