A) 256 yr
B) 128 yr
C) 64 yr
D) 24 yr
Correct Answer: D
Solution :
Radioactive decay is a set of various processes by which unstable atomic nuclei emit subatomic particles. From Rutherford-Soddy law the number of radioactive nuclei left after n half-lives is \[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] where\[{{N}_{0}}\]is original number of atoms. Given, \[N=\frac{{{N}_{0}}}{8},{{T}_{1/2}}=8\,yr\] \[\therefore \] \[\frac{{{N}_{0}}}{8}={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] \[\Rightarrow \] \[\frac{1}{8}={{\left( \frac{1}{2} \right)}^{3}}={{\left( \frac{1}{2} \right)}^{n}}\] \[\Rightarrow \] \[n=3\] \[\therefore \] \[3=\frac{t}{{{T}_{1/2}}}\] \[\Rightarrow \] \[t=3{{T}_{1/2}}\] Given, \[{{T}_{1/2}}=8yr\] \[\therefore \] \[t=3\times 8=24\text{ }yr.\]
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