Quantum numbers and Nomenclature

By quantum numbers the atomic orbitals of hydrogen are entitled. Three integers are needed for a complete specification.

1. The principal quantum number n can obtain the values 1, 2, 3... It concludes how far from the nucleus the electron is most expected to be found.
2. The angular momentum (or azimuthal) quantum number l can take values from zero up to a maximum of n -1. It concludes the total angular momentum of the electron about the nucleus.
3. The magnetic quantum number m can take positive and negative values from -l to +l. It concludes the direction of rotation of the electron. Sometimes m is written ml to differentiate it from the spin quantum number ms.

Table 1 depicts how these rules determine the allowed values of l and m for orbitals with n=1-4. The values decide the structure of the periodic table of elements.

s orbitals are atomic orbitals with l=0, those with l=1, 2, 3 are called p, d, f orbitals, correspondingly. It is general to specify the value of n as well, so that, for instance, 1s denotes the orbital with the n=1, l=0, and 3d the orbitals with n=3, l=2. These labels are also displayed in Table 1. For any type of orbital 2l+1 values of m are possible; so there are always three p orbitals for any n, five d orbitals and the seven f orbitals.