If a drug has a half-life of, say, 16 hours, how does the concentration in the body reach zero at some point?
In: 2
You can think of half life as the time it takes half of a substance to disappear, or you can think of it as the time over which one piece of that substance has a 50% chance of disappearing. In most cases these get you to the same place, since when you have enough of something (say trillions of trillions of molecules or atoms) those 50% chances per peice are going to reliably result in half of the pieces disapearing.
But when you have very few pieces left, like one, the first way of thinking of halflife doesn’t apply since you can’t have half a molecule of a drug. So instead you need to think of it as each molecule having a 50% chance of disapearing over one half life.
So with one left, half the time it will disapear after one half life, three quarters of the time it will be gone after two half lifes etc, which technically means there’s a miniscule chance that it never goes away, but long before that you likely have a concentration that’s too small to have a noticable impact anyway.
in short, it’s functionally zero after a few halflives (after 7 it’ll be under 1% of its initial concentration) but will probably be actually zero after a lot more (log base 2 of n) where n is the number of particles.
EDIT: Log base 2 of n, means what x do you need for 2^x = n. So in this case 2^6.6 = 100 which is how I know that after 7 halflives less than 1% will be left.
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