It 80% of a radioactive element undergoing decay is left over after a certain period of time t from the start, how many such periods should elapse from the start for just over 50% of the element to be left over?

Let a = 100, (a - x) = 80 (Amount left).∴ Amount left =a(2)n  [n = number of half lives]80=100(2)n⇒(2)n=108∴nlog⁡2=log⁡10−3log⁡2=1−3×0.3=0.1n=0.1log⁡2=0.10.3=13n=13=t Time for 80% amount  left or 20% decomposed t1/2 Time for 50% amount  left or decomposed ⇒t1/2=3tAlternativelyt80%( left )t1/2( left )=log⁡100800.3=13t1/2=3t80%( left )=3t