A) 4800 year
B) 6400 year
C) 2400 year
D) 3200 year
Correct Answer: D
Solution :
Amount of substance remained is \[M={{M}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] Given, \[{{M}_{0}}=100g,\,\,M=25\,kgm,\,{{T}_{1/2}}\,=1600\] years 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\[t=2{{T}_{1/2}}=2\times 1600=3200\]years
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