### Theory:

How does one determine an element's atomic mass? It is a little more complicated because most naturally occurring elements exist as a mixture of isotopes (each with its unique mass). As a result, while calculating an element's atomic mass, the isotopic mixing must be taken into consideration.
The average atomic mass of an element is the weighted average of the masses of its naturally occurring isotopes.
However, the abundance of isotopes of each element may vary. Hence, the abundance of all of these isotopes is taken into account when determining the atomic mass. So, what is a 'weighted average'? Consider an element made up of $$50%$$ of one isotope with a mass of $$9$$ amu, and $$50%$$ of another isotope with a mass of $$10$$amu. The average atomic mass is then calculated using the equation:

$\mathit{Average}\phantom{\rule{0.147em}{0ex}}\mathit{atomic}\phantom{\rule{0.147em}{0ex}}\mathit{mass}=\left[\begin{array}{l}\left(\mathit{Mass}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}{1}^{\mathit{st}}\phantom{\rule{0.147em}{0ex}}\mathit{isotope}×%\phantom{\rule{0.147em}{0ex}}\mathit{abundance}\phantom{\rule{0.147em}{0ex}}\mathit{of}{1}^{\mathit{st}}\phantom{\rule{0.147em}{0ex}}\mathit{isotope}\right)+\\ \left(\mathit{Mass}\phantom{\rule{0.147em}{0ex}}\mathit{of}{2}^{\mathit{nd}}\phantom{\rule{0.147em}{0ex}}\mathit{isotope}×%\phantom{\rule{0.147em}{0ex}}\mathit{abundance}\phantom{\rule{0.147em}{0ex}}\mathit{of}{2}^{\mathit{nd}}\phantom{\rule{0.147em}{0ex}}\mathit{isotope}\right)\end{array}\right]$
or
$\mathit{Average}\phantom{\rule{0.147em}{0ex}}\mathit{atomic}\phantom{\rule{0.147em}{0ex}}\mathit{mass}=\frac{\sum \left(\mathit{Mass}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{isotopes}×%\phantom{\rule{0.147em}{0ex}}\mathit{natural}\phantom{\rule{0.147em}{0ex}}\mathit{abundance}\right)}{100}$

Thus, for the given element, the average atomic mass

$\begin{array}{l}=\left(9×\frac{50}{100}\right)+\left(10×\frac{50}{100}\right)\\ =4.5+5\\ =9.5\phantom{\rule{0.147em}{0ex}}\mathit{amu}\end{array}$

(Note: In percentage-based calculations, you must convert percentage abundance to fractional abundance. For example, $$50$$ % is converted to $$50/100$$ or $$0.50$$ in the above calculation.)

In the periodic table, the atomic masses of elements are average atomic masses. The term atomic weight is also used to refer to average atomic mass. The periodic chart reveals that the atomic masses of most of the elements are not whole numbers. For example, as stated in the periodic table, the atomic mass of carbon is $$12.01$$ amu, not $$12.00$$ amu. The reason for this is that both of carbon's natural isotopes (carbon-$$12$$ and carbon-$$13$$) are taken into consideration while determining its atomic mass. $$C-$$$$12$$ and $$C-$$$$13$$ have natural abundances of $$98.90$$ percent and $$1.10$$ percent, respectively.

To calculate the average atomic mass of carbon, the following formula is used:

$\begin{array}{l}\mathit{Average}\phantom{\rule{0.147em}{0ex}}\mathit{atomi}\phantom{\rule{0.147em}{0ex}}\mathit{mass}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}C\\ =\left(12×\frac{98.9}{100}\right)+\left(13×\frac{1.1}{100}\right)\\ =\left(12×0.989\right)+\left(13×0.011\right)\\ =11.868+0.143\\ =12.011\phantom{\rule{0.147em}{0ex}}\mathit{amu}\end{array}$

It is important to remember that when the atomic mass of carbon is given as $$12$$ amu, it refers to the average atomic mass of carbon isotopes, not the mass of individual carbon atoms.