A) 40 yr, 0.9173/yr
B) 90 yr, 9.017/yr
C) 80 yr, 0.0173/yr
D) none of these
Correct Answer: C
Solution :
The amount of substance left after n half-lives is \[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] where \[{{N}_{0}}\] is original number of atoms. Here, \[n=\frac{t}{{{T}_{1/2}}}=\frac{t}{40}\] \[\therefore \] \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{t/40}}\] \[{{\left( \frac{1}{2} \right)}^{2}}={{\left( \frac{1}{2} \right)}^{t/40}}\] \[t=80\,yr\] Decay constant \[\lambda =\frac{0.693}{{{T}_{1/2}}}=\frac{0.693}{40}\] \[=0.0173/yr\]
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