What is nuclear waste half life?
Half life is just the time it takes for half of a radioactive substance to decay (turn into something new). Since this is a first order process, the time it takes for this to happen is independent of the starting concentration.
Different radioactive elements have different half lives, so you can't say it is generically some specific time. Rather, you need to know which radioactive elements you have to help you determine how long it will take your "waste" to decay.
Nuclear waste is stuff like radioactive daughter nuclei from a fission reaction, leftover U235, U238, Plutonium, various other nuclei.
If you only have daughter nuclei, most of their times required to decay are much shorter (still long time) compared to Uranium and plutonium.
The amount doesn't matter. If you have 100kg of C-14, it will take approximately 5200 years for half of it to decay, so that you'll still have 50kg of radioactive C-14.
If you started out with 100g of C-14, it would take 5200 years for half of its to decay.
So for waste, you have to isolate it and let it decay for a certain amount of time (when I used P-32 in the lab, I think 5 half lives was the standard). So if you have to wait 5 half lives, for some of this material (daughter products), that'll be close to 250 years before the sample has decayed to sufficiently low levels.
If you have to wait 5 half lives for Uranium and Plutonium, you'll be waiting hundreds of thousands of years.