A) 500 yrs
B) 600 yrs
C) 800 yrs
D) 950 yrs
Correct Answer: A
Solution :
Given that Initial value \[{{N}_{0}}\text{=}0.2\text{ }gm.\] Final value \[(N)=0.025\text{ }gm.\] Time decay \[(T)=1500\text{ }yrs.\] By using: \[\frac{N}{{{N}_{o}}}={{\left( \frac{1}{2} \right)}^{n}}\] \[\frac{0.025}{0.2}={{\left( \frac{1}{2} \right)}^{n}}\] Or \[\frac{1}{8}={{\left( \frac{1}{2} \right)}^{n}}\] Or \[{{\left( \frac{1}{2} \right)}^{3}}={{\left( \frac{1}{2} \right)}^{n}}\] Or \[n=3\] Now by using \[{{t}_{1/2}}=\frac{T}{n}=\frac{1500}{3}\] \[=500\text{ }yrs\]
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