I was not able to find an answer for this question... Some radioactive elements

Question

I was not able to find an answer for this question...

Some radioactive elements have half-life measured in thousands of years and some others even in millions, but over 4.5 billion years all the radioactive material that was part of the initial material that formed the planet earth should have decayed by now?

However, there is still radioactive material with short half-life to be found in nature. How is this possible and if the answer is that the new radioactive material is constantly being generated somehow, can you explain the mechanism of how this happens?

Thanks.

Explanation / Answer

The half-life of Uranium 238 is about the age of the Earth, so only about half of the original supply should have decayed by now. Also, there are some radioactive nuclei that get created by interactions with cosmic rays in the upper atmosphere (carbon-14) or decay from more stable nuclei (all of the daughter nuclei between U-238 and lead, for example).

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