A) \[\frac{N}{n}\sec \]
B) \[\frac{n}{N}\sec \]
C) \[\frac{0.693n}{N}\sec \]
D) \[\frac{0.693N}{n}\sec \]
Correct Answer: D
Solution :
From decay law, \[-\frac{dN}{dt}\propto N\] Or \[-\frac{dN}{dt}=\lambda N\] Here:- \[-\frac{dN}{dt}=n\](\[\alpha -\]particles per second) and N = initial value of substance \[\therefore \] \[n=\lambda N\] \[\lambda =\frac{n}{N}\] \[\therefore \]Half-life \[{{T}_{1/2}}=\frac{0.693}{\lambda }\sec \] \[{{T}_{1/2}}=\frac{0.693N}{n}\sec \]
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