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.