Take the probability for #11 to be: average decays/breath x 100%
How would average decay be calculated? Should we integrate dN/dt = -lambda N for the time interval to find the change in number of radioactive nuclei? dN/N = -lamda dt .. ln(N/N0
) = -lambda t
N(t) = N0
Then average decays would be N(t) - N0
Divide that by the time interval?
For problem 1, do we need to account for the simulatenous decay and production of U-239? I ended up getting a long equation:
let lamda U = A, lamda NP = B, lamda Pu = C (all in day-1
=(7.9 E -8 day-1
)(1/C - exp(-Ct)/C + Aexp(-Bt)/[(C - B)(B-A)] - Aexp(-Ct)/[(C-B)(B-A)] + B(exp(-Ct) - exp (-At))/[(C-A)(B-A)])
Don't know if I have the right equation, but if I do, I hope everyone else enjoys all the work involved in solving it...
EDIT: For problem 11, wouldn't finding the percent of nuclei decayed be more helpful for finding the probability? If 0.06 "nuclei" decay of 8800 possible nuclei, wouldn't the resulting ratio be more helpful? I guess the 0.06 nuclei is just a conceptual number, since a non-integer amount of nuclei can't decay