A) \[3\times {{10}^{-3}}\]/day
B) \[9\times {{10}^{-3}}\]/day
C) \[1\times {{10}^{-3}}\]/day
D) \[6\times {{10}^{-3}}\]/day
Correct Answer: B
Solution :
The time required for the number of parent nuclei to fall to 50% is called half-life \[{{T}_{1/2}}\] and may be related to K as follows. Since, \[0.5\,{{N}_{0}}={{N}_{0}}{{e}^{-{{T}_{1/2}}}}\] we have, \[\lambda {{T}_{1/2}}=\ln (2)=0.693\] or \[{{T}_{1/2}}=\frac{0.693}{\lambda }\] or \[\lambda =\frac{0.693}{{{T}_{1/2}}}\] Given, \[{{T}_{1/2}}=77\] days \[\therefore \] \[\lambda =\frac{0.693}{77}=9\times {{10}^{-3}}/\] days
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