# Half-Life Compound Decay

by Trustworthy
Tags: compound, decay, halflife
 P: 1 A 100 mg sample of magnesium-27 decays by 7% of its previous mass every minute. Determine its half-life and start the half-life decay equation. The textbook that I got this from (Nelson Physics 11) tells me the answer, but uses a long and annoying process to find it: creating a table at different points in time and then graphing. I am just wondering if there is an equation or some sort of trick to this type of question? It would save me a lot of time and trouble, thank you in advance.
 P: 1,057 It's a series.. it tells you that at each minute it loses 7% of what it had before... So it's better to use a table and see it...
 P: 681 Yes, it is very possible to derive a general expression for the amount left after a given time. If the sample loses 7% of its mass every minute, what is the ratio of mass left to original mass after 1 minute? What is the ratio after two minutes? Three minutes? Do you see a pattern? In that case, what should be the mass left after a time T?
 PF Gold P: 2,938 Half-Life Compound Decay To honour the "Compound" in the title of the post... Can someone point to the general formula for a decay chain, with elements having different half-lifes?
 Mentor P: 12,099 The right formula depends on what you want to know, but it is possible to get everything with the right integral for the considered problem.
 Sci Advisor HW Helper PF Gold P: 2,026 The question seems too simple. ##\exp(-t/\tau)=0.93##, so ##\tau=-1/\ln(.93)## in minutes.

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