Find the half-life of a radioactive material if after 1 year 99.67% of the initial amount remains. (round your answer to one decimal place.)

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.