InterviewSolution
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InterviewSolution
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On your birthday, you measure the activity of the sample ""^(210)Bi which has a half - life of 5.01 days. The initial activity that you measure is 1muCi. (a) What is the approximate activity of the sample on your next birthday? Calculate (b) the decay constant (c) the mean life (d) initial number of atoms. |
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Answer» Solution :(a)A YEAR of 365days is equivalent to `(365 d)/(5.01d) APPROX 73` half - lives. Thus , the activity will bereduced after one year to approximately `(1/2)^(73)(1.000 mu Ci) approx 10^(-22)mu Ci`. (b) Initial measure `R_(0) = 1.000 mu Ci` `= 10^(-6) xx 3.7 xx 10^(10)` ` = 3.7 xx 10^(4) Bq` After 1 year, the measure R = `10^(-22)mu Ci` ` = 10^(-22) xx 10^(-6) xx 3.7 xx 10^(10)` ` = 3.7 xx 10^(-18) Bq` decay constant `lambda = (1)/(t) In((R_(0))/(R)) = ((1)/(1 year)) In ((3.7 xx 10^(4))/(3.7 xx 10^(-18)))` `(1)/(3.156 xx 10^(7)) In(10^(22))` `lambda = (50.657)/(3.1567 xx 10^(7)) = 1.6 xx 10^(-6) s^(-1)` (c) Mean life `TAU = (1)/(lambda) = (1)/(1.6 xx 10^(-6))s [ 1s = (1)/(86400) days]` `tau = 7.24` days (d) Initial number of ATOMS `R_(0) = lambda N, N = (R_(0))/(lambda)` `= (3.7 xx 10^(4))/(1.6 xx 10^(6)), N = 2.31 xx 10^(10)` |
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