The atomic mass of germanium is \(72.61\) amu. Is it likely that any individual germanium atoms have a mass of \(72.61 \mathrm{amu}\) ?

Isotopes are forms of an element that have the same number of protons but different numbers of neutrons within their nuclei. As a result, they have the same atomic number, which determines the element’s identity, but different mass numbers. For example, carbon-12 and carbon-13 are both isotopes of carbon, with mass numbers 12 and 13, respectively. The presence of different isotopes leads to variations in atomic mass for an element, as each isotope contributes to the element's average atomic mass based on its natural abundance.

Understanding isotopes is crucial when considering the atomic mass of an element. It explains why the atomic mass listed on the periodic table is a decimal value rather than a whole number. Each isotope of an element will have its own unique mass, closely approximating a whole number when accounting for the mass of its protons and neutrons.

The average atomic mass of an element is a weighted average of the masses of all its naturally occurring isotopes. It takes into account not only the individual masses of each isotope but also their relative proportions in nature, referred to as their natural abundance. This concept provides insight into the reason atomic masses are not whole numbers. For instance, the average atomic mass of germanium is 72.61 amu, which indicates this value represents a calculated average based on all germanium isotopes and their respective abundances.

The average atomic mass is the number typically listed in the periodic table. This value is important for scientists and chemists since it accurately represents the mass of an element's atoms when considering a large number or sample size. When dealing with individual atoms, however, it is improbable that an atom will have the precise average atomic mass listed.

Natural abundance refers to the percentage of a particular isotope relative to the total number of atoms of the same element in a natural sample. This property is essential for calculating the average atomic mass of an element. Isotopes with a higher natural abundance will more heavily influence an element's average atomic mass.

For instance, if one isotope of an element occurs much more frequently in nature than another, the atomic mass of that element will be closer to the mass of the more abundant isotope. It's the relative amounts of each isotope present in nature that determine the final average mass we see on the periodic table, and this figure is crucial for ensuring accurate measurements and calculations in chemistry and physics.

The mass number of an isotope is the sum of the number of protons and neutrons in its nucleus. Since protons and neutrons have roughly the same mass, and electrons have a much lower mass, the mass number is approximately equal to the actual mass of the isotope in atomic mass units (amu). The mass number plays a central role in identifying different isotopes of the same element.

Each isotope of germanium, for example, has a distinct mass number, such as 70 for Ge-70, 72 for Ge-72, and so forth. These numbers represent whole numbers because they count the number of protons and neutrons, ignoring the small mass of the electrons. Hence, when we refer to the mass number of any isotope, we are typically discussing a value that closely represents its actual mass, ignoring the slight variance due to the presence of electrons.