Electron Shells and Valence Electrons

Electron shells are the energy levels around the nucleus in which electrons are arranged, and valence electrons are the electrons in the outermost shell, which determine how an atom bonds and reacts. In brief: the first shell holds up to 2 electrons, the second up to 8 and the third up to 18; sodium has the arrangement 2, 8, 1, with one valence electron, and chlorine has 2, 8, 7, with seven.

The number of valence electrons explains why elements in the same group of the periodic table behave alike, and why atoms gain, lose or share electrons in reactions. This article describes shells, gives the rule for the maximum number of electrons in each shell, shows how to write the shell arrangement of the first twenty elements in a table, explains how to find valence electrons from the periodic table, works through examples and gives the history of the shell model.

What are electron shells?

In a simple picture of the atom, electrons are arranged in shells at increasing distances from the nucleus. Each shell is labeled with a principal quantum number n = 1, 2, 3, and so on, or with letters K, L, M, N. Electrons in shells closer to the nucleus have lower energy, and they are held more strongly. Electrons fill the lowest energy shells first, which gives the most stable arrangement.

How many electrons can each shell hold?

The maximum number of electrons in shell n is 2n².

Maximum electrons in each shell
Shell number n	Letter	Calculation 2n²	Maximum electrons
1	K	2 × 1	2
2	L	2 × 4	8
3	M	2 × 9	18
4	N	2 × 16	32

For the first 20 elements, a simple rule is used: fill the first shell with 2 electrons, the second with up to 8, the third with up to 8, and then start the fourth. The third shell can hold 18 in total, but the 8-electron stage is a stable arrangement and the next electrons go into the fourth shell for potassium and calcium, because of the sub-shell energies explained in later articles.

How do you write the electron arrangement?

Find the atomic number, which gives the number of electrons in a neutral atom.
Place 2 electrons in the first shell.
Place up to 8 electrons in the second shell.
Place up to 8 electrons in the third shell, and continue to the fourth shell.
Write the numbers separated by commas, for example 2, 8, 6.

Shell diagrams for sodium (2, 8, 1) and chlorine (2, 8, 7). The outermost ring holds the valence electrons: one in sodium, which is easily lost, and seven in chlorine, which needs one more electron to complete its octet.

Electron arrangements of the first 20 elements

Shell arrangements and valence electrons, Z = 1 to 20
Z	Element	Arrangement	Valence electrons
1	Hydrogen (H)	1	1
2	Helium (He)	2	2
3	Lithium (Li)	2, 1	1
4	Beryllium (Be)	2, 2	2
5	Boron (B)	2, 3	3
6	Carbon (C)	2, 4	4
7	Nitrogen (N)	2, 5	5
8	Oxygen (O)	2, 6	6
9	Fluorine (F)	2, 7	7
10	Neon (Ne)	2, 8	8
11	Sodium (Na)	2, 8, 1	1
12	Magnesium (Mg)	2, 8, 2	2
13	Aluminum (Al)	2, 8, 3	3
14	Silicon (Si)	2, 8, 4	4
15	Phosphorus (P)	2, 8, 5	5
16	Sulfur (S)	2, 8, 6	6
17	Chlorine (Cl)	2, 8, 7	7
18	Argon (Ar)	2, 8, 8	8
19	Potassium (K)	2, 8, 8, 1	1
20	Calcium (Ca)	2, 8, 8, 2	2

What are valence electrons?

Valence electrons are the electrons in the outermost occupied shell. They are the farthest from the nucleus and are involved in forming chemical bonds. Atoms with a full outer shell (2 for helium, 8 for the other noble gases) are very stable and unreactive. Other atoms react to reach such a full shell: by losing electrons (metals), gaining electrons (nonmetals) or sharing them. This tendency is described by the octet rule, and for the smallest atoms by the duet rule.

How do valence electrons relate to groups?

For the main-group elements, the number of valence electrons is the same for all the elements in a group. Group 1 has 1, group 2 has 2, and groups 13 to 18 have 3 to 8, which is the group number minus 10. The period number tells the number of occupied shells.

Valence electrons of main-group elements
Group	Valence electrons	Typical behavior
1	1	Lose 1 electron, form 1+ ions
2	2	Lose 2 electrons, form 2+ ions
13	3	Lose 3 electrons or share
14	4	Share 4 electrons
15	5	Gain 3 electrons or share
16	6	Gain 2 electrons or share
17	7	Gain 1 electron or share
18	8 (2 for He)	Stable, rarely react

Worked examples

Phosphorus (Z = 15). 15 electrons: 2 in the first shell, 8 in the second, leaving 15 − 10 = 5 in the third. Arrangement 2, 8, 5; five valence electrons; period 3; group 15.
Predicting an ion. Magnesium has 2, 8, 2. By losing the 2 outer electrons it reaches 2, 8, like neon, so it forms Mg²⁺.
Predicting an ion for a nonmetal. Sulfur has 2, 8, 6. It gains 2 electrons to reach 2, 8, 8 like argon, so it forms S²⁻.
Counting capacity. The third shell can hold 2 × 3² = 18 electrons. The first three shells together can hold 2 + 8 + 18 = 28 electrons, which is consistent with the sum 2(1 + 4 + 9) = 28.
Number of shells from the period. Calcium is in period 4, so it has 4 occupied shells (2, 8, 8, 2) and it is in group 2, so it has 2 valence electrons.
Reactivity trend. Lithium (2, 1), sodium (2, 8, 1) and potassium (2, 8, 8, 1) each have one valence electron, and the electron is further from the nucleus in a larger atom, so it is lost more easily. Reactivity with water increases down the group.

How did the shell model develop?

Niels Bohr proposed in 1913 that electrons occupy energy levels around the nucleus, and in 1921 he explained the periodic table by the filling of shells. Gilbert N. Lewis introduced the idea of the shared electron pair and the “cubical atom” in 1916, and Walther Kossel developed the idea of ion formation by electron transfer in 1916, so that the octet rule became the basis of the electronic theory of valence. The more detailed picture of subshells and orbitals followed from quantum mechanics in the 1920s.

Which mistakes are common?

Mistake 1: Counting all electrons as valence electrons

Only the electrons in the outermost shell are valence electrons. For chlorine, 7 are valence electrons and 10 are inner electrons.

Mistake 2: Applying the 2, 8, 8 pattern beyond calcium

The pattern is a simple model for the first 20 elements. For the transition metals and beyond, subshells must be considered.

Mistake 3: Thinking that the shell is a flat ring

Shells are three-dimensional regions. The ring diagrams are a simplified picture.

Mistake 4: Assuming that helium has eight valence electrons

Helium has 2, which fills its only shell.