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The new atom doesn't form the same kinds of chemical bonds that the old one did. It may not even be able to hold the parent atom's place in the compound it finds itself in, which results in an immediate breaking of the chemical bonds that hold the atom to the others in the mineral. (The exact details of this are rather complicated, so I won't go into them here.) When the number of electrons change, the shell structure changes too.So when an atom decays and changes into an atom of a different element, its shell structure changes and it behaves in a different way chemically. That's the sum total of the chemical and physical basis of radiometric dating.
Some isotopes have very long half-lives, measured in billions or even trillions of years.
Others have extremely short half-lives, measured in tenths or hundredths of a second.
Presented with a new method that gave answers different than existing methods, the scientists involved did not simply assume that either the old method or the new one was wrong.
They viewed the problem as a challenge, dug into it with all their energy, and didn't stop until they understood exactly why their C14 dates disagreed with traditional dates, what was wrong with their C14 procedures, and how to compensate for the problems in the future. When Professor William Libby developed the C14 dating system in 1949, he assumed that the amount of C14 in the atmosphere was a constant.
The second assumption is that the organism in question got its carbon from the atmosphere.