A) \[3.7\times {{10}^{-8}}g\]
B) \[7.4\times {{10}^{-8}}g\]
C) \[3.7\times {{10}^{-8}}g\]
D) \[200g\]
Correct Answer: B
Solution :
\[{{t}_{1/2}}=63.43\min =69.3\times 60s=4158s\] \[\lambda =\frac{0.693}{{{t}_{1/2}}}=\frac{0.693}{4158}{{s}^{-1}}\] \[=1.67\times {{10}^{-4}}{{s}^{-1}}\] Let mass of radioactive sample\[=m\,\,g\] \[\therefore \]number of atoms in the sample, \[N=\frac{m\times 6.02\times {{10}^{23}}}{200}\] \[=3.01\,\,m\times {{10}^{21}}\] Rate\[=\lambda N\] \[3.7\times {{10}^{10}}=(1.67\times {{10}^{-4}})\times (3.01m\times {{10}^{21}})\] \[m=\frac{3.7\times {{10}^{10}}}{(1.67\times {{10}^{-4}})(3.01\times {{10}^{21}})}\]
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