Atomic Orbitals

We have already reviewed the fact that the electrons of an atom are arranged in shells having successively greater capacities as we go outward from the nucleus. Now let us remind ourselves that within each shell the electrons are distributed among a set of orbitals, each containing no more than two electrons. The first shell, with a capacity of two electrons, thus contains only one orbital, called the 1s orbital. The second shell, with a capacity of eight electrons, contains four orbitals, called 2s, 2px, 2py, and 2pz. The hydrogen atom, for example, has one electron in the 1s orbital, while helium has two electrons (with opposite spins) in this same orbital. Continuing down the periodic table, we find that the next element, lithium, has three electrons. Two of them occupy the Is orbital, which is now filled; the third enters the orbital of next higher energy, the 2s orbital. In beryllium the 1s and 2s orbitals are both filled, and beginning with boron the three 2p orbitals begin filling until, with neon, the first row of the periodic table is completed. The orbital structure of the first ten elements is given in Fig. 2-7.

  1s 2s 2px 2py 2pz

Figure 2-7. The electronic configuration of the first ten elements. Each arrow indicates one electron present in the orbital. Arrows in opposite directions indicate electrons of opposite spins.

For some purposes we can think of an electron as a small, discrete particle, constantly moving in the space defined by its orbital. For other purposes, it is necessary to recognize the wavelike properties of the electron (in diffraction phenomena, for example) and to regard an electron in an orbital as a standing wave system. The electron density at any point in space of the standing wave corresponds to the fraction of its time the small-particle electron would spend within a small element of space at the same point, or to the "probability of finding" the electron within that same element of space.

The geometric shape of each orbital can be obtained from the theory of wave mechanics, the details of which are beyond the scope of this book. The Is orbital is spherical in the sense that the electron density varies with distance from the nucleus but not with direction. The probability of finding the electron at any given distance, as derived from the theory, is plotted in Fig. 2-8. Extending such a graph to three dimensions and chopping it off so that we get a region of space in which the electron spends 90 percent of its time gives us a pictorial representation of an atomic 1s orbital, as seen in the right-hand part of Fig. 2-8. An atomic 2s orbital is represented by a similar sphere but with a larger radius. An electron in a 1s orbital is of lower energy than one in a 2s orbital because it spends more of its time close to the atomic nucleus.

Figure 2-8. The graph represents the relative probability of finding an electron at various distances from the nucleus of a hydrogen atom. The most probable distance is 0.53 Å (0.53 x 10-8 cm). The probability is 90 percent of finding it within the gray area (1.4 Å). A 1s orbital may be defined as a region in space within which a 1s electron spends 90 percent of its time. This is a sphere with a radius of 1.4 Å.

Constructed in a similar way, the 2p orbitals have shapes resembling dumbbells. There are three of these atomic 2p orbitals, of identical energy, and only differing from one another by their orientation in space. Placed in an xyz coordinate system, one points along the x axis, one along the y axis and one along the z axis. (Drawings of these three orbitals are given in Fig. 2-9.) Although it is not easy to show this in a drawing, if the three 2p orbitals were all drawn on the same set of axes, they would add together to form a perfect sphere. The electron distribution in neon then, in which each 2p orbital has two electrons, is spherical, just as it is in the nitrogen atom with one electron in each 2p orbital.

Figure 2-9. The three 2p orbitals are dumbbell shaped and arranged at right angles to one another. Each can hold two electrons. Superimposed upon one another, the three orbitals would make a sphere.

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