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# 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 of cerium is [Xe] 6s^2 4f 5d.

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

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.