Answer to Question #21959 in Atomic and Nuclear Physics for rahav
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),
a = -ln(0.75) /24
X(t) = X0e^(-0.011987 t).
Hence fior half life T we have that
e^(-0.011987 *T) = 0.5
Thus the half life of the sample is 57.825 hours.
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