why is there still radioactive material on earth? Why hasn’t it all decayed?
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The radioactive material on earth has a half life long enough for it to have significant quantities left, or comes from the decay of things that do (eg. radon is mostly produced from natural uranium decay).
There were other radioactive elements on Earth in the past in all likelihood, but they decayed more or less entirely before we were there to observe them.
Some elements have enormously long half-lives. A half life is the time it takes a given quantity of a radioactive element to decay. The half life of the most common form of uranium is about 4.5 billion years which is coincidentally about the age of the Earth. So half of the uranium in the original Earth has decayed. Of the remaining half of the original uranium, half will decay in the next 4.5 billion years – and so on.
Some elements with much shorter half lives, like potassium 40 (half life 1.9 billion years) are so common that even though they’ve been through multiple half lives, there are still huge amounts of radioactive potassium in the Earth (and in bananas).
Different substances decay at different rates. Some only exist in the lab for many times less than microseconds. Some exist longer than the age of the universe.
[https://en.wikipedia.org/wiki/List_of_radioactive_nuclides_by_half-life](https://en.wikipedia.org/wiki/List_of_radioactive_nuclides_by_half-life)
The half life of some of these materials is insanely old. The half life if uranium-238 is about 4.5 billion years. That means about half of the uranium here on Earth is only half of what the Earth started with.
Additionally, other things can decay into radioactive elements. Radon-222 only has a half life of 3.8 days, but more is constantly being made
U-238 -> Th-234 -> Pa -> 234 -> U-234 -> Th-230 -> Ra-226 -> Rn-222 -> and then a chain of polonium, lead, and bismuth that eventually becomes a stable lead-206
Naturally-occurring radioactive elements (almost) all decay very slowly, with half-lives in the millions or billions of years, and the Earth is young enough (~4.5 billion years) that some amounts of these isotopes are still around.
Even for those naturally-occurring elements with short half-lives, they can be produced from the decay of heavier elements with longer half-lives. The fastest-decaying natural isotope I could find is Fr-223 (22 minutes), which is a decay product of Uranium-235. That means that at any given time, some trace amount Fr-223 exists in natural Uranium deposits, constantly being replenished by the decay of the Uranium.
Throw a coin. If it’s heads it disappears. If tails it stays. Repeat indefinitely. It won’t be long until it’s gone right? Now do with 2 coins. It will last a little longer. Do it with 10 coins… 5kg of plutonium ^239 are 12.500.000.000.000.000.000.000.000 atoms. And you make a throw every 24.110 years (half life). It’s gonna be a while until it disappears. Francium 223 has the half life of 22 minutes, but it’s estimated that there’s still 1 kg in all the earth crust.
There is radioactive stuff that’s been on earth for a long time because it takes a long time to decay, or that is a decay product of something that takes a long time to decay, and there is new radioactive stuff being created by space radiation bombarding earth and turning stable stuff radioactive, like cosmic rays making thermal neutrons that interact with Nitrogen 14 and turn it into Carbon 14.
When radioactive stuff decays, it sometimes turns into other radioactive stuff. That will eventually decay as well, and ultimately there won’t be any more radioactive stuff, but that will take much longer than the current age of the universe.
In addition to their long half-lives and the chains of decay, there’s also the fact that some radioisotopes still get created through natural processes. For example carbon-14 gets made in the upper atmosphere when stray stable carbon atoms get blasted with cosmic rays. But I assume you mean minerals like uranium-235, so the other answers given here are more relevant.
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