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-lifes is \[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] Given, \[N=16-15=Ig,\text{ }{{N}_{0}}\text{=}16\] \[\therefore \] \[\frac{1}{16}={{\left( \frac{1}{2} \right)}^{n}}\] \[{{\left( \frac{1}{2} \right)}^{4}}={{\left( \frac{1}{2} \right)}^{n}}\] \[\Rightarrow \] \[n=4\] The time to decay 15g of the substance is \[{{T}_{1/2}}\times n=140\times 4=560days.\]
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