Question

\(2 s\) and \(2 \hat{p}\)-atomic erbitals combine to give how many molecular ortitals? (a) \(\underline{\underline{2}}\) (b) 4 (c) 8 (d) 6

Short answer

The combination of 2s and 2p atomic orbitals results in 4 molecular orbitals. (b) 4

Step-by-step solution

Understanding the Concept of Orbital Combination

When atomic orbitals combine, each combination forms two molecular orbitals, one bonding molecular orbital and one antibonding molecular orbital.

Calculating the Total Number of Molecular Orbitals Formed

Since we have two types of atomic orbitals, s and p, and each atomic orbital overlaps to form two molecular orbitals, we simply multiply the number of atomic orbital types by two. That is, 2 (types of orbitals: s and p) times 2 (molecular orbitals formed per atomic orbital) equals 4 molecular orbitals in total.

Determining the Correct Answer

Based on the calculation provided in the previous step, we conclude that when 2s and 2p atomic orbitals combine, they form a total of 4 molecular orbitals.

Key concepts

Atomic Orbitals

To begin with an understanding of molecular orbitals, one must first grasp the concept of atomic orbitals. Atomic orbitals are regions around an atom’s nucleus where the probability of finding an electron is high. Each atomic orbital is characterized by a unique set of quantum numbers and can be visualized as a cloud-like region where electrons reside.

Atomic orbitals come in different shapes such as spherically shaped s orbitals and dumbbell-shaped p orbitals. The number of atomic orbitals increases with the atom’s energy level; for instance, the first energy level has only one 1s orbital, while the second energy level has one 2s orbital and three 2p orbitals, corresponding to the p_x, p_y, and p_z orientations. Understanding the configuration of these orbitals is crucial to predict how they will combine to form molecular orbitals.

Orbital Combination

When atoms come together to form molecules, their atomic orbitals overlap to create molecular orbitals. This is known as orbital combination. It's essential to note that the process adheres to specific rules, primarily based on the principles of quantum mechanics and symmetry considerations.

During the orbital combination, the wave functions of atomic orbitals either add together, resulting in constructive interference, or subtract from one another, causing destructive interference. This ultimately leads to two possibilities - the formation of bonding molecular orbitals and antibonding molecular orbitals.

In our exercise improvement advice, it’s vital to highlight that the overlapping orbitals must be of similar energy and appropriate symmetry to result in effective bonding. Concepts like s-p mixing and the impact of the symmetry of atomic orbitals on molecular formation can be more complex but are important for in-depth chemisty courses.

Bonding and Antibonding Orbitals

The concept of bonding and antibonding orbitals emerges directly from the combination of atomic orbitals. Bonding molecular orbitals are lower in energy compared to the original atomic orbitals because the overlapping wave functions add constructively. These orbitals are favorable for the stability of the molecule, as they increase electron density between the nuclei.

Conversely, antibonding molecular orbitals are the result of destructive interference where wave functions subtract. These are higher in energy and less stable, often remaining unoccupied until lower energy bonding orbitals are filled. It is important for students to understand that, typically, the formation of a bond involves the occupation of a bonding molecular orbital, and the presence of electrons in an antibonding orbital can actually weaken or nullify a bond.

Finally, the question from our exercise illustrates a fundamental rule - for every two atomic orbitals that combine, one bonding and one antibonding molecular orbital will form, helping us determine the correct answer to the provided example.