|Radioactive decay problems|
Message #17 Posted by Tom Sherman on 3 Feb 2004, 8:02 p.m.,
in response to message #1 by Mark Berg
If you have an HP-28S, you can set up the solver to handle any radioactive decay problem that the book or your instructor may throw at you.
Go to the solver and type in the equation:
MORE=LESS*2^(TIME/HFTM), where HFTM stands for half-time.
Store this as a variable (I use EXPN, for exponential), and also store it as your current equation in the Solver. Then ask the solver to solve it. You give any three of the four variables (MORE, LESS, TIME, HFTM), and the solver will find the fourth.
For a decay problem, LESS will be the amount remaining after a period of time, and MORE will be the starting amount. For a growth problem, the reverse will hold. Whatever a problem is, it will have to give you three of the factors, and ask you for the other. So you can use the one equation to solve all four kinds of possible problems.
If you work with decay constants instead of half-lives, you can modify the equation to read:
MORE=LESS*EXP^(TIME/TRTM), where TRTM stands for turnover time = 1.44 x halftime = 1/(decay constant).
You can also use these equations for any other problems involving exponential growth or decay: e.g. microbial population growth, absorption of electromagnetic radiation by matter, discharge of a capacitor.