(a) Which two of the following are isotopes of the same element: \({ }_{16}^{31} \mathrm{X},{ }_{15}^{31} \mathrm{X},{ }_{16}^{32} \mathrm{X} ?\) (b) What is the identity of the element whose isotopes you have selected?

Understanding the atomic number is vital when determining the identity of an element and its isotopes. The atomic number, often represented by the letter 'Z', is a unique property of an element that tells us the number of protons found in the nucleus of an atom. Since each element on the periodic table has a distinct number of protons, the atomic number effectively serves as its fingerprint.

As an example, in the provided exercise, when comparing \( _{16}^{31} \mathrm{X} \) and \( _{16}^{32} \mathrm{X} \), we note that the '16' in the subscript position is the atomic number for both, indicating that they are indeed different forms (isotopes) of the same element due to their consistent proton count. This is instrumental for students who struggle to grasp the concept of isotopes; by focusing on the atomic number, they can easily distinguish whether they are working with isotopes or completely different elements.

Mass number, denoted by 'A', is another crucial aspect which determines an atom's identity, particularly when distinguishing between isotopes of an element. It represents the total number of protons and neutrons within an atom's nucleus. However, unlike the atomic number, the mass number is not unique to each element because isotopes have different numbers of neutrons but the same number of protons.

Take for instance the isotopes \( _{16}^{31} \mathrm{X} \) and \( _{16}^{32} \mathrm{X} \). Despite having the same atomic number, their mass numbers are '31' and '32', respectively. This tells us that \( _{16}^{32} \mathrm{X} \) has one additional neutron compared to \( _{16}^{31} \mathrm{X} \). This distinction is invaluable for students to understand that isotopes are variations of the same element with different mass numbers due to varying amounts of neutrons.

The periodic table is not merely a chart of elements; it's a comprehensive tool that organizes all known elements based on their chemical properties, including atomic number and mass number. Each element is positioned in a way that groups elements with similar properties together, making it simpler to predict how an element will behave in chemical reactions.

Using the exercise, once students have identified atomic number '16' as belonging to the isotopes of sulfur (S), they can refer to the periodic table to learn more. This element is found in the oxygen group, indicating that sulfur (like other elements in this group) is commonly involved in forming covalent bonds. A user-friendly periodic table that clearly labels atomic numbers, mass numbers, and chemical symbols can greatly assist students in connecting theoretical isotope information with practical chemical knowledge.