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?

Question

Noah Aldrich · Accepted Answer

#"107.96 u"#

As you are aware, the weighted average of an element's naturally occurring isotopes' atomic masses is used to determine the element's average atomic mass.

Put simply, the average mass of an element is determined by the proportionate contribution of each isotope 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 #100#.

What then would be the two isotopes of silver's decimal abundances?

Well, you know that for every #25# atoms of silver, you get

This means that the decimal abundance of silver-107 will be equal to #13/25# and the decimal abundance of silver-109 will be equal to #12/25#.

Therefore, you can presume that the two isotopes' atomic masses, if given by the problem, are

Thus, silver's average atomic mass will be

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

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

Mateo Aguilar · Answer

undefined The average atomic mass of silver is approximately 107.87 atomic mass units (amu).