the number of a certain radioactive nuclide present in a sample decays from 160
ID: 991853 • Letter: T
Question
the number of a certain radioactive nuclide present in a sample decays from 160 to 20 in 39 minutes. what is the half-life of this radioactive species? Please explain thanks the number of a certain radioactive nuclide present in a sample decays from 160 to 20 in 39 minutes. what is the half-life of this radioactive species? Please explain thanks the number of a certain radioactive nuclide present in a sample decays from 160 to 20 in 39 minutes. what is the half-life of this radioactive species? Please explain thanksExplanation / Answer
During a single half - life the initial amount of a substance becomes half of the initial amount. Hence
160 ------(t1/2) ------> 80 -----(2t1/2) -------> 40 ------(3t1/2) --------> 20
Hence the amount of the substance decreases from 160 to 20 in 3t1/2 time.
=> 3xt1/2 = 39 minute
=> t1/2 = 39 / 3 = 13 minutes (answer)
We can also solve this in an alternate way as follows:
Since radioactive decay is a first order reaction, the amount of substance at any time can be calculated as
kt = ln(N0/Nt)
=> k x 39 min = ln(160 / 20)
=> k = 0.05332 min-1
=> t1/2 = 0.693/k = 0.693 / 0.05332 min-1 = 13 min (answer)
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