We are now in a position to consider the arrangements of electrons in atoms. The way in which the electrons are distributed among the various orbitals of an atom is called its electron configuration. The most stable, or ground, electron configuration of an atom 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 1s orbital because it is the lowest in energy (Figure 6.24). The Pauli exclusion principle, however, tells us 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 is equal to its atomic number, Z.) The 1s orbital can accommodate two of the electrons. The third one goes into the next lowest energy orbital, the 2s.
We can summarize 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 1s22s1 (read "1s two, 2s one"). We can also show the arrangement of the electrons as:
In this kind of representation, which we will call an orbital diagram, each orbital is represented by a box and each electron by a half arrow. A half arrow pointing upward represents an electron with a positive spin quantum number (ms = ), and a downward half arrow represents an electron with a negative spin quantum number (ms = ). This pictorial representation of electron spin is quite convenient. In fact, chemists and physicists often refer to electrons as "spin-up" and "spin-down" rather than specifying the value for ms.
Electrons having opposite spins are said to be paired when they are in the same orbital. An unpaired electron is 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.
It is informative to consider 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 in the 1s orbital.
The next element, helium, has two electrons. Because two electrons with opposite spins can occupy an 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 represents a large jump in energy and a corresponding jump in the average distance of the electron from the nucleus. It represents the start of a new shell of electrons. As you can see by examining the periodic table, lithium starts a new row of the periodic 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 doesn't matter which 2p orbital is occupied.
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 others? This question is answered by Hund's rule, which states that for degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized. This means that electrons will occupy orbitals singly to the maximum extent possible, with their spins parallel. Thus, for a carbon atom to achieve its lowest energy, the two 2p electrons will have the same spin. In order for this to happen, the electrons must be in different 2p orbitals, as shown in Table 6.3. We see that 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 2p orbitals. 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.
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 shell. We next encounter sodium, atomic number 11, marking the beginning of a new row of the periodic table. Sodium has a single 3s electron beyond the stable configuration of neon. We can abbreviate the electron configuration of sodium as follows:
The symbol [Ne] represents the electron configuration of the 10 electrons of neon, 1s22s22p6. Writing the electron configuration in this manner helps focus attention on the outermost electrons of the atom. The outer electrons are the ones largely responsible for the chemical behavior of an element. For example, we can write the electron configuration of lithium as:
By comparing this with the electron configuration for sodium, we can appreciate why lithium and sodium are so similar chemically: They have the same type of outer-shell electron configuration. All the members of the alkali metal group (1A) have a single s electron beyond a noble-gas configuration. Electrons in subshells not occupied in the nearest noble-gas element of lower atomic number are referred to as outer-shell electrons, or valence electrons. The electrons in the inner shells are the core electrons.
Draw the orbital diagram representation for the electron configuration of oxygen, atomic number 8.
SOLUTION Figure 6.24 shows the ordering of orbitals. Two electrons each go into the 1s and 2s orbitals. This leaves four electrons for the three 2p orbitals. Following Hund's rule, we put one electron into each 2p orbital until all three have one each. The fourth electron is then paired up with one of the three electrons already in a 2p orbital, so that the correct representation is
The corresponding electron configuration is written 1s22s22p4 or [He]2s22p4. The 1s2 or [He] electrons are the inner-shell, or core, electrons of the oxygen atom. The 2s22p4 electrons are the outer-shell, or valence, electrons.
Write the electron configuration of phosphorus, element 15.
Answer: 1s22s22p63s23p3 = [Ne]3s23p3
The noble-gas element argon marks the end of the row started by sodium. The configuration for argon is 1s22s22p63s23p6. 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 highest-energy electron has not gone into a 3d orbital, which we might have expected it to do. Here the ordering of energy levels is such that the 4s orbital is lower in energy than the 3d (Figure 6.24).
Following complete filling of the 4s orbital (this occurs in the calcium atom), the next set of equivalent 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 of the text.) 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 10 elements wider than the two previous rows. These 10 elements are known as transition elements or transition metals. Note the position of these elements in the periodic table.
In accordance with Hund's rule, electrons are added to the 3d orbitals singly until all five orbitals have one electron each. Additional electrons are then placed in the 3d orbitals with spin pairing until the shell is completely filled. The orbital diagram representations and electron configurations of two transition elements are as follows:
Upon completion of the 3d transition series, 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. For the elements of this fourth row of the table, the 4s, 3d, and 4p electrons are considered the valence, or outer-shell electrons.
Rubidium (Rb) marks the beginning of the fifth row. Refer again to the periodic table on the front inside cover of the text. Notice that this row is in every respect like the preceding one, except that the value for n is 1 greater. The sixth row of the table begins similarly to the preceding one: one electron in the 6s orbital of cesium (Cs) and two electrons in the 6s orbital of barium (Ba). The next element, lanthanum (La), represents the start of the third series of transition elements. But with cerium (Ce), element 58, a new set of orbitals, the 4f, enters the picture. The energies of the 5d and 4f orbitals are very close. For lanthanum itself, the 5d orbital energy is just a little lower than the 4f. However, for the elements immediately following lanthanum, the 4f orbital energies are a little lower, so that the 4f orbitals fill before the 5d orbitals.
There are seven equivalent 4f orbitals, corresponding to the seven allowed values of ml, ranging from 3 to -3. Thus it requires 14 electrons to fill the 4f orbitals completely. The 14 elements corresponding to the filling of the 4f orbitals are elements 58 to 71, known as the lanthanide (or rare earth) elements. To avoid making the periodic table unduly wide, the lanthanide elements are set below the other elements. The properties of the lanthanide elements are all quite similar, and they occur together in nature. For many years it was virtually impossible to separate them from one another.
After the lanthanide series, the third transition element series is completed, followed by the filling of the 6p orbitals. This brings us to radon (Rn), heaviest of the noble-gas elements. The final row of the periodic table begins as the one before it. The actinide elements, of which uranium (U, element 92) and plutonium (Pu, element 94) are the best known, are built up by completion of the 5f orbitals. The actinide elements are radioactive, and most of them are not found in nature.