Question

An element ' \(X\) ' belongs to fourth period and fifteenth group of the periodic table. Which one of the following is true regarding the outer electronic configuration of \(^{4} X^{\prime}\) ? (a) It has partially filled \(d\)-orbitals and completely filled s-orbitals. (b) It has completely filled s-orbitals and completely filled \(p\)-orbitals. (c) It has completely filled s-orbituls and halffilled \(p\)-orbitals. (d) It has half-filled \(d\)-orbitals and completely filled s-orbitals.

Short answer

The element has completely filled s-orbitals and half-filled p-orbitals, making option (c) the correct answer.

Step-by-step solution

Understanding the Periodic Table

The periodic table is arranged in periods (horizontal rows) and groups (vertical columns). The period number indicates the highest energy level an electron in that element occupies in its ground state. The group number for groups 1 to 12 corresponds to the number of valence electrons in the elements of those groups. For groups 13 to 18, the number of valence electrons is equal to the group number minus 10.

Determine the Element's Position

Based on the information given, the element 'X' is in the fourth period and fifteenth group. This means the element has 4 energy levels and 15 - 10 = 5 valence electrons.

Determine the Valence Electron Configuration

Elements in group 15 have the valence electron configuration of ns^2 np^3, where n is the period number. Because 'X' is in the 4th period, the configuration will be 4s^2 4p^3.

Analyze the Options

Option (a) suggests partially filled d-orbitals, which is incorrect because group 15 elements do not have d-electrons as valence electrons. Option (b) suggests completely filled p-orbitals, which is incorrect since it would need 6 p-electrons. Option (d) suggests half-filled d-orbitals, which is incorrect for the same reason as option (a). Therefore, by process of elimination and understanding the valence configuration, option (c) is correct, which states the element has completely filled s-orbitals (2 electrons) and half-filled p-orbitals (3 electrons out of a possible 6).

Key concepts

Valence Electrons

Valence electrons are the electrons that reside in the outermost shell of an atom. These electrons play a crucial role in chemical bonding and reactivity, as they are the ones that engage in interactions with other atoms. For group 15 elements on the periodic table, which include nitrogen, phosphorus, arsenic, antimony, and bismuth, the number of valence electrons is consistent across the group.

Each of the group 15 elements has five valence electrons. This is due to their position on the periodic table, where the group number (also known as the family) dictates the number of valence electrons. However, for those new to chemistry, it's essential to remember that the rule correlates the group number to valence electrons mostly applies to the main group elements (groups 1, 2, and 13 to 18).

The valence electrons can be represented by the electron configuration of the outer shell, such as ns²np³, where 'n' represents the period or principle quantum number. This electron configuration is critically important because it helps explain the reactivity and bonding characteristics of the elements within this group.

Electronic Configuration

The electronic configuration of an atom describes the distribution of electrons in its atomic orbitals. This distribution is governed by a set of principles: the Pauli exclusion principle, Aufbau principle, and Hund's rule. For students to master electronic configurations, they must understand how these principles work together to fill orbitals.

The Aufbau principle suggests that electrons fill orbitals starting from the lowest available energy levels before moving to higher ones. It indicates that 's' orbitals are filled before 'p' orbitals. Following this principle for group 15 elements, and given their position in the periodic table, the electron configuration for the valence shell would start with the 's' orbital followed by the 'p' orbital, precisely ns²np³, indicating 2 electrons in the s orbital and 3 in the p orbital.

For the element 'X' in our exercise, which is situated in the 4th period and 15th group, the valence shell electronic configuration would be 4s²4p³. This translates to an outer shell with a total of 5 valence electrons, 2 of which occupy the 's' orbital and 3 that are distributed in the 'p' orbital.

Periodic Table Periods

Periods refer to the horizontal rows on the periodic table. There are seven periods in the periodic table, each corresponding to the principal energy levels of atoms. Elements in the same period have the same number of atomic orbitals. As you transition from left to right within a period, each element's atomic number increases by one, implying an additional proton in the nucleus and an extra electron.

Understanding the structure of periods is fundamental when determining an element's properties and its position in the periodic table. As the period number increases, the number of occupied energy levels in the atoms also increases. For instance, elements in the first period have their valence electrons in the first shell, while elements in the fourth period have their valence electrons in the fourth shell.

In the context of the exercise, 'X' belongs to the fourth period indicating that the highest energy level is the fourth one. This, along with its placement in the 15th group, reveals the specific distribution of electrons and justifies the previously discussed configuration: the '4s' orbital is completely filled, and the '4p' orbital is half-filled, adhering to the s²p³ pattern typical for group 15 elements in their ground states.