(adsbygoogle = window.adsbygoogle || []).push({}); 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 [tex] \tau = 864 s/decay [/tex]

i got this by dividing the number of counts 100/time in seconds for 1 day

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

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

[tex] \frac{\Delta \tau}{\tau} = \frac{\Delta C}{C} + \frac{\Delta t}{t} [/tex]

which becomes

[tex] \Delta \tau = 436 s [/tex]

But that is way too big isnt it? What have i done wrong? Please help!

Thank you for your help

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# Homework Help: What is the half-life and the error on the half-life?

**Physics Forums | Science Articles, Homework Help, Discussion**