Quantum mechanics orbitals

The chemistry community, understandably, failed to respond at all, even though Bohmian mechanics probably holds the key to the development of a theory of chemistry, soundly based on quantum theory and relativity. The problem with molecular structure is resolved by the ontological interpretation of quantum-mechanical orbital angular momentum and the key to chemical reactivity and reaction mechanism is provided by the quantum potential function. 

The quantum-mechanical model of the atom replaced the Bohr model in the early twentieth century. In the quantum-mechanical model Bohr orbits are replaced with quantum-mechanical orbitals. Orbitals are different from orbits in that they represent, not specific paths that electrons follow, but probability maps that show a statistical distribution of where the electron is likely to be found. The idea of an orbital is not easy to visualize. Quantum mechanics revolutionized physics and chemistry because in the quantums-mechanical model, electrons do not behave like particles flying through space. We cannot, in general, describe their exact paths. An orbital is a probability map that shows where the electron is likely to be found when the atom is probed it does not represent the exact path that an electron takes as it travels through space. 

FIGURE 9.15 Principal quantum numbers The principal quantum numbers (n = 1, 2,3. ..) determine the energy of the hydrogen quantum-mechanical orbitals. 

The letter indicates the subshell of the orbital and specifies its shape. The possible letters are s, p, d, and/, each with a different shape. Orbitals within the s subshell have a spherical shape. Unlike the n = 1 Bohr orbit, which shows the electron s path, the Is quantum-mechanical orbital is a three-dimensional probability map. Orbitals are sometimes represented by dots ( Figure 9.16), where the dot density is proportional to the probability of finding the electron. 

Explain tiie difference between a Bohr orbit and a quantum-mechanical orbital. 

Explain why quantum-mechanical orbitals have "fuzzy" boundaries. 

List all of the quantum-mechanical orbitals through 5s, in the correct energy order for multi-electron atoms. What is the Pauli exclusion principle Why is it important when writing electron configurations ... 

The Bohr orbit describes the path of an electron as an orbit or trajectory (a specified path). A quantum-mechanical orbital describes the path of an electron using a probability map. 

This is an oversimplification, but it will suit otu- purposes. In the quantum mechanical model, Bohr orbits are replaced with quantum mechanical orbitals and quantum shells. The quantum shell with n = 3 can actually hold 18 electrons however, the quantum shell with = 4 begins to fill when there are only 8 electrons in the quantum shell with n = 3. 

Quantum theory explains the atomic spectra of atoms discussed in Section 7.3. Each wavelength in the emission spectrum of an atom corresponds to an electron transition between quantum-mechanical orbitals. When an atom absorbs energy, an electron in a lower energy orbital is excited or promoted to a higher energy orbital, as shown in Figure 7.21 . In this new configuration, however, the atom is unstable, and the... 

In these depictions, blue represents positive phase and red represents negative phase. The Is orbital is all one phase, while the 2p orbital exhibits two different phases. The phase of quantum-mechanical orbitals is important in bonding, as we shall see in Chapter 10. 

The relative size of sodium and potassium ions is an example of a periodic property one that is predictable based on an element s position within the periodic table. In this chapter, we examine several periodic properties of elements, including atomic radius, ionization energy, and electron affinity. We will see that these properties, as well as the overall arrangement of the periodic table, are explained by quantum-mechanical theory, which we examined in Chapter 7. The arrangement of elements in the periodic table— originally based on similarities in the properties of the elements— reflects how electrons fill quantum-mechanical orbitals. 

In previous chapters, we saw that the volume of an atom is taken up primarily by its electrons (Chapter 2) occupying quantum-mechanical orbitals (Chapter 7). We also saw that these orbitals do not have a definite boundary but represent only a statistical probability distribution for where the electron is found. So how do we define the size of an atom One way to define atomic radii is to consider the distance between nonbonding atoms that are in direct contact. For example, krypton can be frozen into a solid in which the krypton atoms are touching each other but are not bonded together. The distance between the centers of adjacent krypton atoms—which can be determined from the solid s density—is then twice the radius of a krypton atom. An atomic radius determined in this way is called the nonbonding atomic radius or the van der Waals radius. The van der Waals radius represents the radius of an atom when it is not bonded to another atom. 

Quantum mechanics explains the periodic table by explaining how electrons fiU the quantum-mechanical orbitals within the atoms that compose the elements. 

An electron configuration for an atom shows which quantum-mechanical orbitals are occupied by the atom s electrons. For example, the electron configuration of helium (D ) indicates that helium s two electrons exist within the D orbital. 

Because quantum-mechanical orbitals fill sequentially with increasing atomic number, we can infer the electron configuration of an element from its position in the periodic table. 

The simpler of the two more advanced bonding theories is called valence bond theory. According to valence bond theory, electrons reside in quantum-mechanical orbitals localized on individual atoms. In many cases, these orbitals are simply the standard s, p, d, and / atomic orbitals that we learned about in Chapter 7. In other cases, these orbitals are hybridized atomic orbitals, a kind of blend or combination of two or more standard atomic orbitals. 

Valence bond theory can explain many aspects of chemical bonding—such as the rigidity of a double bond—but it also has limitations. In valence bond theory, we treat electrons as if they reside in the quantum-mechanical orbitals that we calculated/or atoms. This is a significant oversimplification that we partially compensate for by hybridization. Nevertheless, we can do better. 

Whatever the motivations for such claims might be is not a matter to be entered into in this article. We merely wish to suggest that, as currently understood, in the standard interpretation of quantum mechanics, orbitals cannot possibly be observed. ... 

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