Calculating Half Life Decay

[litlmike]

This is purely an exercise to exercise the brain, but I just can't seem to wrap my brain around this one. To calculate the ending amounts of half life decay the formula is:

E = Ending Amount

B = Beginning Amount

n = Number of Half Lives

E = B/(2^n)

So if there was 100 units of some material, lets say Hydrogen, in a canister and we wanted to find out how much Hydrogen would be left after 1 half life, then we would do this:

100/(2^1) = 50

After 2 half lives:

100/(2^2) = 25

After 3 half lives:

100/(2^3) = 12.5

But, now let us say that while the original amount of Hydrogen is decaying, we put more Hydrogen into the canister, and now we want to know what the ending amount of total hydrogen per half life that remains in the canister. So let us say that after the first half life occurs that we blow more Hydrogen into the canister (100 units), the results would be:

100/(2^1) = 50 + 100 = 150

After the next half life occurs, we must now calculate both half lives and add them together:

100/(2^2) = 25

+

100/(2^1) = 50

= 75 units of Hydrogen

Lastly, let us say that we continue this pattern it would follow:

100/(2^3) = 12.5

+

100/(2^2) = 25

+

100 = 137.5

Then...

100/(2^4) = 12.5

+

100/(2^3) = 25

+

100/(2^1) = 50

+

100 = 187.5

I would like to be able to display the total amounts of Hydrogen as they decay, with the ability to add in X amount of Hydrogen at any given point, and have the resulting figures 'update'. Meaning, maybe after 1 or 5 or 14 half lives more Hydrogen is added and the resulting total amount can be displayed.

TIA

Starter Code:

$B = InputBox ("Amount of Material", "How much material are you starting With?")
$n = InputBox ("Amount of Half Lives", "How many half lives would you like to calculate for?")


For $iCC=0 To $n
    $E = $B/(2^$iCC)
    ConsoleWrite ("The Amount After " & $iCC & " Half Lives have occured equals: " & $E & @CRLF)
Next

[aslani]

Well I'm not the one who understand "half life" or whatever, but what you want to do is pretty simple. What I would do is I would create an Array for each Beginning Amount.

Example:

$stuff = _ArrayCreate($B)

Then you can create a function that calculates each element individually and store them back in their location in the Array. And then when you want to find the Total Ending Amount, you can add each element in the array. And if you only want the first Beginning Amount, just pull $stuff[0]; for second Beginning, pull $stuff[1], etc.

But that's just me.

[PsaltyDS]

I'm too lazy to make this a line graph, or to make the bar graph logarithmic tonight, but this might be a start:

#include <guiconstants.au3>

$B = InputBox ("Amount of Material", "How much material are you starting With?")
$n = InputBox ("Number of Half Lives", "How many half lives would you like to calculate for?")

$hGUI = GUICreate("Half Life", 600, 155)

$Label_InitQty = GUICtrlCreateLabel("Initial quantity = " & $B, 10, 10, 280, 20, $SS_CENTER)
$Label_RemQty = GUICtrlCreateLabel("Remaining quantity = " & $B, 310, 10, 280, 20, $SS_CENTER)
$Progress_Qty = GUICtrlCreateProgress(10, 35, 580, 30, $PBS_SMOOTH)
GUICtrlSetData(-1, 100)

$Slider_HL = GUICtrlCreateSlider(10, 90, 580, 30, $TBS_NOTICKS)
GUICtrlSetLimit(-1, $n, 0)
GUICtrlSetData(-1, 0)
$Label_HL = GUICtrlCreateLabel("Half lives past = 0", 10, 125, 580, 20, $SS_CENTER)
GUISetState()

$HL_Prev = 0
While 1
    If GUIGetMsg() = $GUI_EVENT_CLOSE Then Exit
    $HL_Slide = GUICtrlRead($Slider_HL)
    If $HL_Slide <> $HL_Prev Then
        $HL_Prev = $HL_Slide
        GUICtrlSetData($Label_HL, "Half lives past = " & $HL_Slide)
        $E = $B / (2 ^ $HL_Slide)
        GUICtrlSetData($Label_RemQty, "Remaining quantity = " & $E)
        GUICtrlSetData($Progress_Qty, $E / $B * 100)
    EndIf
WEnd

P.S. Atomic hydrogen doesn't have a half life, it's stable. Neither does deutrium. You have to go to tritium before you get a half life for a hydrogen isotope, at λ = 12.32yrs.

Edited October 11, 2007 by PsaltyDS