Quantum numbers refers to values that exactly describe the energy of electrons within an atom or a molecule. Electrons are known to possess a set of four quantum numbers used in describing the energy state of such electron. These quantum numbers are solutions to the Schrödinger wave equation for the hydrogen atom.
In describing any electron within the atom, the relevant set of four quantum numbers are: principal quantum number (n), orbital, azimuthal, subsidiary or angular momentum quantum number (l), magnetic quantum number (ml), and spin quantum number (ms).
In the arrangement above, the electrons are arranged in order of increasing energy. Each arrangement of quantum numbers corresponds to a particular energy state of the electron.
Ionic bonding is the attraction between positively- and negatively-charged ions. These oppositely charged ions attract each other to form ionic networks (or lattices). Electrostatics explains why this happens: opposite charges attract and like charges repel.