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 :
Rate of disintegration \[\frac{dN}{dt}={{10}^{17}}{{s}^{-1}}\] Half life \[{{T}_{1/2}}=1445\] year = 1445 ´ 365 ´ 24 ´ 60 ´60 = 4.55 ´ 1010 sec Now decay constant \[\lambda =\frac{0.693}{{{T}_{1/2}}}=\frac{0.693}{4.55\times {{10}^{10}}}=1.5\times {{10}^{-11}}\] per sec The rate of disintegration \[\frac{dN}{dt}=\lambda \times {{N}_{0}}\Rightarrow {{10}^{17}}=1.5\times {{10}^{-11}}\times {{N}_{0}}\] Þ N0 = 6.6 ´ 1027.27
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