Difference Between 4f and 5f Orbitals

Main Difference – 4f vs 5f Orbitals

Atoms are composed of a nucleus that is made out of protons and neutrons, which are surrounded by electrons. These electrons are in continuous movement around the nucleus. Therefore, we cannot give a specific location for an electron in an atom. Instead of locating the exact position of an electron, scientists have introduced the concept of “probability.” In other words, the most probable pathway that an electron is most likely to be moving is determined. This pathway is called an orbital. There are different subsets of orbitals such as s orbitals, p orbitals, d orbitals and f orbitals. The number of orbitals in each subset is determined by the magnetic quantum number. For f orbitals, there are 7 possible magnetic quantum numbers, so there are seven f orbitals. 4 f and 5 f orbitals are the first set and second set in f orbitals. The main difference between 4f and 5f orbitals is that 4f orbitals have a number of planes and conical nodes, but no radial nodes whereas 5f have a number of planes and conical nodes, and each orbital have one radial node.

Key Areas Covered

1. What are 4f Orbitals
      – Definition, Seven Orbitals and their Relative Similarities
2. What are 5f Orbitals
     – Definition, Seven Orbitals and their Relative Similarities
3. What are the Similarities Between 4f and 5f Orbitals
     – Outline of Common Features
4. What is the Difference Between 4f and 5f Orbitals
     – Comparison of Key Differences

Key Terms: Atom, Electron, Lobes, Magnetic Quantum Number, Nodes, Nucleus, Orbital, Probability, Subshell

What are 4f Orbitals

4f orbitals are the seven f orbitals of the 4^th electron shell (energy level). 4f orbitals are the first subset of f orbitals. This means 1^st, 2^nd and 3^rd electron shells have no f orbitals. This is shown below in the table of s, p, d and f orbitals.

A set of 4f orbitals has four different shapes, each having a number of planar and conical nodes. But 4f orbitals possess no radial nodes. The seven 4f orbitals are named according to the plane of the orbital. Given below are the seven 4f orbitals.

1. 4f_xyz
2. 4f_z3
3. 4f_z(x2-y2)
4. 4f_y(3×2-y2)
5. 4f_x(x2-3y2)
6. 4f_xz2
7. 4f_yz2

Among these orbitals, both 4f_xyz and 4f_z(x2-y2) orbitals have eight lobes. They are related to each other by a 45^o rotation around the z axis. This means, they are similar in other factors but are different in the plane.

Among the rest of the seven orbitals, 4f_y(3×2-y2) and 4f_x(x2-3y2) orbitals are related to each other by rotating 90^o around the z axis. Each orbital has six lobes separated by three nodal planes having an angle of 60^o among them. The 4f_xz2 and 4f_yz2 orbitals seem similar to 4f_y(3×2-y2) and 4f_x(x2-3y2) orbitals but are different because the three nodal planes of six planes are not separated by 60^o angles. These 4f_xz2 and 4f_yz2 orbitals have two of the six lobes “bean-shaped” in z axis. On the other hand, 4f_xz2 orbital is a similar orbital to that of 4f_xz2 and 4f_yz2 orbitals, but the “bean-shaped” lobes are in the x axis. In 4f_yz2 orbital, the “bean-shaped” orbital is in the y axis.

What are 5f Orbitals

5f orbitals are the seven f orbitals of the 5^th electron shell (energy level). 5f orbitals are the second subset of f orbitals. These orbitals are named based on the planes of orbitals. The seven orbitals are as follows.

1. 5f_xyz
2. 5f_z3
3. 5f_z(x2-y2)
4. 5f_y(3×2-y2)
5. 5f_x(x2-3y2)
6. 5f_xz2
7. 5f_yz2

Figure 1: Seven Different f Orbitals

A set of 5f orbitals has four different shapes, each having a number of planar and conical nodes. Each 5f orbital also possesses one radial node as well.

Among these orbitals, both 5f_xyz and 5f_z(x2-y2) orbitals have eight lobes. They are related to each other by a 45^o rotation around the z axis. This means, they are similar in other factors but are different in the plane to which they are directed.

Among the rest of the seven orbitals, 5f_y(3×2-y2) and 5f_x(x2-3y2) orbitals are related to each other by rotating 90^o around the z axis. Each orbital has six lobes separated by three nodal planes having an angle of 60^o among them. The 5f_xz2 and 5f_yz2 orbitals seem similar to that of 5f_y(3×2-y2) and 5f_x(x2-3y2) orbitals, but they are different because the three nodal planes of six planes are not separated by 60^o angles. These 5f_xz2 and 5f_yz2 orbitals also have two of the six lobes “bean-shaped”. On the other hand, the 5f_xz2 orbital is a similar orbital to that of 5f_xz2 and 5f_yz2 orbitals, but the “bean-shaped” lobes are on the x axis. In 5f_yz2 orbital, the “bean-shaped” orbital is in the y axis.

Similarities Between 4f and 5f Orbitals

• Both are f orbital forms.
• Both have similar shapes on the same planes.
• Both have complicated structures of orbitals.

Difference Between 4f and 5f Orbitals

Definition

4f Orbitals: 4f orbitals are the seven f orbitals of the 4th electron shell (energy level).

5f Orbitals: 5f orbitals are the seven f orbitals of the 5th electron shell (energy level).

Subset

4f Orbitals: 4f orbitals are the first subset of f orbitals.

5f Orbitals: 5f orbitals are the second subset of f orbitals.

Radial Nodes

4f Orbitals: 4f orbitals have a number of planes and conical nodes, but no radial nodes.

5f Orbitals: 5f orbitals have a number of planes and conical nodes, and each 5f orbital possesses a radial node as well.

Size

4f Orbitals: 4f orbitals are smaller than 5f orbitals.

5f Orbitals: 5f orbitals are larger than 4f orbitals.

Conclusion

Atoms are composed of different forms of orbitals in their electron shells: s orbitals, p orbitals, d orbitals and f orbitals. The addition of an f orbital starts from the 4^th electron shell (energy level). The main difference between 4f and 5f orbitals is that 4f orbitals have a number of planes and conical nodes, but no radial nodes whereas 5f have a number of planes and conical nodes, and each orbital have one radial node as well.

Reference:

1. Mark J Winter. “Atomic orbitals: 4f (General set).” The Orbitron: a gallery of atomic orbitals and molecular orbitals, 12 July 2015, Available here.
2. Mark J Winter. “Atomic orbitals: 5f (General set).” The Orbitron: a gallery of atomic orbitals and molecular orbitals, 12 July 2015, Available here.

Image Courtesy:

1. “F orbitals m” By Geek3 – Own work (CC BY-SA 3.0) via Commons Wikimedia