A) 1000 yr
B) 700 yr
C) 500 yr
D) 250 yr
Correct Answer: C
Solution :
Key Idea: Use the following formula to find the half-life of the object. \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}\] and \[{{t}_{1/2}}=\frac{T}{n}\] where, \[{{N}_{0}}=\] initial activity of object = 0.002 g N = activity after time T = 0.00025 g T = 1500 yr. \[\therefore \] \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}\] or \[\frac{0.00025}{0.002}={{\left( \frac{1}{2} \right)}^{n}}\] or \[\frac{1}{8}={{\left( \frac{1}{2} \right)}^{n}}\] or \[{{\left( \frac{1}{3} \right)}^{3}}={{\left( \frac{1}{2} \right)}^{n}}\] \[\therefore \] \[n=3\] \[{{t}_{1/2}}=\frac{T}{n}=\frac{1500}{3}=500\,yr\]
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