# What is the average atomic mass of silver if 13 out of 25 atoms are silver-107 and 12 out of 25 atoms are silver-109?

##### 1 Answer

#### Explanation:

As you know, the **average atomic mass** of an element is calculated by taking the **weighted average** of the atomic masses of its naturally occurring isotopes.

In simple terms, each isotope will contribute to the average mass of the element **proportionally** to its *percent abundance*.

#color(blue)("avg. atomic mass" = sum_i ("isotope"_i xx "abundance"_i))#

For the actual calculations, it's easier to use *decimal abundances*, which are simply percent abundances divided by

So, what would the decimal abundances of the two isotopes of silver be?

Well, you know that **for every**

#13# atoms of silver-107#12# atoms of silver-109

This means that the decimal abundance of silver-107 will be equal to

Now, if the atomic masses of the two isotopes were not provided by the problem, you can assume them to be

#""^107"Ag" -> "107 u"# #""^109"Ag" -> "109 u"#

So, the average atomic mass of silver will be

#"avg. atomic mass" = "107 u" xx 13/25 + "109 u" xx 12/25#

#"avg. atomic mass " = color(green)(" 107.96 u")#