Armed with knowledge of the relative energies of orbitals and the Pauli exclusion principle, we are in a position to consider the arrangements of electrons in atoms. The way electrons are distributed among the various orbitals of an atom is called the electron configuration of the atom.

The most stable electron configuration—the ground state—is that in which the electrons are in the lowest possible energy states. If there were no restrictions on the possible values for the quantum numbers of the electrons, all the electrons would crowd into the ls orbital because it is the lowest in energy (Figure 6.24). The Pauli exclusion principle tells us, however, that there can be at most two electrons in any single orbital. Thus, the orbitals are filled in order of increasing energy, with no more than two electrons per orbital. For example, consider the lithium atom, which has three electrons. (Recall that the number of electrons in a neutral atom equals its atomic number.) The ls orbital can accommodate two of the electrons. The third one goes into the next lowest energy orbital, the 2s.

We can represent any electron configuration by writing the symbol for the occupied subshell and adding a superscript to indicate the number of electrons in that subshell. For example, for lithium we write ls22s1 (read “ls two, 2s one”). We can also show the arrangement of the electrons as

In this representation, which we call an orbital diagram, each orbital is denoted by a box and each electron by a half arrow. A half arrow pointing up () represents an electron with a positive spin magnetic quantum number and a half arrow pointing down () represents an electron with a negative spin magnetic quantum number . This pictorial representation of electron spin, which corresponds to the directions of the magnetic fields in Figure 6.25, is quite convenient.

Electrons having opposite spins are said to be paired when they are in the same orbital (). An unpaired electron is one not accompanied by a partner of opposite spin. In the lithium atom the two electrons in the 1s orbital are paired and the electron in the 2s orbital is unpaired.

Hund's Rule

Consider now how the electron configurations of the elements change as we move from element to element across the periodic table. Hydrogen has one electron, which occupies the 1s orbital in its ground state:

The choice of a spin-up electron here is arbitrary; we could equally well show the ground state with one spin-down electron. It is customary, however, to show unpaired electrons with their spins up.

TABLE 6.3 • Electron Configurations of Several Lighter Elements

The next element, helium, has two electrons. Because two electrons with opposite spins can occupy the same orbital, both of helium's electrons are in the 1s orbital:

The two electrons present in helium complete the filling of the first shell. This arrangement represents a very stable configuration, as is evidenced by the chemical inertness of helium.

The electron configurations of lithium and several elements that follow it in the periodic table are shown in TABLE 6.3. For the third electron of lithium, the change in principal quantum number from n = 1 for the first two electrons to n = 2 for the third electron represents a large jump in energy and a corresponding jump in the average distance of the electron from the nucleus. In other words, it represents the start of a new shell occupied with electrons. As you can see by examining the periodic table, lithium starts a new row of the table. It is the first member of the alkali metals (group 1A).

The element that follows lithium is beryllium; its electron configuration is 1s22s2 (Table 6.3). Boron, atomic number 5, has the electron configuration 1s22s22p1. The fifth electron must be placed in a 2p orbital because the 2s orbital is filled. Because all the three 2p orbitals are of equal energy, it does not matter which 2p orbital we place this fifth electron in.

With the next element, carbon, we encounter a new situation. We know that the sixth electron must go into a 2p orbital. However, does this new electron go into the 2p orbital that already has one electron or into one of the other two 2p orbitals? This question is answered by Hund's rule, which states that for degenerate orbitals, the lowest energy is attained when the number of electrons having the same spin is maximized. This means that electrons occupy orbitals singly to the maximum extent possible and that these single electrons in a given subshell all have the same spin magnetic quantum number. Electrons arranged in this way are said to have parallel spins. For a carbon atom to achieve its lowest energy, therefore, the two 2p electrons must have the same spin. For this to happen, the electrons must be in different 2p orbitals, as shown in Table 6.3. Thus, a carbon atom in its ground state has two unpaired electrons.

Similarly, for nitrogen in its ground state, Hund's rule requires that the three 2p electrons singly occupy each of the three 2p orbitals. This is the only way that all three electrons can have the same spin. For oxygen and fluorine, we place four and five electrons, respectively, in the 2porbitals. To achieve this, we pair up electrons in the 2p orbitals, as we will see in Sample Exercise 6.7.

Hund's rule is based in part on the fact that electrons repel one another. By occupying different orbitals, the electrons remain as far as possible from one another, thus minimizing electron–electron repulsions.

SAMPLE EXERCISE 6.7 Orbital Diagrams and Electron Configurations

Draw the orbital diagram for the electron configuration of oxygen, atomic number 8. How many unpaired electrons does an oxygen atom possess?


Analyze and Plan Because oxygen has an atomic number of 8, each oxygen atom has 8 electrons. Figure 6.24 shows the ordering of orbitals. The electrons (represented as arrows) are placed in the orbitals (represented as boxes) beginning with the lowest-energy orbital, the 1s. Each orbital can hold a maximum of two electrons (the Pauli exclusion principle). Because the 2p orbitals are degenerate, we place one electron in each of these orbitals (spin-up) before pairing any electrons (Hund's rule).

Solve Two electrons each go into the 1s and 2s orbitals with their spins paired. This leaves four electrons for the three degenerate 2p orbitals. Following Hund's rule, we put one electron into each 2p orbital until all three orbitals have one electron each. The fourth electron is then paired up with one of the three electrons already in a 2p orbital, so that the orbital diagram is

The corresponding electron configuration is written 1s22s22p4. The atom has two unpaired electrons.


(a) Write the electron configuration for phosphorus, element 15. (b) How many unpaired electrons does a phosphorus atom possess?

Answers: (a) 1s22s22p63s23p3, (b) three

Condensed Electron Configurations

The filling of the 2p subshell is complete at neon (Table 6.3), which has a stable configuration with eight electrons (an octet) in the outermost occupied shell. The next element, sodium, atomic number 11, marks the beginning of a new row of the periodic table. Sodium has a single 3selectron beyond the stable configuration of neon. We can therefore abbreviate the electron configuration of sodium as

The symbol [Ne] represents the electron configuration of the ten electrons of neon, 1s22s22p6. Writing the electron configuration as [Ne]3s1 focuses attention on the outermost electron of the atom, which is the one largely responsible for how sodium behaves chemically.

We can generalize what we have just done for the electron configuration of sodium. In writing the condensed electron configuration of an element, the electron configuration of the nearest noble-gas element of lower atomic number is represented by its chemical symbol in brackets. For lithium, for example, we write

We refer to the electrons represented by the bracketed symbol as the noble-gas core of the atom. More usually, these inner-shell electrons are referred to as the core electrons. The electrons given after the noble-gas core are called the outer-shell electrons. The outer-shell electrons include the electrons involved in chemical bonding, which are called the valence electrons. For the elements with atomic number of 30 or less, all of the outer-shell electrons are valence electrons. By comparing the condensed electron configurations of lithium and sodium, we can appreciate why these two elements are so similar chemically. They have the same type of electron configuration in the outermost occupied shell. Indeed, all the members of the alkali metal group (1A) have a single s valence electron beyond a noble-gas configuration (FIGURE 6.29).

Transition Metals

The noble-gas element argon (1s 22s 22p 3s2 3p6) marks the end of the row started by sodium. The element following argon in the periodic table is potassium (K), atomic number 19. In all its chemical properties, potassium is clearly a member of the alkali metal group. The experimental facts about the properties of potassium leave no doubt that the outermost electron of this element occupies an s orbital. But this means that the electron with the highest energy has not gone into a 3d orbital, which we might expect it to do. Because the 4s orbital is lower in energy than the 3dorbital (Figure 6.24), the condensed electron configuration of potassium is

Following the complete filling of the 4s orbital (this occurs in the calcium atom), the next set of orbitals to be filled is the 3d. (You will find it helpful as we go along to refer often to the periodic table on the front inside cover.) Beginning with scandium and extending through zinc, electrons are added to the five 3d orbitals until they are completely filled. Thus, the fourth row of the periodic table is ten elements wider than the two previous rows. These ten elements are known as either transition elements or transition metals. Note the position of these elements in the periodic table.

In writing the electron configurations of the transition elements, we fill orbitals in accordance with Hund's rule—we add them to the 3d orbitals singly until all five orbitals have one electron each and then place additional electrons in the 3d orbitals with spin pairing until the shell is completely filled. The condensed electron configurations and the corresponding orbital diagram representations of two transition elements are as follows:

FIGURE 6.29 The outer-shell electron configurations of the alkali metals (group 1A in the periodic table).

Once all the 3d orbitals have been filled with two electrons each, the 4p orbitals begin to be occupied until the completed octet of outer electrons (4s24p6) is reached with krypton (Kr), atomic number 36, another of the noble gases. Rubidium (Rb) marks the beginning of the fifth row. Refer again to the periodic table on the front inside cover. Notice that this row is in every respect like the preceding one, except that the value for n is greater by 1.


Based on the structure of the periodic table, which becomes occupied first, the 6s orbital or the 5d orbitals?

The Lanthanides and Actinides

The sixth row of the periodic table begins with one electron in the 6s orbital of cesium (Cs) and two electrons in the 6s orbital of barium (Ba). Notice, however, that the periodic table then has a break, with elements 57–70 placed below the main portion of the table. This break point is where we begin to encounter a new set of orbitals, the 4f.

There are seven degenerate 4f orbitals, corresponding to the seven allowed values of ml, ranging from 3 to −3. Thus, it takes 14 electrons to fill the 4f orbitals completely. The 14 elements corresponding to the filling of the 4f orbitals are known as either the lanthanide elements or therare earth elements. These elements are set below the other elements to avoid making the periodic table unduly wide. The properties of the lanthanide elements are all quite similar, and these elements occur together in nature. For many years it was virtually impossible to separate them from one another.

Because the energies of the 4f and 5d orbitals are very close to each other, the electron configurations of some of the lanthanides involve 5d electrons. For example, the elements lanthanum (La), cerium (Ce), and praseodymium (Pr) have the following electron configurations:

Because La has a single 5d electron, it is sometimes placed below yttrium (Y) as the first member of the third series of transition elements; Ce is then placed as the first member of the lanthanides. Based on their chemistry, however, La can be considered the first element in the lanthanide series. Arranged this way, there are fewer apparent exceptions to the regular filling of the 4f orbitals among the subsequent members of the series.

After the lanthanide series, the third transition element series is completed by the filling of the 5d orbitals, followed by the filling of the 6p orbitals. This brings us to radon (Rn), heaviest of the known noble-gas elements.

The final row of the periodic table begins by filling the 7s orbitals. The actinide elements, of which uranium (U, element 92) and plutonium (Pu, element 94) are the best known, are then built up by completing the 5f orbitals. The actinide elements are radioactive, and most of them are not found in nature.