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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.