 Chapter 71 Atomic Structure Chapter 7. 2 Electromagnetic Radiation -Visible light is a small portion of the electromagnetic spectrum.

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Chapter 71 Atomic Structure Chapter 7

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

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

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

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

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

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

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

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

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

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.

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

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

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 ).

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.

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

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

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

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

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.

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.

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

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

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

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

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

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

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

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

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

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

Chapter 732 Quantum Mechanics Quantum Numbers

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.

Chapter 734 Representation of Orbitals The s Orbitals

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.

Chapter 736 Representation of Orbitals The p Orbitals

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.

Chapter 738 Representation of Orbitals The d and f Orbitals

Chapter 739 32, 34, 42 Homework Problems

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