Describe how electrons are grouped within atoms. Determine the energy levels of electrons for the first 20 elements.

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Although we have discussed the general arrangement of subatomic particles in atoms, we have said little about how electrons occupy the space about the nucleus. Do they move around the nucleus at random, or do they exist in some ordered arrangement? Previously we discussed the concept of electron shells and subshells.It is the arrangement of electrons into shells and subshells that most concerns us here, so we will focus on that.

General Rules of Electron Configuration

There are a set of general rules that are used to figure out the electron configuration of an atomic species: Aufbau Principle, Hund"s Rule and the Pauli-Exclusion Principle. Before continuing, it"s important to understand that each orbital can be occupied bytwoelectrons.

Rule 1 (Aufbau Principle):Electrons occupy the lowest-energy orbitals possible, starting with 1s andcontinuing in the order dictated by quantum mechanics Rule 2 (Hund"s Rule): Electrons occupy degenerate orbitals (i.e. same (n) and (ell)quantum numbers), they must first occupy the empty orbitals before double occupying them. Furthermore, the most stable configuration results when the spins are parallel (i.e. all same (m_s) quantum numbers). Rule 3 (Pauli-Exclusion Principle): Each electron can be described with a unique set of four quantum numbers. Therefore, if two electrons occupy the same orbital, they have different spin magnetic quantum numbers ((m_s=+1/2) and (m_s=-1/2)).

We use numbers to indicate which shell an electron is in. As shown in Table (PageIndex1), the first shell, closest to the nucleus and with the lowest-energy electrons, is shell 1. This first shell has only one subshell, which is labeled 1s and can hold a maximum of 2 electrons. We combine the shell and subshell labels when referring to the organization of electrons about a nucleus and use a superscript to indicate how many electrons are in a subshell. Thus, because a hydrogen atom has its single electron in the s subshell of the first shell, we use 1s1 to describe the electronic structure of hydrogen. This structure is called an electron configuration, which areshorthand descriptions of the arrangements of electrons in atoms.

Table (PageIndex1): Shells and Subshellns Shell Number of Subshells Names of Subshells
1 1 1s
2 2 2s and 2p
3 3 3s, 3p and 3d
4 4 4s, 4p, 4d and 4f

Helium atoms have 2 electrons. Both electrons fit into the 1s subshell because s subshells can hold up to 2 electrons; therefore, the electron configuration for helium atoms is 1s2 (spoken as “one-ess-two”). Different subshells hold a different maximum number of electrons. Any s subshell can hold up to 2 electrons; p, 6; d, 10; and f, 14 (Table (PageIndex2)). Hence, the 1s subshell cannot hold 3 electrons (because an s subshell can hold a maximum of 2 electrons), so the electron configuration for a lithium atom cannot be 1s3(Figure (PageIndex1)). Two of the lithium electrons can fit into the 1s subshell, but the third electron must go into the second shell. The second shell has two subshells, s and p, which fill with electrons in that order. The 2s subshell holds a maximum of 2 electrons, and the 2p subshell holds a maximum of 6 electrons. Because lithium’s final electron goes into the 2s subshell, we write the electron configuration of a lithium atom as 1s22s1. The shell diagram for a lithium atom (Figure (PageIndex1)). The shell closest to the nucleus (first shell) has 2 dots representing the 2 electrons in 1s, while the outermost shell (2s) has 1 electron.    Figure (PageIndex1): Shell diagrams of hydrogen (H), helium (He), lithium (Li), and Berryellium (Be) atoms. (CC BY-SA 2.0 UK; Greg Robsonmodified by Pumbaavia Wikipedia) Table (PageIndex2): Number of Electrons in subshells Subshell Maximum Number of Electrons
s 2
p 6
d 10
f 14

The next largest atom, beryllium, has 4 electrons, so its electron configuration is 1s22s2. Now that the 2s subshell is filled, electrons in larger atoms start filling the 2p subshell. With neon, the 2p subshell is completely filled. Because the second shell has only two subshells, atoms with more electrons now must begin the third shell. The third shell has three subshells, labeled s, p, and d. The d subshell can hold a maximum of 10 electrons. The first two subshells of the third shell are filled in order—for example, the electron configuration of aluminum, with 13 electrons, is 1s22s22p63s23p1. However, a curious thing happens after the 3p subshell is filled: the 4s subshell begins to fill before the 3d subshell does. In fact, the exact ordering of subshells becomes more complicated at this point (after argon, with its 18 electrons), so we will not consider the electron configurations of larger atoms. A fourth subshell, the f subshell, is needed to complete the electron configurations for all elements. An f subshell can hold up to 14 electrons.

Table (PageIndex3): Atomic Electron Configuration Z Element Outer most Shell Configuration Noble Gas Configuration
1 H 1 1s1 1s1
2 He 1 1s2 1s2
3 Li 2 1s22s1 2s1
4 Be 2 1s2 2s2 2s2
5 B 2 1s2 2s22p1 2s22p1
6 C 2 1s2 2s22p2 2s22p2
7 N 2 1s2 2s22p3 2s22p3
8 O 2 1s2 2s22p4 2s22p4
9 F 2 1s2 2s22p5 2s22p5
10 Ne 2 1s2 2s22p6 2s22p6
11 Na 3 1s2 2s22p6 3s1 3s1
12 Mg 3 1s2 2s22p6 3s2 3s2
13 Al 3 1s2 2s22p6 3s23p1 3s23p1
14 Si 3 1s2 2s22p63s23p2 3s23p2
15 P 3 1s2 2s22p6 3s23p3 3s23p3
16 S 3 1s2 2s22p6 3s23p4 3s23p4
17 Cl 3 1s2 2s22p6 3s23p5 3s23p5
18 Ar 3 1s2 2s22p6 3s23p6 3s23p6
19 K 4 1s2 2s22p6 3s23p6 4s1 4s1
20 Ca 4 1s2 2s22p6 3s23p6 4s2 4s2

Electron filling always starts with 1s, the subshell closest to the nucleus. Next is 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, etc., shown in the electron shell filling order diagram in Figure (PageIndex2). Follow each arrow in order from top to bottom. The subshells you reach along each arrow give the ordering of filling of subshells in larger atoms. Figure (PageIndex2):The order of electron filling in an atom.

## More Configurations

We construct the periodic table by following the aufbau principle (from German, meaning “building up”). First we determine the number of electrons in the atom; then we add electrons one at a time to the lowest-energy orbital available without violating the Pauli principle. We use the orbital energy diagram of Figure (PageIndex1), recognizing that each orbital can hold two electrons, one with spin up ↑, corresponding to ms = +½, which is arbitrarily written first, and one with spin down ↓, corresponding to ms = −½. A filled orbital is indicated by ↑↓, in which the electron spins are said to be paired. Here is a scivicpride-kusatsu.netatic orbital diagram for a hydrogen atom in its ground state: Figure (PageIndex1): One electron in.

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From the orbital diagram, we can write the electron configuration in an abbreviated form in which the occupied orbitals are identified by their principal quantum number n and their value of l (s, p, d, or f), with the number of electrons in the subshell indicated by a superscript. For hydrogen, therefore, the single electron is placed in the 1s orbital, which is the orbital lowest in energy (Figure (PageIndex1)), and the electron configuration is written as 1s1 and read as “one-s-one.”

A neutral helium atom, with an atomic number of 2 (Z = 2), has two electrons. We place one electron in the orbital that is lowest in energy, the 1s orbital. From the Pauli exclusion principle, we know that an orbital can contain two electrons with opposite spin, so we place the second electron in the same orbital as the first but pointing down, so that the electrons are paired. The orbital diagram for the helium atom is therefore This electron configuration is written as 1s22s1.

The next element is beryllium, with Z = 4 and four electrons. We fill both the 1s and 2s orbitals to achieve a 1s22s2 electron configuration:

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When we reach boron, with Z = 5 and five electrons, we must place the fifth electron in one of the 2p orbitals. Because all three 2p orbitals are degenerate, it doesn’t matter which one we select. The electron configuration of boron is 1s22s22p1: