How does uranium's long half-life explain why it is still found in nature?

Answer 1

Having a very long half life (especially the isotope 238U) uranium remain in the earth (in the earth crust and also in the interior). The age of the earth (and also the age of the universe) is too small to permit the decay of the total quantity of uranium.

It is also important to understand exactly what is meant by half life. There can be a misconception that the half life is equal to half the time which a radioactive material will remain radioactive. This is incorrect. Instead half life can be considered as the time taken for 50% of a radioactive material to undergo radioactive decay.

It is impossible to tell exactly which atoms of the whole material sample will decay or exactly when, the only certainty is that after a length of time equal to the half life, 50% of them will have undergone decay. After another length of time equal to the half life 50% of the remaining original element will have decayed. This is an example of exponential decay. The half life of Uranium is 4.468×109 years. An illustrative example of the decay of a 1kg mass of uranium 238 is given below:

Starting with:

1kg Uranium 238

4.468×109 years pass:

0.5 kg of Uranium 238 remains, along with 0.5 kg of decay product.

A further 4.468×109 years pass leaving:

0.25 kg of Uranium 238 and 0.75 kg of assorted decay products.

Another 4.468×109 years pass leaving:

0.125 kg of Uranium 238 and 0.875 kg of assorted decay products.

Note that this span of time is approximately equal to 13.5 billion years. Which is approximately equal to the current estimates for the age of our universe as explained at the start of the answer and should help to demonstrate how uranium's long half life means it is still found in nature.

Answer 2

Elements with short half lives are not in appreciable amounts in the earth crust. By disintegration they disappear.