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Quantum Theory

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The Quantum Model of the Atom Heisenberg Uncertainty Principle: This idea involves the detection of electrons. Electrons are detected by their interaction with photons (a particle of electromagnetic radiation) Because photons have about the same energy as electrons, any attempt to locate a specific electron off its course. The Heisenberg Uncertainty Principle states that it is impossible to determine simultaneously both the position and velocity of an electron or any other particle.

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The Schrödinger Wave Equation: In 1926, Erwin Schrödinger used the hypothesis that electrons have a dual wave particle nature to develop an equation that treated electrons with atoms as waves. Together with the Heisenberg Uncertainty Principle, the Schrödinger Wave Equation helped develop the Modern Quantum Theory. The quantum theory describes mathematically the wave properties of electrons and other very small particles. Solutions to the Schrödinger wave equation are known as wave functions. Wave functions, though, give on the probability of finding an electron at a given place around the nucleus. Electrons can exist in certain regions called orbitals; orbitals are three dimensional region around the nucleus that indicate the probable location of an electron.

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Atomic Orbitals and Quantum Numbers: According to the Schrödinger Equation, electrons in atomic orbitals also have quantized energies. In order to describe orbitals, scientist use quantum numbers. Quantum numbers specify the properties of atomic orbitals and the properties of electrons in orbitals. The 1st three quantum numbers indicate: main energy level, shape, and orientation of an orbital. The 4th, the spin quantum number, describes a fundamental state of the electron that occupies the orbital.

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Principle Quantum Number: The principle quantum number, symbolized by “n”, indicates the main energy level occupied by the electron. Values of “n” are positive integers only: 1,2,3... An electron for which n=1 occupies the first, or lowest, main energy level and is located closest to the nucleus. More than one electron can have the same “n” value. These electrons are said to be in the same electron shell. The total number of orbitals that exist in a given shell or main energy level is equal to n2.

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Angular Momentum Quantum Number: The angular momentum quantum number, symbolize by “l”, indicates the shape of the orbital. For a specific main energy level, the number of orbital shapes possible is equal to “n”. The values of “l” allowed are zero and all positive integers, less than or equal t n-1. Depending on the value of ‘l” an orbital is assigned a letter as shown in the table below. “l” Letter 0s 1p 2d 3f

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S orbitals are spherical, P orbitals are dumb-bell shapes, D orbitals are more complex, F orbitals are too complex to discuss here. In the 1st energy level, n=1, there is only one sublevel possible --- an s orbital, The 2nd energy level, n=2, has two sublevels --- s & p orbitals. The 3rd energy level, n=3, has three sublevels --- s, p & d orbitals. The 4th energy level, n=4, has four sublevels --- s, p, d, & f orbitals. In an nth main energy level, there are n sublevels. Each atomic orbitals is designated by the principal quantum number followed by the letter of the sublevel. For example, the 1st sublevel is the s orbitals in the first main energy level, while the 2p sublevel is the set of p orbitals in the second main energy level.

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Magnetic Quantum Number: Atomic Orbitals can have the same shape but different orientation around the nucleus. The magnetic quantum number, symbolized by “m”, indicates the orientation of the orbital around the nucleus. Because the s orbital is spherical and is centered around the nucleus, it has only one possible orientation. This corresponds to a magnetic quantum number of m=0. There is, therefore, only one s orbital in each sublevel. (refer to FIGURE 5-15 in your textbook – p. 133) The lobes of the p orbital can extend along the x, y, or z axis of a 3-D coordinate system. There are 3 p orbitals in each p sublevel, which are labeled as Px, Py, Pz orbitals. These correspond to the values of m=-1, m=0, m=+1. (refer to FIGURE 5-16 in your textbook – p.133) There are five different d orbitals in each d sublevel. The five orientations correspond to : m=-2, m=-1, m=0, m=+1, m=+2 (refer to the drawings in the class notes—transparencies) There are seven different f orbitals in each f sublevel. The # of orbitals at each main energy level equals the square of the principle quantum number (n2).

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Spin Quantum Number: An electron spins in one or two possible directions. As it spins, it creates a magnetic field. The spin quantum number has only two possible values --- (+1/2, - 1/2)--- which indicate the two spin states of an electron in an orbital. A single orbital can hold max. of 2 electrons, which must have opposite spins.

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Electron Configurations: The arrangement of electrons in an atom is known as the atom’s electron configuration. Because atoms of different elements have different numbers of electrons, a distinct electron configuration exists for the atoms of each element. The lowest energy arrangement of the electrons is called the element’s ground state electron configuration.

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Electron Configuration Rules: RULE #1 – Aufbau Principle: --- An electron occupies the lowest energy orbital that can receive it. The orbital with the lowest energy is the 1s orbital (1s, 2s, 2p, 3s, etc.) Rule #2 – Pauli Exclusion Principle:--- No two electrons in the same set of four quantum numbers. Thismans an orbital can hold two electrons of opposite spin. ____ Rule #3Hund’s Rule:--- Orbitals of equal energy are each occupied by one electron before any orbital is occupied by a second electron, and all electrons in singly occupied orbitals must have the same spin. ___ ___ ___

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Four (4) Types of Notation: 1) Orbital Notation: H ____ He ___ Li ____ ____ 1s 1s 1s 2s 2) Electron-Configuration Notation: H= 1s1 He= 1s2Li= 1s2 2s1 Be= 1s2 2s2 3) Noble Gas Notation: Na = [Ne] 3s1Mg= [Ne] 3s2Al= [Ne] 3s2 3p1

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4) Electron Dot Notation: Electron dot notation is an electron configuration notation in which only the valence electrons (electrons in the outer-most energy level--- that are available to be lost, gained, or shared to form compounds) of an atom of a particular element are shown, indicated by dots placed around the element’s symbol. For example: Sulfur S= 1s2 2s2 2p6 3s2 3p4 may be written as:

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