Atomic Orbitals, Heisenberg uncertainty principle | Organic Chemistry
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Atomic Orbitals

We have seen that electrons are distributed into different atomic orbitals (Table 1.2). An orbital is a three-dimensional region around the nucleus where there is a high probability of finding an electron. But what does an orbital look like? Mathematical calculations indicate that the s atomic orbital is a sphere with the nucleus at its center, and experimental evidence supports this theory. The Heisenberg uncertainty principle states that both the precise location and the momentum of an atomic particle cannot be simultaneously determined. This means that we can never say precisely where an electron is—we can only describe its probable location. Thus, when we say that an electron occupies a 1s atomic orbital, we mean that there is a greater than 90% probability that the electron is in the space defined by the sphere.

Because the average distance from the nucleus is greater for an electron in a 2s atomic orbital than for an electron in a 1s atomic orbital, a 2s atomic orbital is represented by a larger sphere. Consequently, the average electron density in a 2s atomic orbital is less than the average electron density in a 1s atomic orbital.
atomic orbitals 1s 2s
An electron in a 1s atomic orbital can be anywhere within the 1s sphere, but a 2s atomic orbital has a region where the probability of finding an electron falls to zero. This is called a node, or, more precisely—since the absence of electron density is at one set distance from nucleus—a radial node. So a 2s electron can be found anywhere within the 2s sphere—including the region of space defined by the 1s sphere—except in the node.

To understand why nodes occur, you need to remember that electrons have both particlelike and wavelike properties. A node is a consequence of the wavelike properties of an electron. Consider the following two types of waves: traveling waves and standing waves. Traveling waves move through space; light is an example of a traveling wave. A standing wave, in contrast, is confined to a limited space. A vibrating string of a guitar is an example of a standing wave—the string moves up and down, but does not travel through space. If you were to write a wave equation for the guitar string, the wave function would be (+) in the region above where the guitar string is at rest and (−) in the region below where the guitar string is at rest—the regions are of opposite phase. The region where the guitar string has no transverse displacement is called a node. A node is the region where a standing wave has an amplitude of zero.
vibrating string of a guitar
An electron behaves like a standing wave, but—unlike the wave created by a vibrating guitar string—it is three dimensional. This means that the node of a 2s atomic orbital is actually a surface—a spherical surface within the 2s atomic orbital. Because the electron wave has zero amplitude at the node, there is zero probability of finding an electron at the node.

Unlike s atomic orbitals that resemble spheres, p atomic orbitals have two lobes. Generally, the lobes are depicted as teardrop-shaped, but computer-generated representations reveal that they are shaped more like doorknobs. Like the vibrating guitar string, the lobes are of opposite phase, which can be designated by plus (+) and minus (−) signs or by two different colors. (In this context, (+) and (−) do not indicate charge, just the phase of the orbital.) The node of the p atomic orbital is a plane that passes through the center of the nucleus, bisecting its two lobes. This is called a nodal plane. There is zero probability of finding an electron in the nodal plane of the p orbital.
2p atomic orbitalsIn Section 1.2, you saw that there are three degenerate p atomic orbitals. The px orbital is symmetrical about the x-axis, the py orbital is symmetrical about the y-axis, and the pz orbital is symmetrical about the z-axis. This means that each p orbital is perpendicular to the other two p orbitals. The energy of a 2p atomic orbital is slightly greater than that of a 2s atomic orbital because the average location of an electron in a 2p atomic orbital is farther away from the nucleus.
Px, Py, Pz Orbital

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