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1 August, 16:02

After the release of radioactive material into the atmosphere from a nuclear power plant in a country in 1986 , the hay in that country was contaminated by a radioactive isotope (half-life 6 days). If it is safe to feed the hay to cows when 15 % of the radioactive isotope remains, how long did the farmers need to wait to use this hay?

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  1. 1 August, 17:35
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    t = 16.42 days

    Explanation:

    From the Law of Radioactive Decay, we know that:

    N = N₀ e^ (-λt)

    where,

    N = Final Amount of Substance

    N₀ = Initial Amount of Substance

    λ = Decay Constant

    t = time period

    For a period of one half-life, we have:

    N = 0.5*N₀

    t = 6 days

    Therefore,

    0.5*N₀ = N₀ e^ (-λ*6 days)

    -λ*6days = ln (0.5)

    λ = 0.1155 day⁻¹

    So, now for 15% of the element, we can re-write the formula as:

    0.15*N₀ = N₀ e^ (0.1155 day⁻¹ * t)

    t * 0.1155 day⁻¹ = ln (0.15)

    t = 16.42 days
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