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Quantum Theory

Quantum Theory. 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)

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Quantum Theory

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  1. Quantum Theory

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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 • 0 s • 1 p • 2 d • 3 f

  7. 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.

  8. 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).

  9. 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.

  10. 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.

  11. 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. • ___ ___ ___

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

  13. 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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