Question: Problem 5.6. At time t, a radioactive sample contains n identical undecayed nuclei, each with a probability per unit time, A, of decaying. The probability

Problem 5.6. At time t, a radioactive sample contains n identical undecayed nuclei, each with a probability per unit time, A, of decaying. The probability of a decay during the time tt+At is AnAt. Assume that at time t = 0 there are no undecayed nuclei present.

(a) Write down and solve the master equation for this process [find P (n,t)].

(b) Compute the mean number of undecayed nuclei and the variance as a function of time.

(c) What is the half-life of this decay process?

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