Why is half-life dependent upon number of particles? For example, if I have two glasses of water, one full and one half full and let them evaporate, it would seem weird to come back and find the half full one a quarter full and the completely full one down to a half full. Why do radioactive nuclei have different rates of decay depending on how much you have?

Question

Why is half-life dependent upon number of particles?   For example, if I have two glasses of water, one full and one half full and let them evaporate, it would seem weird to come back and find the half full one a quarter full and the completely full one down to a half full. Why do radioactive nuclei have different rates of decay depending on how much you have?

anonymous · Answer

half-life is constant for a given isotope. Knowing the number of particles that you begin and end with allows you to determine how much time has passed for radiometric dating. If you know how much time has passed and the number of particles remaining you can figure out how man particles were there initially etc.

anonymous · Answer

If all of the water particles had the same probability of evaporating at any given time, and some portion of them did spontaneously evaporate, and that was a constant known quantity  (what random amount of any given mass of water would evaporate) then water evaporation would function in a similar way. However, in reality only water at the surface of the volume is evaporating and thus the surface area that is exposed to air of the glass of water (plus temp and pressure) is what is determining the rate of evaporation.

anonymous · Answer

Half-life is independent of number of particle. It's a characteristic of given isotope.
Decay rate, in other hand, depends on number of particle.
Half life's more like probability of given nuclei to decay. Like the probability for a coin to show head is 0.5.

preetha · Answer

I can see how you would be confused.  Think of it this way, half life is the TIME taken for half the atoms to decay.  So if you had 100 atoms, it would be the time for 50 of them to decay.  Lets say that is 5 minutes.  So if you had 100 atoms in one container and 50 in the other, you came back in 5 minutes, you would have 50 in one and 25 in the other.  Its different to evaporation in that sense.  Every five minutes, half the original amount decays.
So after another 5 minutes, you would have 25 in the first container and 12.5 in the next.

kainui · Answer

I hate to say it, but none of you answered my question. I know _what_ a half-life is, but I am asking, _why_ is it this way? I showed you how my intuition with the glasses of water leads me down the wrong path, show me what the intuition is for radioactive decay so that I can understand. What's going on with the particles for instance?