The way radioactive half life works is it is the time period over which statistically half of the radioactive material will have decayed. This does not mean that two half lives will result in *all* the material having decayed, it would be half of the remainder decaying. So for any particular radioactive atom there is no telling how long it will take to decay, it might be in the next minute or not for dozens of half lives.
For radioactive uranium its half life is around 4.5 billion years, about the same as the age of Earth. This means we can expect that about half of the radioactive uranium which existed on Earth has decayed throughout its lifespan. That is the straightforward answer to why that material hasn’t “run the course of depletion already”.
Plutonium on the other hand is a byproduct of uranium decay in reactors so we are in fact creating that material. It has a half life of between 87 and 24,065 years depending on the isotope, and while probably some exists in natural deposits it is generally produced by humanity.
The elements are constantly decaying and emitting radioactive decay. The time taken for elements to decay to a point where we can no longer detect them is governed by their half lives. The half life is the time it takes for a half of any given quantity of a radioactive element to decay. So if we start with a kilo of an element, after one half life you would have half a kilo of the original element (and half a kilo of whatever it decays to). After two half lives you have half of half a kilo (250g) of the original element; after three half-lives half of half of half a kilo (125g) and so on…
So if an element has a long half life, enough of it will remain for us to mine it. For instance, the half life of the most common form of uranium (uranium 238) is about 4.5 billion years – which is coincidentally about the age of the Earth. We can say that half of the U238 that originally existed on the Earth has decayed. Another form of uranium (U235) has a shorter half life of only 700 million years, so we know it has been through more than six half lives and only about 1/64th of the original U235 is still found on Earth – but there’s enough left that we can still extract it and use it in power stations.
For elements like plutonium, the half lives are very short indeed (about 25,000 years); so even if there had been any on Earth in the beginning, it would have been through so many half lives that any concentrations in nature would be below our detection thresholds. So plutonium is considered a ‘synthetic element’ – it had to be made by humans from uranium.
I believe the main radioactive material we mine for are Uranium and possibly Thorium. Which have very long half lives.
Most other radioactive materials you hear about are created in nuclear reactors or other facilities for various purposes. They usually only have a half-life of a few years, sometimes even less. There are some medical isotopes that have half lives measured in hours or less. So they isotopes must be made almost [immediately before use](https://www.youtube.com/watch?v=eMTZvA8iFgI).
We don’t mine plutonium. It is synthetic. We produce it through nuclear chemistry – we bombard something else with neutrons in a nuclear reactor to create it.
We’re mostly limited to mining long-lived isotopes. Things like uranium that only decay very slowly. Often, so slowly that they’re left over from when they formed from stars eons ago.
Lots of short-halflife radio-isotopes used for medical or industrial purposes have to be manufactured in specialized reactors or particle accelerators.
Cosmic radiation from space ensures an ongoing generation of isotopes such as Carbon-14. Radiation from lightning is also responsible for shortlived isotopes of Oxygen and Nitrogen.
The majority of the isotopes used for nuclear fuel has decayed into other elements, but because they have such massive halflifes, we can still mine them, or extract useful isotopes from spent nuclear fuel.
Also fun fact. For nuclear power the percentage of U-235 needs to be 3-5 percent. It is currently about 0.72 percent in natural uranium.
About 1.7 Billion years ago the natural percentage WAS around 3-5 percent. In certain places in the world there were areas of natural uranium that got flooded with water, which is a neutron moderator. Allowing the natural neutrons to slow down and collide with other uranium atoms, causing a chain reaction. Creating [Natural Nuclear Reactors](https://en.wikipedia.org/wiki/Natural_nuclear_fission_reactor). We found them because as we were mining there was missing U-235, it was coming out at .6% instead of .72%. Which was a major issues as the first though is where did it go? Did someone steal it and fudge the percentages.
Some radioactive isotopes have been here as long as the Earth, and we’re just “starting with what’s left”. Uranium is the 48th most abundant element on Earth and takes billions of years for half of a sample to decay. Potassium-40 is common enough that you can detect it in all bananas with a Geiger counter, and it’s half-life is 1.25 billion years old. Most of our supplies of isotopes like these are “old”.
Some radioisotopes are produced when other radioisotopes decay. There’s a Cesium-131 that’s produced when Barium-131 decays. It’s half-life is 9.7 days. Iodine-131 is produced by nuclear power plant fuel and has a half-life of 8 days. So these “daughter isotopes” are typically either detected as part of an ongoing process, or manufactured intentionally for use while “fresh”.
Some radioisotopes are created in the atmosphere by lightning or cosmic radiation. Nitrogen in the upper atmosphere can be turned into carbon-14, which can become carbon dioxide and apples and people and everything else that carbon-12 can become. It’s not terribly rare, and it takes 5700 years for half of a sample to decay. But it’s always being replenished in the upper atmosphere.
When radioactive atoms decay, they don’t just go away. They decay into other atoms, some of which are also radioactive.
Radioactive elements have different half-lives. Heavier elements don’t necessarily have shorter half-lives than lighter ones. The radioactive elements that we are likely to encounter are ones with long half-lives, or ones that other radioactive atoms decay into.
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