A) \[140\,\,days\]
B) \[280\,\,days\]
C) \[420\,\,days\]
D) \[560\,\,days\]
Correct Answer: D
Solution :
From Rutherford-Soddy law, the number of radioactive nuclei left after \[n\] half-life's is \[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] Given,\[N=16-15=1\,\,g,\,\,{{N}_{0}}=16\] \[\frac{1}{16}={{\left( \frac{1}{2} \right)}^{n}}\] The time to decay 15 g of the substance is \[{{T}_{1/2}}\times n=140\times 4\] \[=560\,\,days\]
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