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Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-1 Electronic Structure of Atoms Chapter 6 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

7-2 Waves To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation. The distance between corresponding points on adjacent waves is the wavelength ( ).

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-3 Waves The number of waves passing a given point per unit of time is the frequency ( ). For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency.

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-4 Electromagnetic Radiation All electromagnetic radiation travels at the same velocity: the speed of light (c), 3.00  10 8 m/s. Therefore, c:speed of light (3.00  10 8 m/s) :wavelength (m, nm, etc.) :frequency (Hz) c =

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-5 The yellow light given off by a sodium vapor lamp used for public lighting has a wavelength of 589 nm. What is the frequency of this radiation? Sample Problems A laser used to weld detached retinas produces radiation with a frequency of 4.69 x 10 14 s -1. What is the wavelength of this radiation?

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-6 Max Planck and Quantized Energy So an atom can change its energy by emitting or absorbing quanta To understand quantization consider walking up a ramp versus walking up stairs: –For the ramp, there is a continuous change in height whereas up stairs there is a quantized change in height.

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-7 The Nature of Energy Max Planck explained it by assuming that energy comes in packets called quanta.

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-8 The Nature of Energy Einstein used this assumption to explain the photoelectric effect. He concluded that energy is proportional to frequency: E = h where h is Planck’s constant, 6.626  10 −34 J-s. A change in an atom’s energy results in the gain or loss of “packets” of fixed amounts energy called a quantum.

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-9 Quantum staircase.

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-10 The Nature of Energy Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light: c = E = h

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-11 Sample Problem SOLUTION: PLAN: Calculating the Energy of Radiation from Its Wavelength PROBLEM:A cook uses a microwave oven to heat a meal. The wavelength of the radiation is 1.20cm. What is the energy of one photon of this microwave radiation? After converting cm to m, we can use the energy equation, E = h combined with = c/ to find the energy. E = hc/ E = 6.626X10 -34 J*s3x10 8 m/s 1.20cm 10 -2 m cm x = 1.66x10 -23 J

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-12 The Nature of Energy Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: 1.Electrons in an atom can only occupy certain orbits (corresponding to certain energies). 2.Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom. 3.Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by E = h

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-13 Quantum Numbers and Atomic Orbitals An atomic orbital is specified by three quantum numbers. n the principal quantum number - a positive integer, indicates the relative size of the orbital or the distance from the nucleus. The values of n are integers ≥ 1 l the angular momentum quantum number - an integer from 0 to n-1, related to the shape of the orbital m l the magnetic moment quantum number - an integer from - l to + l, orientation of the orbital in the space around the nucleus 2 l + 1 Schrodinger Wave Equation M s spin quantum number m s = +½ or -½

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-14  = fn(n, l, m l, m s ) angular momentum quantum number l for a given value of n, l = 0, 1, 2, 3, … n-1 n = 1, l = 0 n = 2, l = 0 or 1 n = 3, l = 0, 1, or 2 l = 0 s orbital l = 1 p orbital l = 2 d orbital l = 3 f orbital Schrodinger Wave Equation 7.6 Value of l0123 Type of orbitalspdf

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-15 s Orbitals The value of l for s orbitals is 0. They are spherical in shape. The radius of the sphere increases with the value of n.

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-16 p Orbitals The value of l for p orbitals is 1. They have two lobes with a node between them.

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-17  = fn(n, l, m l, m s ) magnetic quantum number m l for a given value of l m l = -l, …., 0, …. +l orientation of the orbital in space if l = 1 (p orbital), m l = -1, 0, or 1 if l = 2 (d orbital), m l = -2, -1, 0, 1, or 2 Schrodinger Wave Equation 7.6

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-18 m l = -1m l = 0m l = 1 m l = -2m l = -1m l = 0m l = 1m l = 2 7.6

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-19  = fn(n, l, m l, m s ) spin quantum number m s m s = +½ or -½ Schrodinger Wave Equation m s = -½m s = +½ 7.6

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-20 Electron configuration is how the electrons are distributed among the various atomic orbitals in an atom. 1s 1 principal quantum number n angular momentum quantum number l Gives you the shape of the subshell number of electrons in the orbital or subshell Orbital diagram H 1s 1 7.8

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-21 “Fill up” electrons in lowest energy orbitals (Aufbau principle) H 1 electron H 1s 1 He 2 electrons He 1s 2 Li 3 electrons Li 1s 2 2s 1 Be 4 electrons Be 1s 2 2s 2 B 5 electrons B 1s 2 2s 2 2p 1 C 6 electrons ?? 7.9

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-22 C 6 electrons The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins (Hund’s rule). C 1s 2 2s 2 2p 2 N 7 electrons N 1s 2 2s 2 2p 3 O 8 electrons O 1s 2 2s 2 2p 4 F 9 electrons F 1s 2 2s 2 2p 5 Ne 10 electrons Ne 1s 2 2s 2 2p 6 7.7

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-23 Order of orbitals (filling) in multi-electron atom 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s 7.7

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-24 Outermost subshell being filled with electrons 7.8

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-25 7.8 Not in your book. This edition took it out from the book

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-26 Energy of orbitals in a single electron atom Energy only depends on principal quantum number n n=1 n=2 n=3 7.7

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-27 Energy of orbitals in a multi-electron atom Energy depends on n and l n=1 l = 0 n=2 l = 0 n=2 l = 1 n=3 l = 0 n=3 l = 1 n=3 l = 2 7.7

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-28 Existence (and energy) of electron in atom is described by its unique wave function . Pauli exclusion principle - no two electrons in an atom can have the same four quantum numbers. Schrodinger Wave Equation  = fn(n, l, m l, m s ) Each seat is uniquely identified (E, R12, S8) Each seat can hold only one individual at a time 7.6

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7-29 The Hierarchy of Quantum Numbers for Atomic Orbitals Name, Symbol (Property) Allowed ValuesQuantum Numbers Principal, n (size, energy) Angular momentum, l (shape) Magnetic, m l (orientation) Positive integer (1, 2, 3,...) 0 to n-1 - l,…,0,…,+ l 1 0 0 2 01 0 3 0 12 0 0 +1 0+1 0 +2-2