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Tips for Half-Life Calculations - Concept

Teacher/Instructor Jonathan Fong
Jonathan Fong

M.Ed.,San Francisco State Univ.

Jonathan has been teaching since 2000 and currently teaches chemistry at a top-ranked high school in San Francisco.

Here are some tips and tricks for dealing with half-life calculations. So here I’ve written a simple equation that deals with half-life. And so, we have three different variables. So if you know two of the variables, YOU can solve for the third one related to a half-life calculation.

So just to know, this first n is your number of particles, or your mass after n number of half lives. So that means that this end is lower case AND like I have in quotation marks. This is the number of half lives that have passed. Now remember each half-life for a certain radioactive element, would be the same like the time. So for the first half-life, the first half-life is say time would be 5 seconds. That means the second half-life would also be another 5 seconds.

The third half-life would be another 5 seconds, fourth half-life would be another 5 seconds. So after 4 half lives, then the total would be 20 seconds that you have there. So remember each half-life is identical in terms of amount of time.

But the amount that you have, say if I started off in grams with 10 grams, after the first half-life. Maybe I started off with 20 initially. Then what happens is after the second half-life another half it will drop down and half to 5. And then after another half-life, I would have 2 and a half grams remaining. After another half-life, I would have 1.25.

It’s pretty easier to drop stuff in half, but this equation here will help us figure out just in case we don’t have a whole number for a half-life. Like maybe it’s after 2 and a half lives, how much is left? So n0 is basically the number of particles, or the mass initially. So how much did you start off with at the very very beginning?