Natural silver (#A_text(r) = 107.868#) consists of two isotopes: silver-107 and silver-109. If the relative abundance of silver-107 (#A_text(r) = 106.905#) is 51.82 %, what is the atomic mass of silver-109?

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Answer 1 · 2017-10-27T01:41:18

The atomic mass of silver-109 is 108.9 u.

The atomic mass of an element is the weighted average of the atomic masses of its isotopes.

That means that we multiply the atomic mass of each isotope by a number representing its relative importance (that is, its percent abundance).

If the abundance of Ag-107 is 51.82 %, the abundance of Ag-109
is 100 % - 51.82 % = 48.18 %.

Let #x# represent the atomic mass of Ag-107.

Then,

#"At. mass of Ag = 0.5182 × At. mass of Ag-107 + 0.4818 × At mass of Ag-109"#

#"107.868 u" = "0.5182 × 106.905 u" + 0.4818x#

#"107.868 u" = "55.398 u" + 0.4818x#

#0.4818x = "52.470 u"#

#x= "52.470 u"/0.4818 = "108.9 u"#

Note: The answer can have only four significant figures, because that is all you gave for the percentage of Ag-107.