Given, T(half life of radioactive substance)= 38 hrs
N1(Remaining radioactive substance after first decay) = 50
N2(Remaining radioactive substance after 90% decay) =
100 - 90 =10
t1(time of first decay),
t2(time of 90% decay)
t2 -t1 =(T/ln2)×(ln(N1/N2))
= 88.23 hrs
t2 =88.23+38=126.23 hrs = time for 90 % radioactive substance to be dissipated.