A) 75 h
B) 100 h
C) 125 h
D) 150 h
Correct Answer: B
Solution :
The mass of radioactive substance remained is, \[M={{M}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] \[Here,\,\,M=1\,g,\,\,{{M}_{0}}=256\,g,\,{{t}_{1/2}}=12.5\,h\] \[So,1=256\,{{\left( \frac{1}{2} \right)}^{n}}\] \[or\frac{1}{256}={{\left( \frac{1}{2} \right)}^{n}}\] \[or{{\left( \frac{1}{2} \right)}^{8}}={{\left( \frac{1}{2} \right)}^{N}}\] Comparing the powers on both the sides, we get \[n=8=\frac{t}{{{T}_{1/2}}}\] \[\therefore t=8{{T}_{1/2}}=8\times 12.5=100\,h\]
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