Naturally occurring magnesium has an atomic mass of 24.312 and consists of three isotopes. The major isotope is \({ }^{24} \mathrm{Mg},\) natural abundance \(78.99 \%\), relative atomic mass 23.98504 . The next most abundant isotope is \({ }^{26} \mathrm{Mg},\) relative atomic mass \(25.98259 .\) The third most abundant isotope is \({ }^{25} \mathrm{Mg},\) whose natural abundance is in the ratio of 0.9083 to that of \({ }^{26} \mathrm{Mg}\). Find the relative atomic mass of \({ }^{25} \mathrm{Mg}\).

Isotopes are variants of a chemical element that have the same number of protons but a different number of neutrons. This difference in neutron count affects the mass of the isotopes. Relative atomic mass is a measure of how heavy, on average, an atom of an element is compared to the atomic mass unit (amu), which is one-twelfth the mass of a carbon-12 atom. The relative atomic mass of an isotope takes into account only the mass of that specific isotope as opposed to the average mass of all the element's naturally occurring isotopes.

To determine the relative atomic mass of an isotope when you have the abundance and relative atomic mass of other isotopes, as in the case of ^{25}Mg, you can use the weighted average formula. The atomic mass of the element is the sum of the product of the relative atomic mass and the natural abundance of each of its isotopes. By knowing this formula and the relative atomic masses and abundances of the other isotopes, you can deduce the relative atomic mass of the unknown isotope.

The atomic mass unit, or amu, is a standard unit of mass that quantifies mass on an atomic or molecular scale. It is defined as one twelfth of the mass of an unbound neutral carbon-12 atom in its nuclear and electronic ground state, and it is equivalent to 1.66053906660(50) x 10^{-27} kilograms.

Using the amu is instrumental in chemistry for comparing the masses of different atoms and molecules. Calculations of relative atomic mass become convenient because it provides a common scale where the mass of a carbon-12 atom is exactly 12 amu. This is paramount when calculating the average mass of an element's isotopes, as their masses are often close to whole numbers.

Chemical elements may exist in several different forms known as isotopes, which are distinguished by the number of neutrons in the nucleus. While all isotopes of an element have the same number of protons and hence share the same chemical properties, they have different masses due to the varying neutron count. Many elements have naturally occurring isotopes, such as magnesium, which in the given exercise has three: ^{24}Mg, ^{25}Mg, and ^{26}Mg.

Understanding isotopes is fundamental in chemistry and physics as they can have different stability, with some being radioactive. Moreover, isotopes can be used in various fields, like medicine for imaging and treatment, in archeology for radiocarbon dating, or in climate science for understanding past atmospheres.

Natural abundance ratios indicate the proportion of each isotope that occurs in nature for a given element. Unlike artificially created isotopes in a lab, the naturally occurring isotopes of an element each have a definitive abundance that is consistent across any natural sample of the element. These ratios are vital to determining the average atomic mass of an element as listed on the periodic table, which is calculated based on the abundances and masses of its natural isotopes.

In the context of our exercise involving magnesium isotopes, natural abundance ratios are used to calculate the precise atomic mass of an element. When the exact natural abundance of one isotope isn't directly given, such as for ^{25}Mg, it may be expressed in relation to the abundance of another isotope, like the ratio 0.9083 to ^{26}Mg. By understanding the concept of natural abundance ratios, the mass of ^{25}Mg can be determined using algebraic methods combined with the concept of average atomic masses.