Question

Describe the characteristics of an \(s\) orbital, a \(p\) orbital, and a \(d\) orbital. Which of the following orbitals do not exist: \(1 p, 2 s, 2 d, 3 p, 3 d, 3 f, 4 g ?\)

Short answer

S orbitals are spherical and present at all energy levels. P orbitals are dumbbell-shaped, located along the axes, and start from the second energy level. D orbitals have a clover shape, five possible orientations, and start from the third energy level. Of the specified orbitals, 1p, 2d, 3f, and 4g do not exist.

Step-by-step solution

Describe s orbital

An s orbital is spherical and can hold up to two electrons. S orbitals exist at all energy levels (shells), starting from 1.

Describe p orbital

A p orbital is dumbbell-shaped and can hold up to six electrons. There are three p orbitals at each energy level, each orientated along one of the three Cartesian axes. P orbitals start from the second energy level.

Describe d orbital

A d orbital is clover-shaped and can hold up to ten electrons. There are five d orbitals at each energy level, each with different orientations in space. D orbitals start from the third energy level.

Evaluate specified orbitals

1p - This orbital will not exist because p orbitals start from the second energy level. 2s - This orbital will exist because s orbitals are present at all energy levels. 2d - This orbital will not exist because d orbitals start from the third energy level. 3p - This orbital will exist because p orbitals start from the second energy level. 3d - This orbital will exist because d orbitals start from the third energy level. 3f - This orbital does not exist because f orbitals start from the fourth energy level. 4g - This orbital does not exist because g orbitals start from the fifth energy level.

Key concepts

S Orbital Characteristics

The s orbitals represent one of the simplest types of atomic orbitals that play a fundamental role in the structure of atoms. They possess a spherical shape, symmetrical about the nucleus in all directions.

Furthermore, the most distinctive characteristic of these orbitals is their ability to house up to two electrons by the Pauli Exclusion Principle. Each s orbital can be found at every energy level, starting from the very first shell, denoted as 1s, then 2s, and so forth.

These s orbitals are the first to be filled with electrons as we move across the periods in the periodic table, thus making them crucial in understanding atomic and molecular configurations. An understanding of s orbitals is also essential for grasping concepts in chemical bonding, as s electrons often participate in forming chemical bonds.

P Orbital Shape

In contrast to the spherically uniform s orbitals, p orbitals have a unique dumbbell or figure-eight shape. This configuration is due to the presence of two lobes located on opposite sides of the atomic nucleus, with a node, a region of zero electron probability, at the nucleus itself.

Within a particular energy level, electrons can exist in three separate p orbitals, each oriented along a Cartesian axis: the px orbital along the x-axis, the py orbital along the y-axis, and the pz orbital along the z-axis. Commencing from the second energy level (2p), and continuing on to higher levels, these orientations allow p orbitals to accommodate up to six electrons – two in each orientation.

The shape of p orbitals is significantly important when determining the geometry of molecules and the directions of electron clouds during bond formation.

D Orbital Electron Capacity

Moving beyond the s and p orbitals, we encounter the more complex d orbitals, which start from the third principal energy level (3d). The d orbitals exhibit a clover-like shape, which can be more complex than the simple shapes of s and p orbitals.

The d subshell contains five orbitals: dxz, dyz, dxy, dx2-y2, and dz2. Each of these orbitals has its own unique geometric arrangement in three-dimensional space that allows them to house a maximum of ten electrons, with two electrons per orbital.

Understanding the electron capacity of d orbitals is essential for predicting the behavior of transition metals, which commonly have partially filled d subshells. These elements often exhibit multiple oxidation states and complex chemistry due to the variable occupancy of their d orbitals.