# Question #794f9

##### 1 Answer

#### Answer:

Here's what I got.

#### Explanation:

You know that europium has two naturally occurring isotopes, so right from the start, you can say that the abundance of the second isotope is equal to

#100% - 52.19% = 47.81%#

This is the case because the abundance of the two isotopes **must** add up to give **all the contribution** to the average atomic mass of the element.

Before moving on, take a second to note that europium has an average atomic mass of **here**.

Now, the average atomic mass of the element is calculated by taking the **weighted average** of the atomic mass of its naturally occurring isotopes.

This means that you can write--remember to use **decimal abundances**, i.e. the percent abundance divided by

#"151.9641 u" = overbrace("152.9212 u" * 0.5219)^(color(blue)("the contribution of isotope 1")) + overbrace(? * 0.4781)^(color(blue)("the contribution of isotope 2"))#

Rearrange to find the atomic mass of the second isotope

#? = ("151.9641 u " - " 152.9212 u" * 0.5219)/0.4781 = color(darkgreen)(ul(color(black)("150.9 u")))#

The answer is rounded to four **sig figs**, the number of sig figs you have for the abundance of the first isotope.

Now, in order to find the **mass number** of the second isotope, round its atomic mass to the **nearest whole number**.

You will end up with

#150.9 ~~ 151#

This is the **mass number** of the second isotope, i.e. the number of protons **and** neutrons located inside its nucleus.