Atomic theory hydrogen orbitals

Valence bond and molecular orbital theory both incorporate the wave description of an atom s electrons into this picture of H2, but in somewhat different ways. Both assume that electron waves behave like more familiar waves, such as sound and light waves. One important property of waves is called interference in physics. Constructive interference occurs when two waves combine so as to reinforce each other (in phase) destructive interference occurs when they oppose each other (out of phase) (Figure 2.2). Recall from Section 1.1 that electron waves in atoms are characterized by then- wave function, which is the same as an orbital. For an electron in the most stable state of a hydrogen atom, for example, this state is defined by the I5 wave function and is often called the I5 orbital. The valence bond model bases the connection between two atoms on the overlap between half-filled orbitals of the two atoms. The molecular orbital model assembles a set of molecular- orbitals by combining the atomic orbitals of all of the atoms in the molecule. 

Atomic hydrogen spectrum, 253 Atomic number. 88 and periodic table, 89 table, inside back cover Atomic orbitals, 262. 263 Atomic pile, 120 Atomic theory, 17, 22, 28, 234 as a model, 17 chemical evidence for, 234 of John Dalton, 236 review, 34... 

Although structures involving methyl groups bonded simultaneously to two carbon atoms by means of an overlap between the hydrogen orbitals and the />-orbitals of the carbon atoms may be readily enough assimilated, the state of structural theory is such that most of the cyclic intermediate or transition state structures are dubbed non-classical. In many cases they are best depicted by molecular orbitals, usually by diagramming the component atomic orbitals in the best position for overlap. Since maximum overlap of the component atomic orbitals imposes certain geometric requirements, pre-... 

If we prefer to describe the bonding of a polyatomic molecule using localized two-center, two-electron (2c-2e) bonds, we can turn to the hybridization theory, which is an integral part of the valence bond method. In this model, for AX systems, we linearly combine the atomic orbitals on atom A in such a way that the resultant combinations (called hybrid orbitals) point toward the X atoms. For our BeH2 molecule in hand, two equivalent, colinear hybrid orbitals are constructed from the 2s and 2pz orbitals on Be, which can overlap with the two Is hydrogen orbitals to form two Be-H single bonds. (The 2p and 2py... 

Since the hydrogen molecule consists of protons and electrons, the same components found in separated hydrogen atoms, it seems reasonable to use a theory similar to the atomic theory discussed in Chapter 12, which assumes that the electrons in an atom exist in orbitals of a given energy. Can we apply this same type of model to the hydrogen molecule Yes in fact, describing the H2 molecule in terms of quantum mechanics is quite straightforward. 

The atom of hydrogen, of atomic number Z = i, in its ground state has a single electron in the K shell of principal quantum number n — i the atom of helium (Z = z) has two electrons in this orbit. This, however, is the maximum number of electrons that can be accommodated in the first shell, for it is an essential feature of the Bohr theory that an orbit of principal quantum number n can accept not more than 2tz2 electrons. Thus the maximum permissible number of electrons in each shell is as follows ... 

Bohr s theory was in close agreement with many experimental facts regarding one-electron atoms (the hydrogen atom and hydrogen-fike atoms, snch as He and LF ), bnt it conld not explain the fine stmctnre of the spectral lines that is, the fact that certain lines were actnally a set of closely spaced lines. In 1915 and 1916 respectively, W. Wilson and A. Sommerfeld refined Bohr s theory by admitting elliptical orbits. Flowever, it became evident to many physicists, including Bohr himself, that is was time for a scientific revolution. 

This chapter revises basic atomic orbital theory. The chapter begins with the exact results for the case of the hydrogen atom and the orbital concept for many-electron atoms. It is very important to understand these details about atomic orbitals, since the orbital concept is essential in the approximation to chemical bonding known as the Linear Combination of Atomic Orbitals — Molecular Orbital [LCAO-MO] theory. Only in the case of the hydrogen atom are these atomic orbitals, as exact solutions to Schrddinger s equation, available as functions. 

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