stunner5000pt
Jan29-08, 02:58 PM
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
But that is way too big isnt it? What have i done wrong? Please help!
Thank you for your help
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 isnt it? What have i done wrong? Please help!
Thank you for your help