A radioactive sample decays (7)/(8) times its original quantity in...

Remaining amount of sample is$= 1 - \dfrac{7}{8} = \dfrac{1}{8}$

Using radioactive decay law

$N = {N}_{0}\left(2\right)\dfrac{- t}{{T}_{\dfrac{1}{2}}}$

We have, \left(2\right)\dfrac{t}{{T}_{\dfrac{1}{2}}} = \dfrac{{N}_{0}}{N} = \dfrac{{N}_{0}}{\dfrac{{N}_{0}}{8}} = 8 = {\left(2\right)}^{3}$</p><p>Then,$\dfrac{t}{{T}_{\dfrac{1}{2}}} = 3$</p><p>Thus, half life of the sample is$T\dfrac{1}{2} = 5min.