<P> Each shell can contain only a fixed number of electrons: 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) electrons . Since electrons are electrically attracted to the nucleus, an atom's electrons will generally occupy outer shells only if the more inner shells have already been completely filled by other electrons . However, this is not a strict requirement: atoms may have two or even three incomplete outer shells . (See Madelung rule for more details .) For an explanation of why electrons exist in these shells see electron configuration . </P> <P> If the potential energy is set to zero at infinite distance from the atomic nucleus or molecule, the usual convention, then bound electron states have negative potential energy . </P> <P> If an atom, ion, or molecule is at the lowest possible energy level, it and its electrons are said to be in the ground state . If it is at a higher energy level, it is said to be excited, or any electrons that have higher energy than the ground state are excited . If more than one quantum mechanical state is at the same energy, the energy levels are "degenerate". They are then called degenerate energy levels . </P> <P> Quantized energy levels result from the relation between a particle's energy and its wavelength . For a confined particle such as an electron in an atom, the wave function has the form of standing waves . Only stationary states with energies corresponding to integral numbers of wavelengths can exist; for other states the waves interfere destructively, resulting in zero probability density . Elementary examples that show mathematically how energy levels come about are the particle in a box and the quantum harmonic oscillator . </P>

The lowest possible energy level for an electron is known as