Zinc has five naturally occurring isotopes: \(48.63 \%\) of \({ }^{64} \mathrm{Zn}\), with an atomic weight of \(63.929 \mathrm{amu}\); \(27.90 \%\) of \(^{66} \mathrm{Zn}\), with an atomic weight of \(65.926\) amu; \(4.10 \%\) of \({ }^{67} \mathrm{Zn}\), with an atomic weight of \(66.927 \mathrm{amu} ; 18.75 \%\) of \({ }^{68} \mathrm{Zn}\), with an atomic weight of \(67.925\) amu; and \(0.62 \%\) of \({ }^{70} \mathrm{Zn}\), with an atomic weight of \(69.925\) amu. Calculate the average atomic weight of \(Z n\).

Isotopic abundance refers to the relative amount of each different isotope present in a naturally occurring element. Every element can have multiple isotopes, which are atoms with the same number of protons but differing numbers of neutrons. The isotopic abundance is usually expressed as a percentage, indicating how much of an element's total natural occurrence is made up of a particular isotope.

For instance, if we say an isotope of zinc has an abundance of 48.63%, it means that nearly half of all zinc atoms found in nature are of this specific isotope. To use isotopic abundances in calculations such as the average atomic weight, we first convert the percentages to decimal form by dividing by 100. These decimal values are then multiplied by the atomic mass units (amu) of each isotope to reflect the contribution of each isotope to the element's weighted average atomic mass.

The atomic mass unit, abbreviated as amu, is a standard unit of mass that quantifies the mass of atoms or molecules. It is defined as one twelfth of the mass of a carbon-12 atom, roughly equivalent to the mass of a single proton or neutron. The amu provides a convenient way to express atomic and molecular masses on a scale suitable for scientific calculations.

In the context of isotope studies, the amu is indispensable. The mass of each isotope of an element is different due to the variant number of neutrons, and these masses are expressed in amu. For example, one isotope of zinc might have an atomic mass of 63.929 amu, while another could have 65.926 amu. These precise measurements allow scientists and educators to calculate the average atomic weight of an element by considering the isotopic abundance and atomic masses of all its stable isotopes.

Zinc, like many elements, has several stable isotopes that differ in their neutron number, leading to distinct atomic masses. The isotopes of zinc mentioned in the exercise include ⁶⁴Zn, ⁶⁶Zn, ⁶⁷Zn, ⁶⁸Zn, and ⁷⁰Zn, with atomic weights ranging from about 63.929 amu to 69.925 amu.

The abundances of these isotopes determine their contribution to the average atomic weight of zinc. For instance, ⁶⁴Zn, being the most abundant isotope with an abundance of 48.63%, will contribute more to the average atomic weight than ⁷⁰Zn, which is much less abundant. When calculating the average atomic weight, it's important to consider this, as it impacts the calculated value, which is essential for a variety of scientific and industrial purposes where precision is crucial.