The radioactive decay law as you might be remembering well is expressed mathematically as
N = N0e-λt with usual notations.
In most entrance examinations such as Medical and Engineering entrance examination, you wont be allowed to use calculators or logarithm tables. The above equation, modified in terms of half life will be very useful in this context. If N is the number of nuclei remaining undecayed after ‘n’ half life periods, it is related to the initial number N0 as,
N = N0/2n.
Now let us discus the following M.C.Q.:
Out of 1.414×1024 nuclei, only 1024 nuclei remain undecayed after 15 minutes in a radioactive sample. The half life period of the sample in minutes is
(a) 64 (b) 55 (c) 40 (d)30 (e) 24
We have, 1024 = (1.414×1024)/2n from which 2n = 1.414 so that n= ½. This means that 15 minutes is half of the half life period. The half life of the sample therefore is 30 minutes.
The above question can be asked in a modified manner, involving the activity of the sample as follows:
The activity of a radioactive sample drops from 1.414×108 disintegrations per second to 108 disintegrations per second in 15 minutes. The half life period of the sample in minutes is
(a) 64 (b) 55 (c) 40 (d)30 (e) 24
N = N0e-λt with usual notations.
In most entrance examinations such as Medical and Engineering entrance examination, you wont be allowed to use calculators or logarithm tables. The above equation, modified in terms of half life will be very useful in this context. If N is the number of nuclei remaining undecayed after ‘n’ half life periods, it is related to the initial number N0 as,
N = N0/2n.
Now let us discus the following M.C.Q.:
Out of 1.414×1024 nuclei, only 1024 nuclei remain undecayed after 15 minutes in a radioactive sample. The half life period of the sample in minutes is
(a) 64 (b) 55 (c) 40 (d)30 (e) 24
We have, 1024 = (1.414×1024)/2n from which 2n = 1.414 so that n= ½. This means that 15 minutes is half of the half life period. The half life of the sample therefore is 30 minutes.
The above question can be asked in a modified manner, involving the activity of the sample as follows:
The activity of a radioactive sample drops from 1.414×108 disintegrations per second to 108 disintegrations per second in 15 minutes. The half life period of the sample in minutes is
(a) 64 (b) 55 (c) 40 (d)30 (e) 24
Since the activity of a sample is directly proportional to the number of nuclei present at the instant, we can express the activity ‘A’ after ‘n’ half lives in terms of the initial activity ‘A0’ as,
A = A0/2n
Substituting the values of A and A0, we have 108 = (1.414×108)/2n from which n=½. So 15 minutes is half of the half life period of the sample and the answer to the question is 30 minutes [option (d)].
A = A0/2n
Substituting the values of A and A0, we have 108 = (1.414×108)/2n from which n=½. So 15 minutes is half of the half life period of the sample and the answer to the question is 30 minutes [option (d)].
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