A) \[3.61\times {{10}^{10}}\]
B) \[3.6\times {{10}^{12}}\]
C) \[3.1\times {{10}^{15}}\]
D) \[31.1\times {{10}^{15}}\]
Correct Answer: A
Solution :
Rate of disintegration \[\frac{dN}{dt}=\lambda N\] From Avagadros principle Number of atoms in 1 gram radium \[=\frac{6\times {{10}^{23}}}{226}\] decay constant \[\lambda =\frac{1}{\tau }\] \[=\frac{0.093}{1620}years\] \[=\frac{0.693}{1620\times 365\times 24\times 60\times 60}\] \[=\frac{0.693}{1620\times 3.15\times {{10}^{7}}}{{\sec }^{-1}}\] \[\therefore \] \[\frac{dN}{dt}=\frac{0.693}{1620\times 3.15\times {{10}^{7}}}\times \frac{6\times {{10}^{23}}}{226}\] \[=3.61\times {{10}^{10}}per\,\sec .\]
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