Write the appropriate symbol for each of these isotopes: (a) \(Z=11, A=23 ;\) (b) \(Z=28, A=64\)

The atomic number, often denoted as 'Z', is a fundamental characteristic of an element which defines its identity in the universe of elements. Every atom of a particular element has the same atomic number, which is precisely the number of protons found within the nucleus of the atom. In the periodic table, elements are arranged in ascending order of their atomic numbers.

Understanding the atomic number is crucial when dealing with isotope notation, as it allows you to identify the element in question. For example, in the given exercise, the atomic number 11 corresponds to Sodium (Na), and the atomic number 28 corresponds to Nickel (Ni). These identifications are the first step in writing the correct isotopic symbols.

The mass number, denoted as 'A', represents the total number of protons and neutrons in an atomic nucleus. Unlike the atomic number, the mass number can vary for a given element, leading to the formation of isotopes—atoms of the same element with different numbers of neutrons.

For instance, as illustrated in the exercise, Sodium with a mass number of 23 (\(^{23}_{11}\)Na) has 12 neutrons (23 - 11 = 12), while Nickel with a mass number of 64 (\(^{64}_{28}\)Ni) has 36 neutrons (64 - 28 = 36). It's important to grasp that while isotopes of an element share the same atomic number, their differing mass numbers reflect the variation in the number of neutrons in the nucleus.

The periodic table is a tabular arrangement of all known chemical elements organized by increasing atomic number. It provides a valuable framework allowing chemists and students to easily access a vast array of information about the elements and their relationships to one another. Each row on the table is called a period, and each column is known as a group.

Elements that share a column tend to have similar properties. The periodic table not only aids in identifying elements based on their atomic number—critical when addressing exercises involving isotopes—but also in predicting the properties of elements and their ions, and in understanding the trends in their reactivity and behavior.