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

1. Jan 29, 2008

### stunner5000pt

1. The problem statement, all variables and given/known data
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
$$\Delta \tau = 436 s$$

2. Jan 31, 2008

### stunner5000pt

So can anyone offer any advice on this one?

3. Jan 31, 2008

### malawi_glenn

4. Jan 31, 2008

### hage567

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

5. Jan 31, 2008

### 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