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Radiometric dating is a means of determining the "age" of a mineral specimen by determining the relative amounts present of certain radioactive elements.
By "age" we mean the elapsed time from when the mineral specimen was formed.
Radioactive elements "decay" (that is, change into other elements) by "half lives." If a half life is equal to one year, then one half of the radioactive element will have decayed in the first year after the mineral was formed; one half of the remainder will decay in the next year (leaving one-fourth remaining), and so forth.
The formula for the fraction remaining is one-half raised to the power given by the number of years divided by the half-life (in other words raised to a power equal to the number of half-lives).
If we knew the fraction of a radioactive element still remaining in a mineral, it would be a simple matter to calculate its age by the formula To determine the fraction still remaining, we must know both the amount now present and also the amount present when the mineral was formed.
The number of protons in the nucleus of an atom is called its atomic number.
The sum of protons plus neutrons is the mass number.
We designate a specific group of atoms by using the term "nuclide." A nuclide refers to a group of atoms with specified atomic number and mass number.
Potassium-Argon dating: The element potassium (symbol K) has three nuclides, K39, K40, and K41. K40 can decay in two different ways: it can break down into either calcium or argon.
The ratio of calcium formed to argon formed is fixed and known.
Therefore the amount of argon formed provides a direct measurement of the amount of potassium-40 present in the specimen when it was originally formed.