Silicon has three naturally occurring isotopes: \(92.23 \%\) of \({ }^{28} \mathrm{Si}\), with an atomic weight of \(27.9769\) amu; \(4.68 \%\) of \({ }^{29} \mathrm{Si}\), with an atomic weight of \(28.9765 \mathrm{amu} ;\) and \(3.09 \%\) of \({ }^{30} \mathrm{Si}\), with an atomic weight of \(29.9738\) amu. On the basis of these data, confirm that the average atomic weight of \(S i\) is \(28.0854 \mathrm{amu}\).

Understanding the concept of isotope percentage is key when delving into the composition of elements. Isotopes are different forms of a single element, which have the same number of protons but different numbers of neutrons. The isotope percentage, also known as natural abundance, refers to the proportion of each isotope found in nature for a given element.

The atomic weight, or atomic mass, of an element is not just a simple number but a weighted average of all the isotopic masses, taking into account the isotope percentages of each naturally occurring isotope of that element. Each isotope's mass contributes to the overall atomic weight in proportion to its natural abundance. For example, a large abundance of a lighter isotope will decrease the atomic weight, while a heavier isotope in great proportion will increase it.

When calculating atomic weight, it is crucial to use the standard atomic mass unit (amu), which defines the mass on an atomic scale and ensures consistency across calculations.

Calculating the average atomic weight of an element requires the concept of a weighted average. This calculation takes into account the mass of each isotope as well as its relative abundance.

To find this average, each isotope's atomic weight is multiplied by its percentage (converted into a fractional form by dividing by 100). The results of these products are then added together to yield the weighted average, which is essentially the atomic weight of the element. In our example with Silicon isotopes, the weighted average leads us towards the average atomic weight of Silicon in nature.

In conclusion, understanding these three key concepts enables students to unravel the layered nature of atomic weights and how isotopes combine to form the unique fingerprint of each element on the periodic table.