Answer to Question #21959 in Atomic and Nuclear Physics for rahav
75% of a sample was decayed in 24 hours , find the half life of the sample.
Let X0 be the initial amount of the sample. Assume that the amount of sample at time t is given bythe formula X(t) = X0 e^(-at) for some constant a>0. We should find T such that X(T)/X0 = e^(-aT) = 0.5
For this we need to know value of a. By assumption at time t=24 hours 0.75 = X(24)/X0= e^(-a*24), whence a = -ln(0.75) /24 = 0.011987
Thus X(t) = X0e^(-0.011987 t).
Hence fior half life T we have that e^(-0.011987 *T) = 0.5 and so T =-ln(0.5)/0.011987 = 57.825hours