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 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, 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 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 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 = 6.626X J*s3x10 8 m/s 1.20cm m cm x = 1.66x J
Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display 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 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 = 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 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 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 = 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 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 = 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 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 “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 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 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 Outermost subshell being filled with electrons 7.8
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Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display 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 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 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 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