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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 thanks

Explanation / 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)