# Question 794f9

Oct 8, 2017

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 100%. Simply put, if you only have two naturally occurring isotopes, they must make up 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 $\text{151.9641 u}$ $\to$ see 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 100%, for this equation

"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

$150.9 \approx 151$

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