Tabulated atomic mass

The tabulated atomic mass of an element (ie - The Periodic Table of the Elements) is a weighted average of the masses of all naturally occurring isotopes for the element. Most elements have several naturally occurring isotopes in varying abundance.

For example, hydrogen and carbon have 2 naturally occurring isotopes. Others like Magnesium has 3 naturally occurring isotopes, and Strontium has 4 naturally occurring isotopes.

Atomic masses that are on the periodic table are calculated based on knowledge of the following information:

the mass of all the naturally occurring isotopes for the element
the natural abundance of each of these naturally occurring isotopes (usually expressed as a percentage)

The formula that you need is to calculate the atomic mass of an element is:

atomic mass =	(the fraction of isotope 1)(mass of isotope 1) +
	(the fraction of isotope 2)(mass of isotope 2) +
	(the fraction of isotope 3)(mass of isotope 3) + ...

where

the fractions of the isotopes is the natural abundance of the isotope written as a decimal.
the masses of the isotopes, depending on the accuracy at which they are determined, can have varying numbers of significant figures.

Example

Carbon, as we find it in our universe, does not exist as solely as ¹²C. There is another naturally occurring isotope of carbon, ¹³C. ¹³C also contributes to the atomic mass of carbon.

To calculate the atomic mass of carbon, we need to obtain the following information.

All the naturally occurring isotopes of carbon.
The abundance of each naturally occurring isotope.

Isotopic data can be retrieved from many sources. Below shows the data obtained from WebElements, from the University of Sheffield. Depending on the source, isotopic measurements reported may varying in the number of significant figures.

Naturally occurring isotope	Fractional abundance	Mass (amu)
¹²C	0.9893(8)	12.0000000(0)
¹³C	0.0107(8)	13.0033548378(10)

The following are some points to note about the isotopic data of carbon.

There are two naturally occurring isotopes of carbon:
- ¹²C
- ¹³C

These isotope masses will contribute to the atomic mass of carbon.

From the fraction of abundance column, note that there are much more ¹²C isotopes than ¹³C isotopes. (i.e. 98.93(8)% for ¹²C and 1.07(8)% for ¹³C)
The sum of all the fractions of abundance of each naturally occurring isotopes (ie - add up column 2) should equal 1.0000 or 100%. (i.e. 98.93(8) % + 1.07(8) % = 100.016%) Any deviation from 100% observed in the 2nd or 3rd decimal places is usually a result from measurement uncertainty.
By definition, a carbon-12 atom is given the atomic mass of exactly 12.0000000(0) amu. This is used as the basis upon which the atomic mass of other isotopes is determined.
As expected, ¹³C, with one more neutron, is heavier than ¹²C.

Calculate the atomic mass of carbon

atomic mass =	(0.9893(8))(12.0000000(0) amu) +
	(0.0107(8) )(13.0033548378(10) amu) +
	12.01 amu

Carbon-14

The isotope, ¹⁴C, is not a naturally occurring isotope of carbon. ¹⁴C is formed in the upper atmosphere from the bombardment of ¹⁴N atoms with neutrons. In the calculation of atomic mass of carbon, ¹⁴C does not contribute to the atomic mass of carbon.