[Kealan]

My chemistry teacher just moved us into nuclear physics today. I usually grasp whatever she teaches instantly, if I didn't already know it from reading it somewhere else, but I just don't get this, in particular I mean half-lifes. That is the time it takes for 1/2 of a sample of the element to decay. It is supposed to be very simple to calculate, but I don't see how it can be. For example:

Say we have 100 grams of a substance that has a 5 day halflife, ok? Now, going with what she said, that would mean there is 50 grams left after 5 days, 25 after 10, ect. But I don't see how this is possible. It would seem like the halflife would be impossible to calculate, since with every atom that decays the rate slows. See, if you use the above example of 100 grams with a 5 day halflife and do it like this, it is completely different. Start with 100 grams, but do it day-by-day, instead of 5 days at a time. So, after the first day, 20% of the halflife, 1/10th of it would be gone, leaving 90 grams. The next day, another 1/10th gone, leaving 81 grams this time. Next day, 72.9. Next, 65.61, and on the 5th day, 59.049. See the problem I am having? And it would be an even more extreme differance if there was a way to re-calculate it every instant, as it should be for an accurate number. I don't see how it could be an average of the decay over that time, either, since a larger number of atoms would change the time it takes for half to decay. Anyone understand the problem I am having, and have a way to explain it correctly?