We saw that for a radioactive substance with half life equal to T, the amount of the substance at time t is given by A(t) A0e kt , where k ln(2 T) (a) Show that the probability that a radioactive particle decays after time t is given by (b) The book Atomic Adventures mentions that the mean life span of a muon is 1 44 times its half life Verify this fact by calculating the expected life of a particle with half life T f(t) In 2 (t In 2) T e T

Question: We saw that for a radioactive substance with half-life equal to T, the amount of the substance at time t is given by A(t) =

We saw that for a radioactive substance with half-life equal to T, the amount of the substance at time t is given by A(t) = A0e^kt, where k = -ln(2/T).
(a) Show that the probability that a radioactive particle decays after time t is given by f(t) = In 2 -(t In 2)/T e T

(b) The book Atomic Adventures mentions that the mean life span of a muon is 1.44 times its half-life. Verify this fact by calculating the expected life of a particle with half-life T.

f(t) = In 2 -(t In 2)/T e T

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