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1 July, 14:57

You have 42,784 grams of a radioactive kind of curium. If its half-life is 18 years, how much will be left after 72 years?

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  1. 1 July, 15:05
    0
    2,674.14 g

    Step-by-step explanation:

    Recall that the formula for radioactive decay is

    N = N₀ e^ (-λt)

    where,

    N is the amount left at time t

    N₀ is the initial amount when t=0, (given as 42,784 g)

    λ = coefficient of radioactive decay

    = 0.693 : Half Life

    = 0.693 : 18

    = 0.0385

    t = time elapsed (given as 72 years)

    e = exponential constant (approx 2.7183)

    If we substitute these into our equation:

    N = N₀ e^ (-λt)

    = (42,787) (2.7183) ^[ (-0.0385) (72) ]

    = (42,787) (2.7183) ^ (-2.7726)

    = (42,787) (0.0625)

    = 2,674.14 g
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