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At a given instant there are 25% undecayed radio-active nuclei in a sample. After 10 seconds the number of undecayed nuclei reduces to 12.5% Calculate (i) mean-life of the nuclei, and (ii) the time in which the number of undecayed nuclei will further reduce to 6.25% of the reduced number

At a given instant there are 25% undecayed radio-active nuclei in a sample. After 10 seconds the number of undecayed nuclei reduces to 12.5% Calculate (i) mean-life of the nuclei, and (ii) the time in which the number of undecayed nuclei will further reduce to 6.25% of the reduced number 

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
7 years ago
Hello Student,
Please find the answer to your question
(i) From the given information, it is clear that half life of the radioactive nuclei is 10 sec (since half the amount is consumed in 10 second 12.5% i half of 25% pls. note). Mean life
τ = 1/ λ = 1/ 0.693 / t1/2 = t1/2 / 0.693 = 10 / 0.693 = 14.43 sec
(ii) N = N0eλt
N/ N0 = 6.25 / 100
Λ = 0.0693 s-1
6.25 / 100 = e-0.0693t
e+0.693t = 100 / 6.25 = 16
0.0693t = In 16 = 2.773
Or t = 2.733 / 0.0693 = 40 sec.
Thanks
Navjot Kalra
askIITians Faculty

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