## Structure 1.3.4—A more detailed model of the atom describes the division of the main energy level into s, p, d and f sublevels of successively higher energies.

Structure 1.3.4—A more detailed model of the atom describes the division of the main energy level
into s, p, d and f sublevels of successively higher energies.

What You’ll Learn:

• Recognize the shape and orientation of an s atomic orbital and the three p atomic orbitals.

Keywords

Structure 3.1—How does the trend in IE values across a period and down a group explain the trends in properties of metals and non-metals?

A more detailed model of the atom, based on quantum mechanics, describes the division of the main energy levels into sublevels, also known as subshells. These subshells are denoted by the letters s, p, d, and f, and they represent different types of atomic orbitals with distinct shapes and energies. Each type of atomic orbital corresponds to a specific electron distribution around the nucleus, and the number of orbitals in each subshell increases as their energies rise.

1. s atomic orbital: The s subshell has only one orbital, regardless of the main energy level (n). The shape of the s orbital is spherical, with the electron cloud distributed symmetrically around the nucleus. The size of the sphere increases as the main energy level increases (e.g., 2s is larger than 1s). Since there is only one s orbital in each energy level, it has no specific orientation in space.
2. p atomic orbitals: The p subshell has three orbitals, denoted as px, py, and pz. These orbitals are present from the second main energy level (n = 2) and above. The shape of the p orbitals is dumbbell-like or figure-eight, with two lobes on opposite sides of the nucleus. Each of the three p orbitals has a different orientation in space, aligning along one of the three Cartesian axes. The px orbital aligns along the x-axis, the py orbital along the y-axis, and the pz orbital along the z-axis. The electron cloud is distributed around the nucleus along these axes, with a nodal plane passing through the nucleus where the probability of finding an electron is zero.

In summary, the division of the main energy levels into sublevels provides a more detailed model of the atom. The s atomic orbital has a spherical shape and no specific orientation, while the three p atomic orbitals have a dumbbell-like shape and align along the x, y, and z axes.

The d orbitals are found in the d subshell, which is present from the third main energy level (n = 3) and above. There are five d orbitals in total, each with a distinct shape and orientation. The shapes of the d orbitals are more complex than those of the s and p orbitals, and they can be described as follows:

1. dxy, dxz, and dyz orbitals: These three orbitals are similar in shape and are often referred to as the “double-lobe” d orbitals. Each of these orbitals consists of four lobes arranged in a cloverleaf pattern, with a nodal plane between each pair of lobes. The lobes lie in the plane specified by their respective subscripts. For example, the dxy orbital has lobes in the xy-plane, the dxz orbital has lobes in the xz-plane, and the dyz orbital has lobes in the yz-plane.
2. dx2-y2 orbital: The dx2-y2 orbital consists of four lobes, arranged in a square pattern, with the lobes pointing along the positive and negative x and y axes. There is a nodal plane between each pair of lobes, and the nucleus lies at the center of the square.
3. dz2 orbital: The dz2 orbital has a unique shape, often referred to as a “dumbbell with a doughnut” or “prolate spheroid with a torus.” It consists of two lobes aligned along the z-axis, with a torus (ring-shaped) region encircling the nucleus in the xy-plane. There is a nodal plane in the xy-plane that separates the two lobes along the z-axis.

In summary, the d orbitals have more complex shapes compared to the s and p orbitals. They include the double-lobe dxy, dxz, and dyz orbitals, the square-shaped dx2-y2 orbital, and the uniquely shaped dz2 orbital. Each of these orbitals has distinct orientations and nodal planes, which contribute to the overall electronic structure of atoms.

Questions

1. How is the main energy level divided in the quantum mechanics model of the atom?
2. What are subshells and what are they denoted by?
3. How do the shapes of the s and p orbitals differ?
4. How many orbitals does the s subshell have?
5. What is the orientation of the three p orbitals in space?
6. What is the nodal plane and where is it located in the p orbitals?
7. At what main energy level do the d orbitals appear?
8. How many d orbitals are there in total and what are their shapes?
9. How does the dx2-y2 orbital differ in shape from the double-lobe d orbitals?
10. What is unique about the shape of the dz2 orbital and where is its nodal plane located?