Define half-life period of a radioactive substance. Establish its relationship with the decay constant.

Explanation

Half-life period of a radioactive substance is the time at which both number of nuclides of radioactive substance as well as its activity (7.e., both N and R) have been reduced to one-half of their initial values.
Thus, at `t =T_(1/2), N=N_(0)/2`
Hence, from relation `N=N_(0)e^(-lambdat)`, we have
`N_(0)/2= N_(0)e^(-lambdaT_(1/2))implies log_(e) 2 = lambda T_(1/2)`
or `T_(1/2)=(log_(e)2)/(lambda)=0.693/(lambda)`.