What is an f orbital?

An f orbital is an orbital for which the secondary quantum number l = 3.

There are seven f orbitals, with #m_l# = -3, -2, -1, 0, 1, 2, and 3.

The f orbitals aren't occupied in the ground state until element 58 (cerium). The electron configuration of cerium is [Xe] #6s^2 4f 5d#.

Even for elements beyond cerium, the f orbitals are deeply buried beneath the valence shell. They rarely play an important role in chemical change or bonding.

But the orbital shapes are useful in interpreting spectra. So here they are.

The yellow and blue colours show lobes with opposite amplitudes.

The #4f_(y^3 - 3x^2y)# orbital corresponds to #n# = 4, #l# = 3, and #m_l# = -3.

The #4f_(xyz)# orbital corresponds to #n# = 4, #l# = 3, and #m_l# = -2.

The #4f_(5yz^2 – yr^2)# orbital corresponds to #n# = 4, #l# = 3, and #m_l# = -1.

The #4f_(z^3 - 3zr^2)# orbital corresponds to #n# = 4, #l# = 3, and #m_l# = 0.

The #4f_(5xz^2 – xr^2)# orbital corresponds to #n# = 4, #l# = 3, and #m_l# = + 1.

The #4f_(zx^2 – zy^2)# orbital corresponds to #n# = 4, #l# = 3, and #m_l# = +2.

The #4f_(x^3 - 3xy^2)# orbital corresponds to n = 4, l = 3, and #m_l# = +3.