Most radioactive processes can only happen once for a givenradioactive nucleus, changing the nucleus into another state(possibly a different radioactive state or even a differentelement) in the process. This means that for a given sample ofradioactive material, the original radioactive substance isconstantly being depleted. Since the rate of these decay events isdirectly proportional to the number of radioactive nuclei present,the decay is governed by the differential equation:
dN(t)/dt = -(lamda)N(t),
where N(t) is the number of nuclei of the original substance attime t, and the decay constant? ?, is positive because the amountof the substance is decreasing. The solution to this equation is anexponential, namely,
N(t) = No(e^(-lamda*t)) or N(t) = No(e^(t/Tao))
1. If the average count rate for a radioactive decay were 10counts per minute, how long would you need to count to measure itto a precision of 5% of its value with 68% confidence (one standarddeviation)?
2. The half-life of a decaying substance is the time it takesfor 1/2 of that substance to disappear. Given an initial samplesize of 1000 particles, how many particles are left after onehalf-life? Two?
