A) \[6.2\times {{10}^{21}}\]
B) \[7.5\times {{10}^{21}}\]
C) \[1.25\times {{10}^{22}}\]
D) \[1.75\times {{10}^{22}}\]
Correct Answer: B
Solution :
Half-life = 15 hrs. \[=\frac{0.693}{\lambda }\] \[\lambda =0.046h{{r}^{-1}}\] \[{{N}_{0}}=\frac{1}{24}\]moles of Na No. of \[\text{ }\!\!\beta\!\!\text{ }-\] particles (disintegrations) \[={{N}_{0}}-{{N}_{0}}{{e}^{-(\lambda \times 7.5)}}\] \[\frac{1}{24}moles\left( 1-{{e}^{-0.35}} \right)\] \[=0.0122\]moles \[\therefore \]no. of \[\text{ }\!\!\beta\!\!\text{ }-\]particles \[=7.5\times {{10}^{21}}\]
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