You're comparing natural decay with induced fission.

In ambient conditions, radioactive elements with unstable atomic structure are basically falling apart slowly. In turn, they only released a small amount of energy as they do so.

With fission, you speed up the process by shooting a bunch neutrons at the radioactive atoms so they fall apart much, much faster. So much faster that neutrons in the radioactive atoms explode out, hit other atoms and cause them to break apart too. If the effect is strong enough, you get a chain reaction that produces a lot of energy (but also causes all your radioactive fuel to "fall apart" faster).

Natural decay is a rickety building falling apart slowly over years or decades into rubble. Fission is when you topple that rickety building so that it hits the rickety building beside it, which then also tips over and hits another building, and another, etc. domino effect.

That's like comparing the rate at which wood rots to the rate at which it burns. Radioactive decay is the spontaneous decomposition of unstable atoms. Nuclear fission inside a reactor is a chain-reaction which causes the atoms to split, harnessing the exothermic products of the reaction to heat water and drive aturbine.

The U235 decay chain goes like this:

>Uranium-235 →Thorium-231 → Protactinium-231 →Actinium-227 →Thorium-227 →Radium-223 →Radon-219 →Polonium-215 →Lead-211 →Bismuth-211 →Thallium-207→ Lead-207 (stable)

The fission products of a nuclear reactor are far less predictable, but include isotopes of Iodine, Caesium, Strontium, Xenon, and Barium. That's because the neutrons which collide with the U235 nuclei crack them apart.

A fission reactor is actively smashing the fuel to pieces, in order to release the energy faster. There are RTGs that only use the normal decay as its energy source, but they produce far less energy.

They're not the same reactions

Normal decay is random. A U-235 decays and then nothing else happens, there's no chain reaction

In nuclear reactors the fuel is refined and set up in the reactor so it'll be critical so each atom that splits causes one other atom to split. Now you're not waiting for each one to randomly breakdown by instead trigging a chain reaction that works its way through the fuel fairly rapidly splitting the available atoms into smaller ones. If they need more power from the reactor they briefly adjust the control rods so each split triggers more than one other split to get up to a higher power level then reduce it back to 1-1 to hold at that level. The more power you need to pull from the reactor the faster you need to burn through the fuel

They also don't burn through all the fuel of the fuel rod, but it starts building up byproducts that muck with the power you can get out of it so they have to swap it out. Unfortunately the byproducts are wayyy less stable than the starting uranium/plutonium so now the random decay is occurring at a much faster rate creating a lot more radiation but less useful kinetic energy(heat) from the process. The really angry byproducts are mostly cleared out after a year because they decay that rapidly

Think of it like a bunch of dominoes standing on end - and "half-life" is how long it typically takes half of all independent dominos to tip over because of a tiny breeze, etc.

If these dominoes are set up very far apart, then one domino randomly tipping over only releases a tiny amount of kinetic energy and isn't likely to knock any others over. This is where the natural independent "radioactive decay" idea comes into play, and is how "half-life" is defined.

On the other hand, if there are very many dominoes standing next to each other, then one domino tipping over might push two others, which might push into four others, with might push into eight others, etc. All of these dominoes (except the very first one) didn't "decay" naturally, they were all pushed! So, the amount of fallen dominoes is more a question of "How closely packed are the dominoes?" and "How long on average does a chain-reaction of domino falls last?" rather than a question of isolated "half-life".

Nuclear reactors burn through fuel quickly compared to the fuel half-life because they are designed to sustain those long chain-reactions that release more energy faster.

The half-life is due to spontaneous decay. They're kind of unstable so there is a chance of them just going "poof" and decaying. Half-life is the time it takes for half of the atoms in any given amount of material to undergo this spontaneous decay.

However, in a reactor we've arranged it so that there is a pretty big chance that when one atom decays the neutron (small sub-atomic particle) shoots out and hits another atom, which will cause that atom to split and shoot off more neutrons, which will hit other particles and cause a cascade effect. Compare it to just shooting a billiard ball on a pool table randomly vs stacking the balls into a pyramid (shooting a ball into that pyramid will cause a whole bunch of other balls to move around).

That effect is used in a reactor, because when a whole bunch of little atoms decay quickly they release heat. In our normal powerplants they're stacked so that it happens very quickly (although our current generation is kind of inefficient and only a small percentage of the fuel is used up before the effect slows down or becomes too difficult to handle due to dangerous byproducts), and that generates a lot of heat which is used to heat water into steam and drive a steam turbine.

There is also something called a radioisotope thermoelectric generator, a nuclear battery of sorts. Basically a radioactive element that has been arranged to encourage it to just react a little bit faster. Not cascade, just generate enough heat that it can be used to generate power through the thermoelectric effect. Those batteries last a lot longer, so they're used on deep space satellites like Voyager (that travel far enough away from the sun that solar panels aren't useful anymore). Voyagers nuclear battery produced something like 60% of its original power back in 2001 (some 25 years after its launch) but theoretically a battery like this could be designed to last thousands of years.

Nuclear fission works by a neutron (a tiny particle) hitting an atom of uranium-235, causing it to split into two new atoms, both of which are smaller.

These new atoms can't be used in a nuclear reaction but still have a lot of mass (only a teeny amount is turned into energy) so the spent fuel rod still has a mass which is almost identical to the "new" rod, hence a lot of waste being produced after the reaction because these new atoms are quite unstable in their own right.

Uranium-235's half-life is 700 million years. It's not even warm to the touch. Fissioning it releases much more energy than it would decaying to lead, and much, much, much faster. So that's useful for human purposes.

I wouldn't say it's a large amount of spent fuel, considering the amount of energy released. Each fuel pellet -- the size of a fingertip -- releases about as much a ton of coal.

The nuclear fuel used in reactors gets spent quickly because the fission process breaks the atoms apart, releasing energy and creating radioactive byproducts that can interfere with the reaction. It's like burning wood in a fire -- it's gone quickly because the chemical reaction releases energy and changes the wood into ash.

Because inside the reactor we use unnatural practices to slow the neutrons down so they collide into each other and create fission.