Physics 306 Regression worksheet

You conduct an experiment to test the following hypothesis; the activity at time t of a radioactive sample of initial activity A0 (in decays per second, at time t = 0) is

A(t) = dC(t)-= A0 e-λt dt
Use this to get a formula for the number of decays C(t) that should occur between time t and t + dt.

Suppose that you now measure the number of decays that are actually emitted by a sample for dt = 1.0s intervals, and come up with this data;

Start t (sec)End t (sec)C
0 1 18
1 2 13
2 3 11
3 4 8
4 5 7
5 6 5
6 7 4
7 8 4
8 9 2
9 10 1

Perform a linear regression fitting the natural log of the number of counts

lnC(t) = a+ b,t
From your formula for the number of counts per time interval dt versus time t, get an expression for the initial activity and λ as functions of a and b. Use this as an experimental determination of λ from your fit, and report it to me.