Final answer:
The length of periods in the periodic table is determined by the number of electrons that can be accommodated in the sublevels being filled at each principal energy level. The first period contains only two elements as it fills the 1s sublevel. Subsequent periods increase in length as additional sublevels are filled, with the second and third containing eight elements each, and further periods containing more as the d and f sublevels contribute additional capacity.
Step-by-step explanation:
The relationship between electrons in sublevels and the length of each period in the periodic table is a foundational aspect of the electronic structure of atoms. The periodic table is organized into seven horizontal rows, known as periods, which correspond to the principal energy levels of the atoms' electrons. Each period begins with a new principal energy level; thus, the number of elements in a period depends on the sublevels being filled with electrons at that energy level.
The first period is the shortest because it involves filling only the 1s sublevel, which can hold two electrons. Hence, it consists of only two elements, hydrogen and helium. In the second and third periods, the s and p sublevels are being filled. Since the 2p and 3p sublevels each contain three orbitals and each orbital can hold two electrons, the second and third periods each contain a total of eight elements.
Moving further, the fourth and fifth periods see the addition of the d sublevel, which contains five orbitals and can accommodate ten electrons. This means the fourth and fifth periods have 18 elements each. The sixth period is more complex because it includes the filling of the 4f sublevel, with its seven orbitals and 14 electrons, followed by the 5d and the 6p sublevels, cumulating in a period length of 32 elements. The seventh period also has the potential for 32 elements, but since some of these elements are yet to be discovered or are only artificially created, the current number is slightly less.
Quantum theory specifies that each electron within an energy level occupies a specific sublevel designated by letters s, p, d, and f. These sublevels can hold varying numbers of electrons: the s sublevel holds two, the p holds six, the d holds ten, and the f holds fourteen. This arrangement dictates the length of each period on the periodic table based on the number of electrons needed to fill the available sublevels for that principal energy level.