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Chemistry - Relative atomic mass

Relative atomic mass

The mass of the 'average' atom in a sample of an element is referred as
the relative atomic mass, symbol - Ar. The relative atomic mass of an
element is a weighted average of the masses of the isotopes of an element,
on a scale where a C-12 atom has a mass of 12 exactly.

Carbon-12 is the reference point for relative isotopic masses and relative
atomic masses, but naturally-occurring carbon has a relative atomic mass of
12.011, i.e. Ar(C) = 12.011

This reflects the fact that naturally-occurring carbon consists mainly of
carbon-12 atoms along with very small amounts of carbon-13 and carbon-14.
So the 'average' carbon atom in a naturally-occurring sample of carbon has
a relative mass very close to, but greater than, the mass of a carbon-12
atom.

Relative atomic masses are determined via the output of a mass
spectrometer. The numbers in this table were obtained from passing a sample
of pure iron through a mass spectrometer:

The mathematical process of calculating the relative atomic mass from
relative isotopic masses can be simplified by using the supplied percentage
abundances.

Using the data from the table:

In effect, this is like assuming we have a sample of 100 atoms, and is
often described as taking the weighted mean of the isotopic masses, i.e.
the average allowing for the different amounts of each isotope in the
sample. Note that mathematically it is the sum of the products of the
relative isotopic mass and percentage abundance of each isotope, divided by
100.

This is reflected in the general formula:

This average relative mass of one atom of an element is the relative
atomic mass - Ar. Although no Fe atom actually has a relative mass of
55.84, we use 55.84 - the relative atomic mass of iron, i.e. Ar(Fe) - as
the representative mass of iron atoms in any sample.

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