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Chapter 71 Atomic Structure Chapter 7

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2 Electromagnetic Radiation -Visible light is a small portion of the electromagnetic spectrum

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Chapter 73 Frequency (v, nu – The number of times per second that one complete wavelength passes a given point. Wavelength ( lambda) – The distance between identical points on successive waves. v = c c = speed of light, 2.997 x 10 8 m/s Electromagnetic Radiation

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Chapter 74 -When talking about atomic structure, a special type of wave is important: Standing Wave: A special type of wave with two or more stationary point with no amplitude. Electromagnetic Radiation

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Chapter 75 -We can also say that light energy is quantized -This is used to explain the light given-off by hot objects. -Max Planck theorized that energy released or absorbed by an atom is in the form of “chunks” of light (quanta). E = h v h = planck’s constant, 6.63 x 10 -34 J/s - Energy must be in packets of (hv), 2(hv), 3(hv), etc. Planck, Einstein, Energy and Photons Planck’s Equation

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Chapter 76 Planck, Einstein, Energy and Photons The Photoelectric Effect

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Chapter 77 The Photoelectric Effect -The photoelectric effect provides evidence for the particle nature of light. -It also provides evidence for quantization. -If light shines on the surface of a metal, there is a point at which electrons are ejected from the metal. -The electrons will only be ejected once the threshold frequency is reached. -Below the threshold frequency, no electrons are ejected. -Above the threshold frequency, the number of electrons ejected depend on the intensity of the light. Planck, Einstein, Energy and Photons

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Chapter 78 The Photoelectric Effect -Einstein assumed that light traveled in energy packets called photons. -The energy of one photon, E = h. Planck, Einstein, Energy and Photons

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Chapter 79 Bohr’s Model of the Hydrogen Atom Line Spectra

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Chapter 710 Bohr’s Model of the Hydrogen Atom Line Spectra

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Chapter 711 Bohr’s Model of the Hydrogen Atom Line Spectra Line spectra can be “explained” by the following equation: - this is called the Rydberg equation for hydrogen.

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Chapter 712 Bohr’s Model of the Hydrogen Atom Bohr’s Model -Assumed that a single electron moves around the nucleus in a circular orbit. -The energy of a given electron is assumed to be restricted to a certain value which corresponds to a given orbit. k = 2.179 x 10 -18 Jz = atomic number n = integer for the orbit

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Chapter 713 Bohr’s Model of the Hydrogen Atom Bohr’s Model -Assumed that a single electron moves around the nucleus in a circular orbit. -The energy of a given electron is assumed to be restricted to a certain value which corresponds to a given orbit. n = integer for the orbita o = 0.0529 angstroms z = atomic number

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Chapter 714 Bohr’s Model of the Hydrogen Atom Bohr’s Model – Important Features -Quantitized energy and angular momentum -The first orbit in the Bohr model has n = 1 and is closest to the nucleus. -The furthest orbit in the Bohr model has n close to infinity and corresponds to zero energy. -Electrons in the Bohr model can only move between orbits by absorbing and emitting energy in quanta (h ).

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Chapter 715 Bohr’s Model of the Hydrogen Atom Bohr’s Model – Line Spectra Ground State – When an electron is in its lowest energy orbit. Excited State – When an electron gains energy from an outside source and moves to a higher energy orbit.

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Chapter 716 Bohr’s Model of the Hydrogen Atom Bohr’s Model – Line Spectra

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Chapter 717 Bohr’s Model of the Hydrogen Atom Bohr’s Model – Line Spectra

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Chapter 718 Bohr’s Model of the Hydrogen Atom Bohr’s Model – Line Spectra

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Chapter 719 Bohr’s Model of the Hydrogen Atom Bohr’s Model – Line Spectra

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Chapter 720 Bohr’s Model of the Hydrogen Atom Bohr’s Model -Since the energy states are quantized, the light emitted from excited atoms must be quantized and appear as line spectra.

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Chapter 721 Quantum Mechanical View of the Atom -DeBroglie proposed that there is a wave/particle duality. -Knowing that light has a particle nature, it seems reasonable to assume that matter has a wave nature. -DeBroglie proposed the following equation to describe the relationship: -The momentum, mv, is a particle property, where as is a wave property.

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Chapter 722 The Uncertainty Principle Heisenberg’s Uncertainty Principle - on the mass scale of atomic particles, we cannot determine exactly the position, speed, and direction of motion simultaneously. -For electrons, we cannot determine their momentum and position simultaneously. Quantum Mechanical View of the Atom

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Chapter 723 -These theories (wave/particle duality and the uncertainty principle) mean that the Bohr model needs to be refined. Quantum Mechanics Quantum Mechanical View of the Atom

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Chapter 724 -The path of an electron can no longer be described exactly, now we use the wavefunction( ). Wavefunction ( ) – A mathematical expression to describe the shape and energy of an electron in an orbit. -The probability of finding an electron at a point in space is determined by taking the square of the wavefunction: Probability density = Quantum Mechanics Schrödinger’s Model

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Chapter 725 Quantum Mechanics -The use of wavefunctions generates four quantum numbers. Principal Quantum Number (n) Angular Momentum Quantum Number (l) Magnetic Quantum Number (m l ) Spin Quantum Number (m s ) Quantum Numbers

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Chapter 726 Quantum Mechanics Principal Quantum Number (n) - This is the same as Bohr’s n - Allowed values: 1, 2, 3, 4, … (integers) - The energy of an orbital increases as n increases - A shell contains orbitals with the same value of n Quantum Numbers

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Chapter 727 Quantum Mechanics Angular Momentum Quantum Number (l) -Allowed values: 0, 1, 2, 3, 4,., (n – 1) (integers) -Each l represents an orbital type lorbital 0s 1p 2d 3f Quantum Numbers

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Chapter 728 Quantum Mechanics Angular Momentum Quantum Number (l) -Allowed values: 0, 1, 2, 3, 4,., (n – 1) (integers) -Each l represents an orbital type -Within a given value of n, types of orbitals have slightly different energy s < p < d < f Quantum Numbers

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Chapter 729 Quantum Mechanics Magnetic Quantum Number (m l ). -This quantum number depends on l. -Allowed values: -l +l by integers. -Magnetic quantum number describes the orientation of the orbital in space. lOrbitalmlml 0s0 1p - 1, 0, + 1 2d - 2, - 1, 0, + 1, + 2 Quantum Numbers

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Chapter 730 Quantum Mechanics Magnetic Quantum Number (m l ). -This quantum number depends on l. -Allowed values: -l +l by integers. -Magnetic quantum number describes the orientation of the orbital in space. -A subshell is a group of orbitals with the same value of n and l. Quantum Numbers

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Chapter 731 Quantum Mechanics Spin Quantum Number (m s ) -Allowed values: - ½ + ½. -Electrons behave as if they are spinning about their own axis. -This spin can be either clockwise or counter clockwise. Quantum Numbers

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Chapter 732 Quantum Mechanics Quantum Numbers

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Chapter 733 Representation of Orbitals The s Orbitals -All s-orbitals are spherical. -As n increases, the s-orbitals get larger. -As n increases, the number of nodes increase. -A node is a region in space where the probability of finding an electron is zero.

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Chapter 734 Representation of Orbitals The s Orbitals

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Chapter 735 Representation of Orbitals The p Orbitals -There are three p-orbitals p x, p y, and p z. (The letters correspond to allowed values of m l of -1, 0, and +1.) -The orbitals are dumbbell shaped.

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Chapter 736 Representation of Orbitals The p Orbitals

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Chapter 737 Representation of Orbitals The d and f Orbitals -There are 5 d- and 7 f-orbitals. -Four of the d-orbitals have four lobes each. -One d-orbital has two lobes and a collar.

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Chapter 738 Representation of Orbitals The d and f Orbitals

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Chapter 739 32, 34, 42 Homework Problems

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