Is gravity the force that binds an electron to the nucleus?

Not actually. It is the Coulomb force, also called electrostatic force or Coulomb interaction, attraction or repulsion of particles or objects because of their electric charge. Two variables affect the strength of this attraction: The distance between the charged particles – The force of attraction has an indirect relationship with the square of the distance. This means that as the distance between the nucleus and the electron increases the electrostatic attraction decreases.

Strong chemical bonds are the intramolecular forces that hold atoms together in molecules. A strong chemical bond is formed from the transfer or sharing of electrons between atomic centers and relies on the electrostatic attraction between the protons in nuclei and the electrons in the orbitals.

The electrons in the outermost electron shell are responsible for forming chemical bonds. These electrons are also known as valence electrons.Chemical bonds are formed when the outermost electron shells are not completely filled and atom needs more (or less) electrons to completely fill the outermost shell.

In an atom, the electrons spin around the center, also called the nucleus. Electrons are found in shells or orbital those surround the nucleus of an atom. Protons and neutrons are found in the nucleus. They group together in the center of the atom.

Each shell can contain only a fixed number of electrons. The electron shells are labeled K, L, M, N, O, P, and Q; or 1, 2, 3, 4, 5, 6, and 7; going from innermost shell outwards. Electrons in outer shells have higher average energy and travel farther from the nucleus than those in inner shells.

The first shell can hold up to two electrons, the second shell can hold up to eight (2 + 6) electrons, the third shell can hold up to 18 (2 + 6 + 10) and so on. The general formula is that the nth shell can in principle hold up to 2(n^2) electrons.

The maximum number of electrons that can occupy the outermost energy level or valence shell of a Representative Element is eight (the exception is helium, which also exhibits a filled valence shell, but it requires only 2 electrons).