A) \[\lambda =\frac{{{\log }_{10}}2}{T}\]
B) \[\lambda =\frac{{{\log }_{e}}2}{T}\]
C) \[\lambda =\frac{T}{{{\log }_{e}}2}\]
D) \[\lambda =\frac{{{\log }_{2}}e}{T}\]
Correct Answer: B
Solution :
The time required for the number of parent nuclei to fall to 50% is called half-life T and may be related to disintegration constant \[\lambda \] as follows. Since, \[0.5\,{{N}_{0}}={{N}_{0}}\,{{e}^{-\lambda T}}\] we have, \[\lambda T={{\log }_{e}}\,2\] \[\therefore \lambda =\frac{{{\log }_{e}}2}{T}\]
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