Explain why the several periods in the periodic table do not all have the same number of members.

An atom consists of a positively charged nucleus, around which negatively charged electrons revolve in different orbits or energy levels. These energy levels are often referred to as shells and are designated by the letters K, L, M, N, and so on or simply by numbers 1, 2, 3, 4, etc.

It is important to understand that each shell is made up of one or more sub-shells, which are also called orbitals. According to the Pauli exclusion principle, each orbital can accommodate a maximum of 2 electrons. The first energy level (K or 1) has only one subshell, which can accommodate 2 electrons. The second energy level (L or 2) has two subshells, which can accommodate a total of 8 electrons. The third energy level (M or 3) has three subshells, which can accommodate a total of 18 electrons, but due to energy considerations, the third shell fills up with 8 electrons and then the fourth energy level starts to fill up. Once the fourth level has 2 electrons, the third level can continue to fill up to its full capacity of 18 electrons. The periodic table is structured in such a way that elements with similar electron configurations and thus similar chemical properties are placed in the same group.

The periodic table has 7 periods, which correspond to the energy levels or shells of atoms for the elements of that period. The first period has 2 elements (H and He), corresponding to the two possible electrons in the first energy level. The second and third periods each have 8 elements, corresponding to the eight electrons that can be hosted by the second and third energy levels, respectively. The fourth and fifth periods have 18 elements, which is related to the 18 possible electrons in the third and fourth energy levels. The sixth and seventh periods have more elements due to the inclusion of f-block elements

The variable number of elements in different periods of the periodic table is thus down to the structure of atoms and the electron configuration rules, which determine how the electron shells of atoms fill up. This pattern is reflected in the physical layout of the periodic table, where each period corresponds to a new energy level in the atoms of the elements, and the number of elements in a period corresponds to the total number of electrons that can be accommodated in that energy level.