n is known as the principal quantum number.
n is known as the what quantum number?
principal
azimuthal quantum number





























the azimuthal quantum number is a quantum number for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital. the azimuthal quantum number is the second of a set of quantum numbers which describe the unique quantum state of an electron (the others being the principal quantum number [following spectroscopic notation], the magnetic quantum number, and the spin quantum number). it is also known as the orbital angular momentum quantum number, orbital quantum number or second quantum number, and is symbolized as ℓ (pronounced "ell").





























section::::derivation.
azimuthal quantum number
the associated quantum number is the main total angular momentum quantum number "j". it can take the following range of values, jumping only in integer steps:





























where "ℓ" is the azimuthal quantum number (parameterizing the orbital angular momentum) and "s" is the spin quantum number (parameterizing the spin).





























the relation between the total angular momentum vector j and the total angular momentum quantum number "j" is given by the usual relation (see angular momentum quantum number)





























the vector's "z"-projection is given by
total angular momentum quantum number