Answer:
209.68 years
Explanation:
Let T be the half life.
t = 1 year
N = 99.67 % of No = 0.9967 No
Use the law of radioactivity
N = No x e ^(- λ t)
Where, λ is decay constant.
λ = 0.6931 / T
So,
0.9967 No = No x e^(- λ t)
0.9967 = e^(- λ t)
e^( λ t) = 1 / 0.9967 = 1.0033
λ t = 3.3 x 10^-3
(0.6931 x 1) / T = 3.3 x 10^-3
T = 209.68 years
Thus, the halflife is 209.68 years.
