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25 November, 10:17

After 15 minutes, 30 g of a sample of polonium-218 remain unchanged. If the original sample had a mass of 960 g, what is the half-life of polonium-218? Suppose you want to separate the leaves, acorns, and twigs from a pile of soil. Filtration and distillation are two processes of separating mixtures. Explain which process you would use and why.

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  1. 25 November, 13:01
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    Q1. The answer is 3 minutes.

    Let's first calculate the remaining amount in percent:

    If 960g is 100 percent (starting amount), 30 g is how many percents:

    960 g : 100% = 30 g : x

    x = 30 g * 100% / 960 g = 3.125% = 0.03125

    Now, using the formula to calculate the number of half-lives:

    (1/2) ⁿ = x,

    where

    x is the remaining amount: x = 0.03125

    n is the number of half-lives

    1/2 stands for half-life.

    (1/2) ⁿ = 0.03125

    ⇒ n*log (1/2) = log (0.03125)

    n = log (0.03125) / log (1/2) = log (0.03125) / log (0.5) = - 1.505/-0.301 ≈ 5

    The number of half-lives is 5.

    Now, the number of half-lives (n) is a quotient of total time elapsed (T) and length of half-life (L):

    n = T/L

    We know:

    n = 5

    T = 15 min

    L = ?

    Thus

    L = T/n

    L = 15 min/5 = 3 minutes

    Q2. Filtration should be chosen.

    Filtration and distillation are used to separate mixtures - filtration for the separation of heterogeneous mixtures and distillation for the separation of homogeneous mixtures. Imagine that your pile of soil is a mixture. It consists of different components (the leaves, acorns, twigs), so it is the heterogeneous mixture. Therefore, to separate the leaves, acorns, twigs you will use filtration.
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