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16 September, 03:11

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.)

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  1. 16 September, 03:19
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    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.
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