Answer:
151.4863 years
Explanation:
Half life, t1/2 = 100 years
Initial concentration,[A]o = 100%
Final concentration, [A] = 35% (after 65% have been decayed)
Time = ?
Half life for a first Order reaction is given as;
t1/2 = ln (2) / k
k = ln(2) / 100
k = 0.00693y-1
The integral rate law for first order reactions is given as;
ln[A] = ln[A]o − kt
kt = ln[A]o - ln[A]
t = ( ln[A]o - ln[A]) / k
t = [ln(100) - ln(35)] /0.00693
t = 1.0498 / 0.00693
t = 151.4863 years
