A) \[8.9\times {{10}^{27}}\]
B) \[6.6\times {{10}^{27}}\]
C) \[1.4\times {{10}^{16}}\]
D) \[1.2\times {{10}^{17}}\]
Correct Answer: B
Solution :
[b] Rate of disintegration \[\frac{dN}{dt}={{10}^{17}}{{s}^{-1}}\] Half-life \[{{T}_{1/2}}=1445\]year \[=1445\times 365\times 24\times 60\times 60=4.55\times {{10}^{10}}\sec \]Now decay constant \[\lambda =\frac{0.693}{{{T}_{1/2}}}=\frac{0.93}{4.55\times {{10}^{10}}}=1.5\times {{10}^{-11}}\]Per sec The rate of disintegration \[\frac{dN}{dt}=\lambda \times {{N}_{0}}\Rightarrow {{10}^{17}}=1.5\times {{10}^{-11}}\times {{N}_{0}}\] \[\Rightarrow {{N}_{0}}=6.6\times {{10}^{27}}\]
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