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# Uncertainty in radioactive half-life experiment

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1. Uncertainty in radioactive half-life experiment
I have conducted an experiment and found the gradient λ of a graph to be (2.15x10^-4) +- (0.15x10^-4)

The graph being ln(A) i.e. the number of disintegrations/unit time - dN/dt against time t

The half-life is
T(1/2) = ln(2)/λ = -3223.9

How do I find the uncertainty in the half-life?

Thank you!
2. Re: Uncertainty in radioactive half-life experiment
The % uncertainty in T1/2 will be the % uncertainty in the value of λ from the graph.
3. Re: Uncertainty in radioactive half-life experiment
(Original post by Stonebridge)
The % uncertainty in T1/2 will be the % uncertainty in the value of λ from the graph.
Do you mean...

The % uncertainty in λ being 0.15/2.15 = 0.069

Therefore multiply T(1/2) of -3223.9 by 0.069 = +-224.9 is the uncertainty?
4. Re: Uncertainty in radioactive half-life experiment
(Original post by little pixie)
Do you mean...

The % uncertainty in λ being 0.15/2.15 = 0.069

Therefore multiply T(1/2) of -3223.9 by 0.069 = +-224.9 is the uncertainty?
Yes. (% or fractional uncertainty will give the same result.)
There is no need for the minus sign in the half life.
You need some units for time.

You also need to consider how to express that final answer, in particular, how many significant figures. It would certainly not be expressed as 3223.9 ± 224.9
5. Re: Uncertainty in radioactive half-life experiment
(Original post by Stonebridge)
Yes. (% or fractional uncertainty will give the same result.)
There is no need for the minus sign in the half life.
Okay.

(Original post by Stonebridge)
You need some units for time.
Seconds.

(Original post by Stonebridge)
You also need to consider how to express that final answer, in particular, how many significant figures. It would certainly not be expressed as 3223.9 ± 224.9
Would it be 3224 +- 224.9
6. Re: Uncertainty in radioactive half-life experiment
(Original post by little pixie)

Would it be 3224 +- 224.9
No, because the uncertainty is in the 2nd figure from the left.
This means you cannot meaningfully express the value to more than 2 significant figures.
7. Re: Uncertainty in radioactive half-life experiment
So it's 3200±200

(Original post by Stonebridge)
No, because the uncertainty is in the 2nd figure from the left.
This means you cannot meaningfully express the value to more than 2 significant figures.
How do you know the uncertainty is in the 2nd figure? I do struggle with uncertainties...
8. Re: Uncertainty in radioactive half-life experiment
(Original post by little pixie)
So it's 3200±200

How do you know the uncertainty is in the 2nd figure? I do struggle with uncertainties...

Yes. I would express it as 3200 ± 200
The ±200 means the probable value is 3200 with max 3400 and min 3000
It's the 2 in the 2nd place from the left that is uncertain.
There's a good higher level treatment of this here.
Particularly section 6 and 7 for this topic
http://www.rit.edu/cos/uphysics/unce...tiespart2.html
9. Re: Uncertainty in radioactive half-life experiment
Thanks very much for the link Stonebridge.

I'll take a look at that now.

Thanks again!

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Last updated: April 5, 2012
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