For any atom, there are seven 4*f* orbitals. The *f*-orbitals are unusual in the there space two set of orbitals in typical use. The very first set is recognized as the *general set, this page*. The second set is the *cubic set, this page* and these could be appropriate to use if the atom is in a cubic environment, for instance. 3 of the orbitals are usual to both sets. These space are the 4*f**xyz*, 4*f**z*3, and 4*f**z*(*x*2-*y*2) orbitals.

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The greater *f*-orbitals (5*f*, 6*f*, and also 7*f*) room more facility since they have one or more spherical nodes.

## 4*f* atom orbitals general set

**The shape of the 7 4 f orbitals (general set).** indigenous left come right: (top row) 4

*f*

*z*3, (next to height row) 4

*f*

*y*

*z*2, 4

*f*

*x*

*z*2, (next come bottom row) 4

*f*

*xyz*, and 4

*f*

*z*(

*x*2-

*y*2), (bottom row) 4

*f*

*y*(3

*x*2-

*y*2), 4

*f*

*x*(

*x*2-3

*y*2). Because that each, the eco-friendly zones space where the wave features have hopeful values and also the white zones denote negative values.

The seven 4*f* orbitals. Use the previous and next icons to see various other views

The 7 4*f* orbitals consisting of orbital nodes. Use the previous and also next symbols to see other views

Nodes of the 7 4*f* orbitals. Usage the previous and also next symbols to see other views

ahead next

In the general set of 4*f* orbitals, there room four unique shapes, each of which possess a variety of planar and also conical nodes. The 4*f* orbitals execute not possess any kind of radial nodes.

The 4*f**z*3 orbital (top heat in the picture above) has a planar node in the *xy* plane and 2 conical nodes with their exes along the *z*-axis.

The 4*f**y**z*2 and also 4*f**x**z*2 orbitals (next to top row in the photo above) are pertained to each other by a 90° rotation around the *z*-axis. At first sight, lock are comparable in form to the 4*f**y*(3*x*2-*y*2) and also 4*f**x*(*x*2-3*y*2) orbitals but they are not. While these orbitals contain six lobes, the nodal planes are not at 60° to each other and also two that the six lobes space "bean-shaped".

The 4*f**xyz* and also 4*f**z*(*x*2-*y*2) (next to bottom heat in the image above) each have eight lobes and are related to each various other by a 45° rotation about the *z*-axis. Every orbital has three nodal planes, which because that the 4*f**xyz* room the *xy*, *xz*, and also *yz* planes.

The 4*f**y*(3*x*2-*y*2) and also 4*f**x*(*x*2-3*y*2) orbitals (bottom heat in the image above) are regarded each other by a 90° rotation about the *z*-axis. Each orbital has actually six lobes be separated by 3 nodal airplane lying in ~ 60° to each other.

## 4*f* atomic orbitals cubic set

**The form of the seven 4 f orbitals (cubic set).** indigenous left come right: (top row) 4

*f*

*y*3, 4

*f*

*z*3, 4

*f*

*x*3, (middle row) 4

*f*

*y*(

*z*2-

*x*2), 4

*f*

*z*(

*x*2-

*y*2), and also 4

*f*

*x*(

*z*2-

*y*2)(bottom row) 4

*f*

*xyz*. For each, the eco-friendly zones are where the wave features have positive values and also the white zones denote negative values.

In the cubic set of 4*f* orbitals, there space two unique shapes, each of which possess a variety of planar and conical nodes. None of the 4*f* orbitals own radial nodes.

The 4*f**xyz*, 4*f**x*(*z*2-*y*2), 4*f**y*(*z*2-*x*2), and 4*f**z*(*x*2-*y*2) (bottom 2 rows in the image above) each have eight lobes. The 4*f**x*(*z*2-*y*2), 4*f**y*(*z*2-*x*2), and also 4*f**z*(*x*2-*y*2) orbitals are pertained to each other by 45° rotations about the *x*, *y*, and *z*-axis respectively. Each orbital has three nodal planes, which for the 4*f**xyz* are the *xy*, *xz*, and also *yz* planes.

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The 4*f**x*3, 4*f**y*3, and also 4*f**z*3 orbitals (top heat in the image above) has actually a planar node in the *xy* aircraft and 2 conical nodes orientated along the *z*-axis. The various other two orbitals are connected through 90° rotations.