Question

The configuration of the valence orbital of an element with atomic number 22 is (a) \(3 d^{5} 4 s^{1}\) (b) \(3 d^{2} 4 s^{2}\) (c) \(4 s^{\prime} 4 p^{1}\) (d) \(3 d^{2} 4 s^{1} 4 p^{1}\)

Short answer

(b) \(3 d^{2} 4 s^{2}\)

Step-by-step solution

Identify the Element

The element with atomic number 22 is Titanium (Ti).

Determine the Electron Configuration

Using the Aufbau principle, the electron configuration begins with the lowest energy orbitals. Titanium has 22 electrons to place in orbitals.

Assign Electrons to Orbitals

Fill the 1s, 2s, 2p, 3s, 3p orbitals first, as they are lower in energy than the 4s orbital. After these are filled, the remaining electrons go into the 4s orbital, and then into the 3d orbital. Titanium's electron configuration up to the 4s orbital is as follows: 1s2 2s2 2p6 3s2 3p6 4s2, with 18 electrons accounted for.

Complete the Electron Configuration for Titanium

Place the remaining 4 electrons into the next available orbital, which is 3d. This results in a 3d orbital with 2 electrons. Therefore, the electron configuration for titanium is 3d2 4s2.

Compare the Configurations

Compare the given options with the determined electron configuration of titanium (3d2 4s2).

Key concepts

Aufbau Principle

In atomic physics, the Aufbau principle is a fundamental concept that guides us through the complex world of electron configurations. It is also known as the 'building-up' principle and essentially describes how electrons fill the atomic orbitals of an atom. According to this principle, electrons are added one by one to the orbitals in order of their increasing energy. This means that electrons first occupy the lowest energy levels before moving on to higher ones.

The sequence in which the orbitals are filled is based on both their energy and their distance from the nucleus. The order typically goes like this: 1s, 2s, 2p, 3s, 3p, 4s, and then the 3d orbitals. There is, however, a slight catch — the 4s orbital is of a lower energy than the 3d, which is why it gets filled first. This can sometimes seem counterintuitive since one might expect the third shell to be filled before the fourth.

Using the Aufbau principle, along with Hund's Rule and the Pauli Exclusion Principle, can help us predict and explain the electron configuration of many elements—laying the groundwork for understanding the structure and properties of atoms.

Valence Orbitals

Valence orbitals are where the 'magic' of chemistry happens. These are the outermost orbitals of an atom and they hold the valence electrons, which are primarily responsible for the chemical bonding and properties of elements. In simple terms, these electrons are the ones that will interact when atoms come together to form chemical compounds.

Understanding which orbitals are valence orbitals is crucial to grasping reactivity patterns and periodic trends. For most main group elements (not transition metals), the highest energy 's' and 'p' orbitals can be thought of as the valence orbitals. For example, for elements in Groups 1 and 2, the 's' orbitals are the valence orbitals, while for Groups 13 to 18, the 'p' orbitals also become involved as valence orbitals.

For transition metals, the 'd' orbitals may also play a role in valence, but it can be more complex due to the varying energy levels of these orbitals in relation to the 's' orbitals. This interplay determine an element's ability to form different types of ions and bonds, which in turn influences the substance’s physical and chemical characteristics.

Titanium Electron Configuration

The electron configuration for titanium, an element marked with atomic number 22, serves as a pragmatic example of applying theoretical concepts like the Aufbau principle. With its electrons distributed across several orbitals, Titanium's configuration can be complex for beginners to understand.

To map out titanium's electron configuration, start by filling in the lower energy orbitals; this will account for 18 of its 22 electrons: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s². The remaining four electrons then go into the next available orbital, 3d, to give a configuration of 3d² 4s².

This distribution distinguishes titanium in the realm of transition metals, where we see the participation of 'd' orbitals in their valence shell. In its electron configuration, the valence orbitals for titanium include the 4s and 3d orbitals, with the latter being partially filled. Understanding these nuances enables us to predict and explain the chemical behavior and bonding patterns of titanium, solidifying our grasp on how such transition metals engage in the fascinating dance of chemistry.