A) 4800 yr
B) 6400 yr
C) 2400 yr
D) 3200 yr
Correct Answer: D
Solution :
Amount of substance remained is \[M={{M}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] Given, \[{{M}_{0}}=100g.M=25g,{{T}_{1/2}}=1600yr\] So, \[25=100{{\left( \frac{1}{2} \right)}^{n}}\] Or \[\frac{25}{100}={{\left( \frac{1}{2} \right)}^{n}}\] Or \[{{\left( \frac{1}{2} \right)}^{2}}={{\left( \frac{1}{2} \right)}^{n}}\] Comparing the power, we have \[n=2\] or \[\frac{t}{{{T}_{1/2}}}=2\] or \[t=2{{T}_{1/2}}=2\times 1600=3200yr\]
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