### Principal Energy Level Definition

The principal energy level is denoted by the principal quantum number n. The first element in a period of the Periodic Table introduces a new principal energy level.

### Energy Levels and the Atomic Model

The concept of energy levels is a part of the atomic model that is based on a mathematical analysis of atomic spectra. Each electron in an atom has an energy signature that is determined by its relationship with other negatively charged electrons in the atom and the positively charged atomic nucleus.

An electron can change energy levels, but only by steps or quanta, not continuous increments. The energy of an energy level increases the further out from the nucleus is is. The lower the number of a principal energy level, the closer together the electrons are to each other and to the nucleus. It's harder to remove an electron from a lower number energy level than from a higher number one.

### Rules for the Principal Energy Level

A principal energy level may contain up to 2n^{2} electrons, with n being the number of each level. The first energy level can contain 2(1)^{2} or 2 electrons; the second can contain up to 2(2)^{2} or 8 electrons; the third can contain up to 2(3)^{2} or 18 electrons, etc.

The first principal energy level has one sublevel that contains one orbital, called the s orbital. The s orbital can contain a maximum of 2 electrons.

The next principal energy level contains one s orbital and three p orbitals.

The set of three p orbitals can hold up to 6 electrons. Thus, the second principal energy level can hold up to 8 electrons, 2 in the s orbital and 6 in the p orbital.

The third principal energy level has one s orbital, three p orbitals, and five d orbitals, which can each hold up to 10 electrons. This allows for a maximum of 18 electrons.

The fourth and higher levels have an f sublevel in addition to the s, p, and d orbitals. The f sublevel contains seven f orbitals, which can each hold up to 14 electrons. The total number of electrons in the fourth principal energy level is 32.

### Writing Electrons in the Principal Energy Level

The notation used to indicate the type of energy level and number of electrons has a coefficient for the number of the principal energy level, the letter for the sublevel, and a superscript for the number of electrons in the sublevel. For example:

4p^{3}

indicates the 4th principal energy level, the p sublevel, and that it contains 3 electrons

Writing the number of electrons in all energy levels and sublevels produces the electron configuration of an atom.