The half-life of Iodine-131 is 8 days. What mass of I-131 remains from an 8.0g sample after 2 half-lives?

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The half-life of Iodine-131 is 8 days. What mass of I-131 remains from an 8.0g sample after 2 half-lives?

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Answer 1 · 2016-02-20T20:13:38

$2 g$ $"2 g"$

Explanation:

The key to this problem lies with how the nuclear half-life of a radioactive isotope was defined.

For a given sample of a radioactive isotope, the time needed for half of the sample to undergo decay will give you that isotope's nuclear half-life.

This means that every passing of a half-life will leave you with half of the sample you started with.

Let's say that you start with a sample $A_{0}$ $A_0$ . Using the definition of a nuclear half-life, you can say that you will be left with

$A_{0} \cdot \frac{1}{2} = \frac{A_{0}}{2} \to$ $A_0 * 1/2 = color(purple)(A_0/2) ->$ after one half-life

What about after the passing of another half-life?

$\frac{A_{0}}{2} \cdot \frac{1}{2} = \frac{A_{0}}{4} \to$ $color(purple)(A_0/2) * 1/2 = color(orange)(A_0/4) ->$ after two half-lives

What about after the passing of another half-life?

$\frac{A_{0}}{4} \cdot \frac{1}{2} = \frac{A_{0}}{8} \to$ $color(orange)(A_0/4) * 1/2 = color(brown)(A_0/8) ->$ after three half-lives

and so on. With every half-life that passes, your sample will be halved.

Mathematically, you can express this as

$A = A_{0} \cdot \frac{1}{2^{n}}$ $color(blue)(A = A_0 * 1/2^n)" "$ , where

$A$ $A$ - the mass of the sample that remains after a period of time
$n$ $n$ - the number of half-lives that pass in that period of time

You know that your sample of iodine-131 has a half-life of $8$ $8$ days. In your case, you are interested in figuring out how much iodine-131 will remain undecayed after the passing of $2$ $2$ half-lives.

This means that here $n = 2$ $n=2$ . You will thus have

$A = A_{0} \cdot \frac{1}{2^{2}} = \frac{A_{0}}{4}$ $A = A_0 * 1/2^2 = A_0/4$

Since you started with an $8-g$ $"8-g"$ sample, you will be left with

$A = 8 g \cdot \frac{1}{4} = 2 g$ $A = "8 g" * 1/4 = color(green)("2 g")$

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The half-life of Iodine-131 is 8 days. What mass of I-131 remains from an 8.0g sample after 2 half-lives?

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Explanation:

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