A radio nuclide sample has `N_(0)` nuclei at t=0. Its number of undecayed nuclei get reduced to `N_(0)/e` at t=`tau`. What does the term ‘`tau`’ stand for ? Write in terms of '`tau`', the time interval T in which half of the original number of nuclei of this radio nuclide would have got decayed.

Explanation

The time ‘`tau`’ in which number of undecayed nuclei get reduced to `N_(0)/e` is called the mean life or average life period.
The time interval T (or more appropriately `T_(1/2)`) in which half of the original number of nuclei would have got decayed is
`T(orT_(1/2)=0.693/(lambda)=0.693lambda)`