# How many orbitals of 4f are possible?

The 4f orbitals refer to the fourth electron shell in an atom and the f subshell within that shell. The f subshell can hold up to 14 electrons. Therefore, there are 14 possible 4f orbitals.

In quantum physics, atomic orbitals describe the shape and energy of an electron’s wave function in an atom. Each orbital can hold up to two electrons of opposite spin. The orbitals are categorized into principal energy levels or electron shells (1, 2, 3, etc.) and subshells within each level (s, p, d, f).

The 4f subshell lies within the fourth electron shell (n=4). It can hold up to 14 electrons, so there are 14 possible 4f orbitals. These orbitals are given the labels 4f1/2 to 4f13/2 and 4f5/2 to 4f14/2. The number indicates the principal energy level and subshell, while the subscript refers to the total angular momentum quantum number (j).

The 4f orbitals have some unique properties. They are relatively small and close to the nucleus compared to other orbitals. This means 4f electrons do not contribute much to bonding. The 4f subshell is often filled starting at lanthanum (atomic number 57) in the periodic table. Atoms that have partially filled 4f subshells display interesting magnetic and spectroscopic behaviors.

## Electron Shells and Subshells

Electrons surrounding an atom are arranged into shells and subshells based on their energy level and angular momentum. Each shell is designated by a principal quantum number n = 1, 2, 3, etc. The shells fill with electrons starting with n=1 (closest to the nucleus), then n=2, and so on.

Within each electron shell are subshells labeled s, p, d, and f. The s subshell can hold up to 2 electrons, p can hold up to 6, d up to 10, and f up to 14. The maximum electrons for a subshell is given by 2(2l + 1), where l is the angular momentum quantum number 0, 1, 2, and 3 for s, p, d, and f respectively.

The order the subshells fill is determined by the Aufbau principle. Lower energy levels fill first. Therefore, the 4f subshell fills after the 4s, 4p, and 4d orbitals. The diagram below summarizes the organization of electron shells and subshells.

Shell n l Subshell Maximum e
1 1 0 1s 2
2 2 0 2s 2
2 2 1 2p 6
3 3 0 3s 2
3 3 1 3p 6
4 4 0 4s 2
4 4 1 4p 6
4 4 2 4d 10
4 4 3 4f 14

Note that within each shell, the s, p, d, and f subshells fill in order of increasing l. The exceptions are when electrons half-fill or completely fill a subshell, causing extra stability.

## The 4f Orbitals

The 4f subshell lies within the fourth electron shell (n=4). Since the angular momentum quantum number l = 3 for f orbitals, the maximum electrons according to 2(2l + 1) is 14.

There are seven 4f orbitals labeled from 4f1/2 to 4f7/2. Each of these consists of a radial and angular part. The radial part describes the distance of the orbital from the nucleus, while the angular part depicts shapes like spheres, dumbbells, and clovers. The seven 4f orbitals are shown below:

4f Orbitals Shape
4f1/2 Spherical
4f3/2 Clover-shaped
4f5/2 Dumbbell-shaped
4f7/2 Complicated clover
4f9/2 Spherical + clover
4f11/2 Dumbbell + clover
4f13/2 Complicated dumbbell

Each orbital can hold up to two electrons of opposite spin. So there are 14 total 4f electrons possible, occupying the seven 4f orbitals.

## Properties of 4f Orbitals

The 4f orbitals have several notable properties:

• They are relatively small in size and buried deep within the atom, close to the nucleus.
• Due to their small size, 4f electrons do not participate much in bonding between atoms.
• The 4f subshell has low energy. It fills after the 5s, 4p, 4d subshells.
• The 4f orbitals display complex angular shapes and density distributions.
• Atoms with partially filled 4f subshells show interesting magnetic properties and spectra.

The fact that 4f orbitals lie close to the nucleus and do not strongly contribute to bonding leads to some unique chemistry for elements with 4f electrons. For example, the lanthanides all have electronic configurations involving the 4f subshell.

Another result is that atoms with partially occupied 4f subshells exhibit complex spectra and paramagnetism. This is because the unpaired 4f electrons can be aligned with magnetic fields and can absorb/emit photons of specific energies.

## Filling of 4f Orbitals

According to the Aufbau principle, atomic orbitals fill starting with the lowest energy level. Electrons occupy each subshell until it is full before moving to the next highest energy subshell.

The order of filling for the fourth shell is 4s, 4p, 4d, 4f. This means the 4f subshell does not start filling until after the 4s, 4p and 4d orbitals have been occupied with electrons.

The 4f subshell is first occupied at element lanthanum (Z = 57) in the periodic table. It fills through element lutetium (Z = 71). Some key elements are:

• Lanthanum (La): [Xe] 6s2 5d1 4f0 – first element with 4f subshell
• Cerium (Ce): [Xe] 6s2 4f15d1 – first electron added to 4f subshell
• Gadolinium (Gd): [Xe] 6s2 4f75d1 – half-filled 4f subshell (extra stable)
• Lutetium (Lu): [Xe] 6s2 4f145d1 – completely filled 4f subshell

The fourteen 4f electrons fill the seven 4f orbitals until all orbitals hold two electrons with opposite spins, as shown below:

Electron Configuration 4f Orbital Occupation
[Xe] 6s2 4f0 4f orbitals empty
[Xe] 6s2 4f1 1 electron in 4f5/2
[Xe] 6s2 4f2 2 electrons in 4f5/2
[Xe] 6s2 4f3 3 electrons in 4f5/2
[Xe] 6s2 4f4 2 electrons in 4f5/2
2 electrons in 4f7/2
[Xe] 6s2 4f5 1 electron in each of
4f5/2, 4f7/2
[Xe] 6s2 4f6 2 electrons in each of

4f5/2, 4f7/2
[Xe] 6s2 4f7 2 electrons in each 4f orbital
[Xe] 6s2 4f13 2 electrons in each 4f orbital
[Xe] 6s2 4f14 2 electrons in each 4f orbital

The order follows Hund’s rules, which state that orbitals fill singly first before pairing up electrons, and that spins align in parallel before pairing up.

## Importance of 4f Orbitals

The 4f orbitals are important for several reasons:

• They explain the electronic configuration of the lanthanides.
• The optical and magnetic properties of lanthanides depend on their 4f electrons.
• Partially filled 4f subshells produce complex spectra.
• They describe the binding energies of core electrons in X-ray spectroscopy.
• Chemical bonding in lanthanide complexes relies on shielding of 4f orbitals.

Overall, the 4f orbitals provide deep insights into the periodic trends and properties of the lanthanide series. Their unique size, energy and filling are critical for understanding much of lanthanide chemistry.

In spectroscopy, transitions involving 4f electrons provide fingerprint information on lanthanide element identification. The hard-to-remove 4f electrons also influence lanthanide complex formation.

Additionally, the 4f orbital energies serve as markers for calibrating X-ray spectroscopy techniques used to probe core electron binding energies. The number and peculiarity of 4f orbitals arise from quantum physics, but their applications span fields from electronics to biochemistry.

## Other f Orbitals

While this article focuses on 4f orbitals, there are also 5f and 6f orbitals at higher principal quantum numbers.

The 5f orbitals lie inside the fifth electron shell (n=5). They fill after the 5s, 5p, 5d subshells. There are 14 possible 5f orbitals that fill with 14 electrons.

The 5f subshell is first occupied at actinium (Ac) and fills through lawrencium (Lr). This includes the actinides, which display analogous chemistry to lanthanides based on their 5f electrons.

Finally, 6f orbitals reside in the sixth electron shell (n=6). 14 orbitals can hold up to 14 electrons. However, elements with occupied 6f subshells have not yet been discovered.

In summary, 4f, 5f, and 6f refer to 14 orbitals within the n=4, 5, and 6 principal electron shells. 4f and 5f play important roles in the lanthanides and actinides, while 6f remains hypothetical for superheavy elements.

## Conclusion

The 4f subshell contains 7 orbitals labeled 4f1/2 through 4f7/2, each holding up to 2 electrons. In total, there are 14 possible 4f orbitals that fill with 14 electrons.

These 4f orbitals display unique size, shape, energy and filling properties. Their inner position shields them from participation in bonding. Partially filled 4f subshells underlie the optical, magnetic and chemical properties of lanthanides.

Overall, the 4f orbitals are essential for characterizing lanthanide elements. Their filling across the periodic table also demonstrates the power of quantum physics to explain atomic properties from first principles.