A) 11460 years
B) 17190 years
C) 22920 years
D) 45840 years
Correct Answer: C
Solution :
After n half-lives (i.e., at \[t=\text{ }nT\]) the number of nudides left undecayed, \[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] Given, \[\frac{N}{{{N}_{0}}}=\frac{1}{16}\] \[\therefore \] \[\frac{1}{16}={{\left( \frac{1}{2} \right)}^{n}}\] or \[{{\left( \frac{1}{2} \right)}^{4}}={{\left( \frac{1}{2} \right)}^{n}}\] Equating the powers, we obtain \[n=4\] i.e., \[\frac{t}{T}=4\] or \[t=4T\] or \[t=4\times 5730=22920years\] years (\[\because \] T= 5730 years)
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