Quantum mechanical model sublevels

The quantum mechanics model is more modern and more mathematical. It describes a volume of space surrounding the nucleus of an atom where electrons reside, referred to earlier as the electron cloud. Similar to the Bohr model, the quantum mechanics model shows that electrons can be found in energy levels. Electrons do not, however, follow fixed paths around the nucleus. According to the quantum mechanics model, the exact location of an electron cannot be known, but there are areas in the electron cloud where there is a high probability that electrons can be found. These areas are the energy levels each energy level contains sublevels. The areas in which electrons are located in sublevels are called atomic orbitals. The exact location of the electrons in the clouds cannot be precisely predicted, but the unique speed, direction, spin, orientation, and distance from the nucleus of each electron in an atom can be considered. The quantum mechanics model is much more complicated, and accurate, than the Bohr model. 

The quantum mechanical model of atomic structure is far too difficult to be explained in detail in an AP Chemistry course. However, some aspects of the theory are appropriate, and you should know them. These include the predicted number and shapes of orbitals in each energy level the number of electrons found in each orbital, sublevel, and energy level and the meaning of the four quantum numbers. 

The quantum mechanical model is both mathematical and conceptual. It keeps the quantized energy levels that Bohr introduced. In fact, it uses four quantum numbers to describe electron energy. These refer to (1) the principal energy level, (2) the sublevel, (3) the orbital, and (4) the number of electrons in an orbital. The model is summarized at the end of this section. You might find it helpful to keep a finger at that summary and refer to it as details of the model are developed. 

The sublevels shown in color are not needed for the elements known today, but the mathematics of the quantum mechanical model predict the order of increasing energy indefinitely. 

Quantum mechanical model of the atom, principal energy level, sublevel, electron orbital, Pauli exclusion principle... 

The modern theory of the atom was initially introduced by Erwin Schrodinger in 1926. It is popularly known as the quantum-mechanical model. This model is based on some very complex mathematics, with which we will not concern ourselves here. The essence of the model is that electrons exist in principal (or main) energy levels, in energy sublevels within these principal levels, and in regions of space called orbitals within the sublevels. The electrons are also thought of as having a particular spin direction. 

By specifying an orbital, we come pretty close to uniquely describing each electron in an atom We can say that a particular electron is in a particular principal level, in a particular sublevel, and in a particular orbital. Any given orbital can only hold two electrons. In order to complete this unique description, we only need to differentiate between the two electrons in the orbital. The quantum-mechanical model states that these two electrons have opposite spin direction. 

It is traditional to divide quantum-mechanical molecular models into three broad bands depending on their degree of sophistication. There are sublevels within each band, and a great deal of jargon accompanied by acronyms. Many authors speak of the level of theory . The Hiickel independent electron model of Chapter 7 typifies the lowest level of theory, and authors sometimes refer to these models as empirical . The Hamiltonian is not rigorously defined, and neither are the basis functions. Nevertheless, these models have been able to produce impressive predictions and rationalizations. 

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