Atomic structure quantum mechanical model

Temperature units/conversions Periodic table Basic atomic structure Quantum mechanical model Atomic number and isotopes Atoms, molecules, and moles Unit conversions Chemical equations Stoichiometric calculations Week 3 Atmospheric chemistry... 

In this chapter, you learned about the electronic structure of the atom in terms of the older Bohr model and the newer quantum mechanical model. You learned about the wave properties of matter, and how to describe each individual electron in terms of its four quantum numbers. You then learned how to write the electron configuration of an atom and some exceptions to the general rules. 

What is the quantum mechanical model of the atom, and how does a understanding of atomic structure enable chemists to explain the properties of substances and their chemical bonding ... 

In this section, you saw how the ideas of quantum mechanics led to a new, revolutionary atomic model—the quantum mechanical model of the atom. According to this model, electrons have both matter-like and wave-like properties. Their position and momentum cannot both be determined with certainty, so they must be described in terms of probabilities. An orbital represents a mathematical description of the volume of space in which an electron has a high probability of being found. You learned the first three quantum numbers that describe the size, energy, shape, and orientation of an orbital. In the next section, you will use quantum numbers to describe the total number of electrons in an atom and the energy levels in which they are most likely to be found in their ground state. You will also discover how the ideas of quantum mechanics explain the structure and organization of the periodic table. 

In this section, you have seen how a theoretical idea, the quantum mechanical model of the atom, explains the experimentally determined structure of the periodic table, and the properties of its elements. Your understanding of the four quantum numbers enabled you to write electron configurations and draw orbital diagrams for atoms of the elements. You also learned how to read the periodic table to deduce the electron configuration of any element. 

The breakthrough in understanding atomic structure came in 1926, when the Austrian physicist Erwin Schrodinger (1887-1961) proposed what has come to be called the quantum mechanical model of the atom. The fundamental idea behind the model is that it s best to abandon the notion of an electron as a small particle moving around the nucleus in a defined path and to concentrate instead on the electron s wavelike properties. In fact, it was shown in 1927 by Werner Heisenberg (1901-1976) that it is impossible to know precisely where an electron is and what path it follows—a statement called the Heisenberg uncertainty principle. 

Schrodinger s quantum mechanical model of atomic structure is framed in the form of a wave equation, a mathematical equation similar in form to that used to describe the motion of ordinary waves in fluids. The solutions (there are many) to the wave equation are called wave functions, or orbitals, and are represented by... 

Now that we ve seen how atomic structure is described according to the quantum mechanical model, let s return briefly to the subject of atomic line spectra first mentioned in Section 5.3. How does the quantum mechanical model account for the discrete wavelengths of light found in a line spectrum ... 

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. 

While semiempirical models which can be applied to molecules the size of 1 and 2 are necessarily only approximate, we were searching for trends rather than absolute values. In concept, the design of semiempirical quantum mechanical models of molecular electronic structure requires the definition of the electronic wavefunction space by a basis set of atomic orbitals representing the valence shells of the atoms which constitute the molecule. A specification of quantum mechanical operators in this function space is provided by means of parameterized matrices. Specification of the number of electrons in the system completes the information necessary for a calculation of electronic energies and wavefunctions if the molecular geometry is known. The selection of the appropriate functional forms for the parameterization of matrices is based on physical intuition and analogy to exact quantum mechanics. The numerical values of the parameters are obtained by fitting to selected experimental results, typically atomic properties. 

Computational models that combine a high level quantum mechanical model of the reaction site surrounded by a layer of lower level semi-empirical or molecular mechanical atoms in the surrounding solvent or enzyme environment will one day make electronic structure calculations of transition states in the condensed phase routine, but these are still some distance in the future. At present, if KIEs calculated from electronic structure models do not match the experimental KIEs, it is necessary to use BOVA to find the transition state. 

Quantum chemistry is the appfication of quantum mechanical principles and equations to the study of molecules. In order to nnderstand matter at its most fundamental level, we must use quantum mechanical models and methods. There are two aspects of quantum mechanics that make it different from previous models of matter. The first is the concept of wave-particle duality that is, the notion that we need to think of very small objects (such as electrons) as having characteristics of both particles and waves. Second, quantum mechanical models correctly predict that the energy of atoms and molecules is always quantized, meaning that they may have only specific amounts of energy. Quantum chemical theories allow us to explain the structure of the periodic table, and quantum chemical calculations allow us to accurately predict the structures of molecules and the spectroscopic behavior of atoms and molecules. 

DEVELOPMENT AND CENTRAL CONCEPTS OF ATOMIC THEORY AND STRUCTURE, INCLUDING THE QUANTUM MECHANICAL MODEL. 

The model that we have developed for the structure of atoms has been further refined. This more sophisticated model, known as the quantum mechanical model, retains most of the general features that we have deduced for atomic structure. Within this model, the electrons in atoms occupy specific regions of space known as orbitals, with a maximum of two electrons occupying each orbital. There are three orbitals in a/ subshell and one orbital in each s subshell. The idea that the two electrons in a given orbital must have opposite spins was first proposed by Wolfgang Pauli in 1925, and is known as the Pauli Exclusion Principle. Most general chemistry texts have some discussion of these ideas. An interesting introduction to the ideas of quantum mechanics can be found in Sections 3.13 and 3.15 of Chemistry Structure Dynamics, by J. N. Spencer, G. M. Bodner, and L. H. Rickard (Fourth Edition). You should read the appropriate sections of your text to become familiar with the terms and basic ideas of this model. 

To begin with, we recall that atomic orbitals are mathematical functions that come from the quantum mechanical model for atomic structure. (Section 6.5) To explain molecular geometries, we can assume that the atomic orbitals on an atom (usually the central atom) mix to form new orbitals called hybrid orbitals. The shape of any hybrid orbital is different from the shapes of the original atomic orbitals. The process of mixing atomic orbitals is a mathematical operation called hybridization. The total number of atomic orbitals on an atom remains constant, so the number of hybrid orbitals on an atom equals the number of atomic orbitals that are mixed. 

The DFT of nano-silicate photocatalyst. Density functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases. With this theory, the properties of a many-electron system can be determined by using functionals, i.e. functions of another function, which in this case is the spatially dependent electron density. DFT is among the most popular and versatile methods available in condensed-matter physics, computational physics, and computational chemistry. Therefore, the DFT calculation was employed to analyse the effects of modified silicates using different modified methods. 

The quantum mechanical model of atomic structure is based on a set of postulates that can only be justified on the basis of their ability to rationalize experimental behavior. However, the foundations of quantum theory have their origins in the field of classical wave mechanics. The fundamental postulates are as follows ... 

According to the quantum mechanical model of the structure of atoms, each electron in an atom can be described as occupying a particular orbital. To try to understand tbe chemical behavior of atoms of different elements, then, we might try to understand how electrons are distributed in orbitals. Let s begin by asking a very basic question How many electrons can occupy an orbital The answer requires the introduction of one more quantum number, the spin quantum number (designated m. ... 

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