Calculation Radioactive Isotope decay rate


I hope someone can help me with this. I have programmers working on something for work, and I need to check their work. I know how to calculate the radioactive isotope decay rate, but I hoping someone can help me program it into my calculator so I can solve for faster. I have 48gx and 35s, 15c, and 28C that I can use. I prefer not use 28c because I have not fixed battery problem yet and I do not feel like losing program after I power it off.

I define formulas for you, but first let me define variables:

Ai = initial activity/radioactivity of isotope
t = elapsed time (hours)
A = current radioactivity (what we solve for)
H = half-life of radioisotope (hours)


A = Ai(1/2)^t/H

t = (H ln (A/Ai))/(ln (1/2)) <<- ln be natural logarithm

I sorry if this overly complicated, as I can do manually, but I would like to program and I am not sure how.


Hello Vincze,

You can use the 48's solver. Press [Right Shift] [Enter] to activate the Equation writer. Enter the first equation; When you're done, press [Enter] to save it to the stack. Then save it as a function, typing a name, such as Activ:
['] [Alpha] [Alpha] ACTIV [STO]

Repeat the process for the second equation, and save it:
['] [Alpha] [Alpha] TIME [STO]

Now go to to the Solver menu, using [Right Shift] [SOLVE] You will see a menu: use the cursor keys to select SOLVE EQUATION and press [Enter] You will get the HP Solve screen, which will prompt you to select an equation. Look for ACTIV and press [Enter] The variables will be created automatically and you can start entering values. After you complete data entry, use the arrow keys to set the cursor in the variable you want to solve and press SOLVE.

The procedure is the same for the other equation.

Hope this helps.


Juan, thank you so much my friend for the help. I know how to program solver but I wonder how it might be done with program to run. I still try and figure out program of calculator, and sometimes it confuse me. I guess solver is easier and for most case, do just fine, as I can solve for any variable, but it would be nice to see how to program the same problem.

Thank you again though.



One of the beauties of RPN and keystroke programming is that you program just as you would work out the problem. For Radioactive Decay, I prefer to use the integral form of first order reactions. All radioactive decay follows first order kinetics, which means that the following equations apply...

rate = k*[A]

upon integration you obtain

[A]t = [A]o Exp(-k*t)

where [A]o is the initial concentration
k is the rate constant which can be found by Ln (2)/half life
t is the time of reaction and
[A]t is the amount left after time t has passed by.

For the HP 28c and the 48gx the programming is the same. Using local variables "a" for [A]o, "b" for half life and "c" for time you can enter the program as follows.

<< -> a b c << 'a * EXP ( - ( LN(2) / b ) * c ) ' >> >>

save it as 'decay' then enter the values into the stack and press 'decay' from the user menu.

for this program the values have to be [A]o , half life and time in that order into the stack.

if you do not want to use local variables a shorter program would be

<< 2 LN SWAP / * NEG EXP * >>

save it as 'dacay' or any name you want to give it then enter [A]o, time and half life into the stack in that order. The program will return the amount left over. This last program should also work for the 35s, even though I do not have one, I believe you just need to change SWAP for x<>y and NEG for +/-.

Good luck

Sorry I had to edit to fix the formatting

Edited: 12 Aug 2007, 9:37 p.m.

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