[little pixie]

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!

[Stonebridge]

The % uncertainty in T_1/2 will be the % uncertainty in the value of λ from the graph.

[little pixie]

(Original post by Stonebridge)
The % uncertainty in T_1/2 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?

[Stonebridge]

(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

[little pixie]

(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

[Stonebridge]

(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.

[little pixie]

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...

[Stonebridge]

(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

[little pixie]

Thanks very much for the link Stonebridge.

I'll take a look at that now.

Thanks again!