I’d argue that the rate of decay per atom is actually random, except that the probability per unit time is scaled according to how long the half life is.
You need a shitton of atoms so that you can average out all that randomness and find the emergent property that is half life.
Fortunately, any amount of radioactive material large enough for us to do anything with it does indeed have a shitton of atoms! Avogadro’s number is one of my favorite scientific constants because it reveals the crazy scale of the atoms we take for granted.
Like with U238 and its 4 billion year half life, one mole of just that atom would weigh 238 grams and have 6.022x10^23 atoms. A half-pound or quarter-kilo chunk of very heavy metal that fits in the palm of your hand contains over 602,200,000,000,000,000,000,000 atoms.
Some of those atoms are going to decay today, and some of them will still be radioactive in 100 billion years.
Yep, once you know the half life, you can use that figure to work out the mean lifetime: the average time you’d expect to be looking at once nucleus before it decays. It works out to be 1.4x the half life of the material. You’re right though, it is random, and you could be waiting three nanoseconds or three million years.
I’d argue that the rate of decay per atom is actually random, except that the probability per unit time is scaled according to how long the half life is.
You need a shitton of atoms so that you can average out all that randomness and find the emergent property that is half life.
Fortunately, any amount of radioactive material large enough for us to do anything with it does indeed have a shitton of atoms! Avogadro’s number is one of my favorite scientific constants because it reveals the crazy scale of the atoms we take for granted.
Like with U238 and its 4 billion year half life, one mole of just that atom would weigh 238 grams and have 6.022x10^23 atoms. A half-pound or quarter-kilo chunk of very heavy metal that fits in the palm of your hand contains over 602,200,000,000,000,000,000,000 atoms.
Some of those atoms are going to decay today, and some of them will still be radioactive in 100 billion years.
Yep, once you know the half life, you can use that figure to work out the mean lifetime: the average time you’d expect to be looking at once nucleus before it decays. It works out to be 1.4x the half life of the material. You’re right though, it is random, and you could be waiting three nanoseconds or three million years.