Question

Question #2e766

Answer 1

`90%`

Explanation:

So, you know that you're dealing with two isotopes, let's say `""^20"X"` and `""^22"X"`.

The relative atomic mass of the element will be determined by the atomic masses of the two isotopes in proportion to their respective abundances.

`"relativ atomic mass" = sum_i ("isotope"""_i xx "abundance"""_i)`

SInce you're only dealing with two isotopes, you can say that their abundances must add to give 100%.

If you take `x` to be the decimal abundance, which is simply the percent abundance divided by `100`, of `""^20"X"`, the abundance of `""^22"X"` will be `(1 - x)`.

This means that you can write

`"20 u" * x + "22 u" * (1-x) = "20.2 u"`

`20x + 22 - 22x = 20.2`

`2x = 1.8 implies x = 1.8/2 = 0.9`

The decimal abundance of `""^22"X"` will thus be `(1- 0.9) = 0.1`.

The percent abundances of the two isotopes are

`""^20"X: " color(green)(90%)`
`""^22"X: " 10%`

The result makes sense because the relative atomic mass of the element is much closer to the atomic mass of `""^20"X"` than it is to the atomic mass of `""^22"X"`, which can only imply that `""^20"X"` has a significantly larger percent abundance that `""^22"X"`.