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.

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.