Question

Table 6.7 shows the number of elements in the first five periods of the periodic table. Explain why some of the periods have different numbers of elements

Short answer

In conclusion, the number of elements in each period of the periodic table varies due to the electron configuration and types of orbitals filled. Different orbitals (s, p, d, and f) have distinct electron capacities which result in different numbers of elements in each period. For example, Period 1 has only two elements because it fills the 1s orbital, Periods 2 and 3 have eight elements due to filling the s and p orbitals (\(2_{s} + 6_{p} = 8\)), and Periods 4 and 5 have 18 elements since they fill the s, p, and d orbitals (\(2_{s} + 6_{p} + 10_{d} = 18\)).

Step-by-step solution

Introduction to the Periodic Table

The periodic table arranges all known elements in a systematic way based on their atomic number, electron configuration, and recurring chemical properties. Elements are arranged horizontally in periods, with each period coinciding with successive electron shells being filled by electrons, which results in varying numbers of elements in different periods.

Period 1

Period 1 is the first period in the periodic table and contains only two elements, Hydrogen (H) and Helium (He). As the first period fills the 1s orbital, it can only accommodate a maximum of 2 electrons. It is the reason why this period has only two elements.

Period 2 and Period 3

Periods 2 and 3 both have eight elements each. This is because these two periods involve the filling of s and p orbitals, which can hold a maximum of 2 and 6 electrons, respectively. Therefore, the second and third periods can accommodate \(2_{s} + 6_{p} = 8\) electrons each.

Period 4 and Period 5

Periods 4 and 5 have 18 elements each. This is because these periods involve the filling of s, p, and d orbitals. The s and p orbitals can hold a maximum of 2 and 6 electrons, respectively, as mentioned earlier. The d orbitals can hold up to 10 electrons. Hence, periods 4 and 5 can accommodate \(2_{s} + 6_{p} + 10_{d} = 18\) electrons each. It is important to note that the d orbitals start filling from the third shell, one shell lower than the respective period number.

Conclusion

In conclusion, the number of elements in each period of the periodic table varies due to the electron configuration and types of orbitals filled. Different orbitals (s, p, d, and f) have distinct electron capacities which result in different numbers of elements in each period.

Key concepts

Atomic Number

The atomic number is a fundamental property of an element that indicates the number of protons found in the nucleus of an atom. In the periodic table, elements are arranged in ascending order of their atomic numbers, starting with Hydrogen, which has an atomic number of 1. This systematic arrangement reflects the overall increase in the positive charge within the nucleus as you move from left to right and from top to bottom across the periodic table.

This progressive increase in atomic number also corresponds to the increase in electron count around the nucleus, given that the atoms are neutral in charge. Therefore, the atomic number not only distinguishes one element from another but also plays a key role in the electron configuration of each element, which in turn influences the distribution of elements across different periods in the periodic table.

Electron Configuration

Electron configuration describes the arrangement of electrons in an atom's electron shells and subshells following the principles of quantum mechanics. The 'address' of each electron is given by four quantum numbers, specifying their energy level, shape of the orbital, three-dimensional orientation, and spin.

Starting from the lowest energy level, electrons fill up the available orbitals in a manner that minimizes the energy of the atom. This is governed by rules such as the Pauli exclusion principle and Hund's rule. The electron configuration not only determines the chemical properties of an element but also its placement on the periodic table. For instance, elements with their outermost electrons in the 's' orbital are grouped in the first two columns, while those with 'p', 'd', or 'f' configurations occupy the subsequent sections of the table.

Periodic Table Periods

The periods of the periodic table are the horizontal rows that categorize elements based on the number of electron shells an atom possesses. Starting from the top of the table, each subsequent period represents atoms with an additional electron shell. There are seven periods corresponding to the principal quantum number 'n', which ranges from 1 to 7.

Each period begins with the filling of a new electron shell, explaining the trend in element quantities per period. For instance, the first period comprises only two elements filling the 1s orbital, while larger periods such as the 4th and 5th have more elements as they incorporate the filling of 'd' orbitals. This concept correlates with the overall structure of the periodic table and defines the lengths of the periods.

Electron Orbitals

Electron orbitals are regions within an atom where electrons of specific energy levels are likely to be found. They are commonly referred to by the letters 's', 'p', 'd', and 'f', each with a distinct shape and orientation in space. An 's' orbital is spherical, 'p' orbitals are dumbbell-shaped, 'd' orbitals are more complex, and 'f' orbitals are even more intricate.

The 's' orbital can hold up to 2 electrons, 'p' can hold 6, 'd' can accommodate 10, and 'f' can contain a maximum of 14 electrons. This explains why different periods in the periodic table have varying numbers of elements. As electrons fill these orbitals, the period length increases according to the maximum electron capacity of the orbitals being filled, culminating in a rich structure of the table that reflects the subatomic intricacies of each element.