These two independent and agreeing dating methods for of the age of two primary members of the solar system formed a strong case for the correctness of his answer within the scientific community.This just goes to show that just because independent estimates of age seem to agree with each other doesn't mean that they're correct - despite the fact that this particular argument is the very same one used to support the validity of radiometric dating today.The energies involved are so large, and the nucleus is so small that physical conditions in the Earth (i.e. The rate of decay or rate of change of the number N of particles is proportional to the number present at any time, i.e.The half-life is the amount of time it takes for one half of the initial amount of the parent, radioactive isotope, to decay to the daughter isotope.The use of radiometric dating was first published in 1907 by Bertram Boltwood and is now the principal source of information about the absolute age of rocks and other geological features, including the age of the Earth itself, and can be used to date a wide range of natural and man-made materials.Among the best-known techniques are radiocarbon dating, potassium-argon dating and uranium-lead dating.

As one answer to his critics, Kelvin produced a completely independent estimate -- this time for the age of the Sun.

The only problem is that we only know the number of daughter atoms now present, and some of those may have been present prior to the start of our clock. The reason for this is that Rb has become distributed unequally through the Earth over time.

We can see how do deal with this if we take a particular case. For example the amount of Rb in mantle rocks is generally low, i.e. The mantle thus has a low If these two independent dates are the same, we say they are concordant.

Thus, if we start out with 1 gram of the parent isotope, after the passage of 1 half-life there will be 0.5 gram of the parent isotope left.

After the passage of two half-lives only 0.25 gram will remain, and after 3 half lives only 0.125 will remain etc.

Although the time at which any individual atom will decay cannot be forecast, the time in which any given percentage of a sample will decay can be calculated to varying degrees of accuracy.

The time that it takes for half of a sample to decay is known as the half life of the isotope.

This is consistent with the assumption that each decay event is independent and its chance does not vary over time.

where is the half-life of the element, is the time expired since the sample contained the initial number atoms of the nuclide, and is the remaining amount of the nuclide.

Symbolically, the process of radioactive decay can be expressed by the following differential equation, where N is the quantity of decaying nuclei and k is a positive number called the exponential decay constant.

The meaning of this equation is that the rate of change of the number of nuclei over time is proportional only to the number of nuclei.

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