What is the half-life and the error on the half-life?

[stunner5000pt]

Homework Statement

You have a kilogram sample of a beta emitter and you want to establish its
half-life. You measure 100 counts over the period of a day. What is the half-life and
the error on the half-life? How would your answer be different if did a measurement
for the same material but only for one hour?


2. The attempt at a solution
To calculate the half life do i calculate the mean lifetime tau, first?

In that case $$\tau = 864 s/decay$$
i got this by dividing the number of counts 100/time in seconds for 1 day

we can calculate the half life now using $$t_{1/2} = \tau \ln 2$$

How would i calculate the error in th half life though?
Experimentally we could calculate it like this: the smallest unit of measurement of time we have is 1s so the error in the measurement of time is 0.5s. Also the error in the counting C was 0.5 counts/sec Then we can calculate the error in the lifetime as follows
$$\frac{\Delta \tau}{\tau} = \frac{\Delta C}{C} + \frac{\Delta t}{t}$$
which becomes
$$\Delta \tau = 436 s$$

But that is way too big isn't it? What have i done wrong? Please help!

Thank you for your help

 

[stunner5000pt]

So can anyone offer any advice on this one?

 

[malawi_glenn]

https://www.physicsforums.com/showthread.php?t=94380

 

[hage567]

Look up counting statistics. I don't have any references on hand.

 

[stunner5000pt]

this question is fine thanks

i just figured it out

whats more important to me in any case is the particles in a tube thread