For any atom, there are 7 5*f* orbitals. The *f*-orbitals room unusual in that there room two sets of orbitals in common use. The first set is well-known as the *general set, this page*. The second set is the *cubic set, this page* and also these could be proper to use if the atom is in a cubic environment, because that instance. 3 of the orbitals are typical to both sets. These space are the 5*f**xyz*, 5*f**z*3, and 5*f**z*(*x*2-*y*2) orbitals.

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The higher *f*-orbitals (6*f* and 7*f*) room more complex since they have more spherical nodes when the reduced orbitals (5*f*) have actually none.

## 5*f* atom orbitals general set

**The shape of the 7 5 f orbitals (general set).** from left to right: (top row) 5

*f*

*z*3, (next to height row) 5

*f*

*y*

*z*2, 5

*f*

*x*

*z*2, (next to bottom row) 5

*f*

*xyz*, and also 5

*f*

*z*(

*x*2-

*y*2), (bottom row) 5

*f*

*y*(3

*x*2-

*y*2), 5

*f*

*x*(

*x*2-3

*y*2). Because that each, the green zones space where the wave features have hopeful values and also the white area denote an adverse values.

The 7 5*f* orbitals. Use the previous and also next icons to see other views

The seven 5*f* orbitals consisting of orbital nodes. Use the previous and next icons to see various other views

Nodes of the 7 5*f* orbitals. Use the previous and next symbols to see various other views

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In the general collection of 5*f* orbitals, there room four unique shapes, every of which own a variety of planar and conical nodes. The 5*f* orbitals carry out not possess any kind of radial nodes.

The 5*f**z*3 orbital (top row in the photo above) has a planar node in the *xy* airplane and 2 conical nodes through their exes follow me the *z*-axis.

The 5*f**y**z*2 and also 5*f**x**z*2 orbitals (next to peak row in the photo above) are related to each other by a 90° rotation around the *z*-axis. At very first sight, castle are comparable in form to the 5*f**y*(3*x*2-*y*2) and also 5*f**x*(*x*2-3*y*2) orbitals yet they space not. While this orbitals contain six lobes, the nodal planes room not at 60° to every other and two of the six lobes space "bean-shaped".

The 5*f**xyz* and also 5*f**z*(*x*2-*y*2) (next to bottom row in the photo above) each have actually eight lobes and also are related to each other by a 45° rotation about the *z*-axis. Every orbital has actually three nodal planes, which for the 5*f**xyz* space the *xy*, *xz*, and also *yz* planes.

The 5*f**y*(3*x*2-*y*2) and 5*f**x*(*x*2-3*y*2) orbitals (bottom heat in the image above) are pertained to each various other by a 90° rotation around the *z*-axis. Each orbital has six lobes be separated by 3 nodal plane lying in ~ 60° to every other.

## 5*f* atomic orbitals cubic set

**The shape of the seven 5 f orbitals (cubic set).** from left come right: (top row) 5

*f*

*y*3, 5

*f*

*z*3, 5

*f*

*x*3, (middle row) 5

*f*

*y*(

*z*2-

*x*2), 5

*f*

*z*(

*x*2-

*y*2), and also 5

*f*

*x*(

*z*2-

*y*2)(bottom row) 5

*f*

*xyz*. Because that each, the environment-friendly zones are where the wave features have confident values and also the white area denote negative values.

In the cubic collection of 5*f* orbitals, there space two unique shapes, every of which own a variety of planar and conical nodes. The 5*f* orbitals each possess one radial node.

The 5*f**xyz*, 5*f**x*(*z*2-*y*2), 5*f**y*(*z*2-*x*2), and also 5*f**z*(*x*2-*y*2) (bottom 2 rows in the image above) each have actually eight lobes. The 5*f**x*(*z*2-*y*2), 5*f**y*(*z*2-*x*2), and 5*f**z*(*x*2-*y*2) orbitals are pertained to each various other by 45° rotations around the *x*, *y*, and *z*-axis respectively. Each orbital has three nodal planes, which for the 5*f**xyz* room the *xy*, *xz*, and also *yz* planes.

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The 5*f**x*3, 5*f**y*3, and 5*f**z*3 orbitals (top row in the picture above) has a planar node in the *xy* plane and two conical nodes orientated along the *z*-axis. The other two orbitals are related through 90° rotations.