Question

Question #c035b

Answer 1

`"26 g"`

Explanation:

You don't actually need to use the formula given to you, all you need to know here is that the initial sample of plutonium-239 will be halved with every passing of a half-life.

This means that you can write

`color(blue)(A = A_0 * 1/2^n) " "`, where

`n` - the number of half-lives that pass in a given period of time
`A` - the mass of the sample that remains undecayed
`A_0` - the initial mass of the sample

So, your goal here is to find the value of `n` by using the fact that

`color(blue)(n = "given period of time"/"half-life")`

In your case, the half-life of plutonium-239 is said to be `2.4 * 10^4` years. This means that after `9500` years, `n` will be

`n = (9500 color(red)(cancel(color(black)("years"))))/(2.4 * 10^4 color(red)(cancel(color(black)("years")))) = 19/48`

If the initial sample had a mass of `34.2` grams, then you'll be left with

`A = "34.2 g" * 1/2^(19/48) = "25.994 g"`

Rounded to two sig figs, the answer will be

`A = color(green)("26 g")`