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Relationship between radioactive isotope and radioactive dating

If and when equilibrium is achieved, each successive daughter isotope is present in direct proportion to its half-life; but since its activity is inversely proportional to its half-life, each nuclide in the decay chain finally contributes as many individual transformations as the head of the chain, though not the same energy.

For example, uranium-238 is weakly radioactive, but pitchblende, a uranium ore, is 13 times more radioactive than the pure uranium metal because of the radium and other daughter isotopes it contains.

Not only are unstable radium isotopes significant radioactivity emitters, but as the next stage in the decay chain they also generate radon, a heavy, inert, naturally occurring radioactive gas.

All the isotopes which have half-lives less than 100 million years have been reduced to % or less of whatever original amounts were created and captured by Earth's accretion; they are of trace quantity today, or have decayed away altogether.

There are only two other methods to create isotopes: artificially, inside a man-made (or perhaps a natural) reactor, or through decay of a parent isotopic species, the process known as the decay chain.

Unstable isotopes decay to their daughter products (which may sometimes be even more unstable) at a given rate; eventually, often after a series of decays, a stable isotope is reached: there are about 200 stable isotopes in the universe.

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The four paths are termed 4n, 4n 1, 4n 2, and 4n 3; the remainder from dividing the atomic weight by four gives the chain the isotope will use to decay.There are other decay modes, but they invariably occur at a lower probability than alpha or beta decay.

Near the end of that chain is bismuth-209, which was long thought to be stable.All the elements created more than 4.5 billion years ago are termed primordial, meaning they were generated by the universe's stellar processes.At the time when they were created, those that were unstable began decaying immediately.These can range from nearly instantaneous to as much as 10 years or more.The intermediate stages each emit the same amount of radioactivity as the original radioisotope (i.e.there is a one-to-one relationship between the numbers of decays in successive stages) but each stage releases a different quantity of energy.