Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: dgt20 on 02/03/2018 02:54:39

I want to compare my decay results using the dice model 1;6 chance experiment and prove that it is not accurate to real life representation of decay. Is it possible to do this by using the decay constant through excel? If so how would you set up the formula on excel?

The formula for the number of decayable nuclei N_{t} remaining after time t is given by:
N_{t} = N_{0}e^{λt}
...where N_{0} is the number of nuclei you are starting with and λ is the decay constant with units s^{1}
So you can write a simple recurring formula that substitutes for t over the range of values that you want to test.
Does that help?

The formula for the number of decayable nuclei N_{t} remaining after time t is given by:
N_{t} = N_{0}e^{λt}
...where N_{0} is the number of nuclei you are starting with and λ is the decay constant with units s^{1}
So you can write a simple recurring formula that substitutes for t over the range of values that you want to test.
Does that help?
I understand the equation however i don't know how to plug in the decay constant in excel? I just dont know how to graph/do this on excel.

Are you trying to replicate the dice experiment in excel?

Are you trying to replicate the dice experiment in excel?
I want to compare decay results from dice experiment to decay using the decay constant on excel

Ok, I've had a go...
I simulate 16 dice 
 Each row represents one half life, numbered in Column A
 Column B shows the theoretical number present after this many halflives. Note that this number becomes a fraction, while real dice can't become a fraction.
 if the dice face shows a number > 3, it continues into the next round.
 Column C counts how many dice are left
 Press F9 to recalculate (start with the full number of dice again)
 The results are slightly different every time you press F9
 You can experiment with more dice by duplicating column S in more columns to the right.
 There is a similar experiment on the "Coin" worksheet, simulating flipping a lot of coins. Only half of them are left after a halflife.
But I can't upload EXCEL files.
Download the file to disk, then remove the JPG suffix.
Scan with a virus scanner. Then it should open in EXCEL.
Dice_Sim.xlsx.jpg (26.99 kB  downloaded 163 times)

Ok, I've had a go...
I simulate 16 dice 
 Each row represents one half life, numbered in Column A
 Column B shows the theoretical number present after this many halflives. Note that this number becomes a fraction, while real dice can't become a fraction.
 if the dice face shows a number > 3, it continues into the next round.
 Column C counts how many dice are left
 Press F9 to recalculate (start with the full number of dice again)
 The results are slightly different every time you press F9
 You can experiment with more dice by duplicating column S in more columns to the right.
 There is a similar experiment on the "Coin" worksheet, simulating flipping a lot of coins. Only half of them are left after a halflife.
But I can't upload EXCEL files.
Download the file to disk, then remove the JPG suffix.
Scan with a virus scanner. Then it should open in EXCEL.
Dice_Sim.xlsx.jpg (26.99 kB  downloaded 163 times)
edit: nvm

But I can't upload EXCEL files.
Hi @evan_au  I've not tried it with Excel, but it should let you send files as attachments in PMs  see this upgrade note: https://www.thenakedscientists.com/forum/index.php?topic=70438.msg517348#msg517348
Let me know if it works please.

Define your decay constant L
Put your starting number into a cell, say B2. I always start with B2 to give me space for annotations.
In B3 write =B2*exp(L)
Now use autofill to give values for B4.....BN where N is as large as you like.
You can calculate the half life t_{½} = ln2/L = 0.693/L and compare it with the graphical value.
The halflife or decay constant you use depends on how you want to reject the dice, usually either 1/6 per throw or 1/2 per throw. 1/6 will give you a smoother curve and a better fit between experiment and calculation  just like real life where measuring short halflives is much more difficult!.

But I can't upload EXCEL files.
Hi @evan_au  I've not tried it with Excel, but it should let you send files as attachments in PMs  see this upgrade note: https://www.thenakedscientists.com/forum/index.php?topic=70438.msg517348#msg517348
Let me know if it works please.
@evan_au  since posting, I've checked the PM attachments settings and .xls and .xlsx files are both permitted in PM attachments.
Obviously, users should always screen attachments before they execute things on their local machine.

The "trick" of putting a dummy "JPG" suffix should work in delivering the EXCEL file via a post.
I tried putting an attachment on a PM (Personal Message) like the one in the link, and it didn't bring up the "Choose File" button?
[ Invalid Attachment ] [ Invalid Attachment ]
Am I looking in the wrong place?

Define your decay constant L
Put your starting number into a cell, say B2. I always start with B2 to give me space for annotations.
In B3 write =B2*exp(L)
Now use autofill to give values for B4.....BN where N is as large as you like.
You can calculate the half life t_{½} = ln2/L = 0.693/L and compare it with the graphical value.
The halflife or decay constant you use depends on how you want to reject the dice, usually either 1/6 per throw or 1/2 per throw. 1/6 will give you a smoother curve and a better fit between experiment and calculation  just like real life where measuring short halflives is much more difficult!.
Using decay formula Nt = N0eλt, I replaced decay constant with 0.166 (dice 1/6 chance) then compared to the results of the formula N=1000(11/6)^t (time). Would this be a fair comparison of expected dice vs expect dice decay results?

No.
N=1000(11/6)^t
is rearranged as
N = 833.33^{t}, which increases with t and is very different from N = 1000/e^{λt}, which decreases with t.
If you use the Excel algorithm I suggested above, N_{p} = ROUND (N_{p1}* 0.833, 0) you will get a succession of integers that look like idealised dice and behave very much like the decay of 100000 nuclei. Real dice will give you a rougher curve because you may get any number of sixes on a single throw, but we get the same effect with very small (10000 or less) numbers of real nuclei due to Geiger counter dead time limitations.

The "trick" of putting a dummy "JPG" suffix should work in delivering the EXCEL file via a post.
I tried putting an attachment on a PM (Personal Message) like the one in the link, and it didn't bring up the "Choose File" button?
Send_Message_Chrome.PNG (47.47 kB . 921x602  viewed 2930 times)
Send_Message_Edge.PNG (33.91 kB . 781x506  viewed 2931 times)
Am I looking in the wrong place?
Hello Evan  I've reset the permissions for the application. It might be that they had been suspended when the forum was rebuilt in January.
I've tested successfully, I think, PM'ing you a picture and a spreadsheet.
The file selection / attachment box now appears below the PM message body input box:
screen_shot.PNG (49.33 kB . 1152x779  viewed 2840 times)