Discuss the theory of nuclear decay as it relates to dating of our Earth.

A chemical element consists of atoms with a specific number of protons in their nuclei but different atomic weights owing to variations in the number of neutrons. Atoms of the same element with differing atomic weights are called isotopes. Radioactive decay is a spontaneous process in which an isotope (the parent) loses particles from its nucleus to form an isotope of a new element (the daughter). The rate of decay is conveniently expressed in terms of an isotope's half-life, or the time it takes for one-half of a particular radioactive isotope in a sample to decay. Most radioactive isotopes have rapid rates of decay (that is, short half-lives) and lose their radioactivity within a few days or years. Some isotopes, however, decay slowly, and several of these are used as geologic clocks. The parent isotopes and corresponding daughter products most commonly used to determine the ages of ancient rocks are listed below:

Parent Isotope   Stable Daughter Product   Currently Accepted Half-life Values

Uranium-238   Lead-206   4.5 billion years

Uranium-235   Lead-207   704 million years

Thorium-232   Lead-208   14.0 billion years

Rubidium-87   Strontium-87   48.8 billion years

Potassium-40   Argon-40   1.25 billion years

Samarium-147   Neodymium-143   106 billion years

 

The mathematical expression that relates radioactive decay to geologic time is called the age equation and is:

t =1/delta ln(1 + D/P)

Where:

t is the age of a rock or mineral specimen,

D is the number of atoms of a daughter product today,

P is the number of atoms of the parent product today,

ln is the natural logarithm (logarithm to base e), and

delta is the appropriate decay constant.

(The decay constant for each parent isotope is related to its half-life, t 1/2, by the following expression:

t 1/2 = ln2/delta

Dating rocks by these radioactive timekeepers is simple in theory, but the laboratory procedures are complex. The numbers of parent and daughter isotopes in each specimen are determined by various kinds of analytical methods. The principal difficulty lies in measuring precisely very small amounts of isotopes.

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The primary source of energy for volcanism is radioactive decay in the Earth's interior, which provides heat that becomes locally concentrated enough to produce partial melting of Earth's rock.