Chapter 7: Atomic Structure

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Chapter 7 Atomic Structure
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• Electromagnetic Spectrum
• Wave behavior
• Quanta Planck's equation
• Bohr Model of the Atom
• Line spectra Rydberg equation
• Bohr model
• Quantum Mechanical Model Atomic Orbitals
• Wave properties of electrons
• Heisenberg uncertainty principle
• Schrödinger model of the atom
• Quantum numbers
• principal quantum number, n
• angular momentum quantum number, l
• magnetic quantum number, ml
• Shapes of orbitals s, p, d, f

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• Electromagnetic Spectrum
• Wave behavior

c speed of light 3.00 x 108 m/s n
frequency (Hz, cps, s-1)
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• Electromagnetic Spectrum
• Quanta Planck's equation

1900, Max Planck light energy is quantized
E hn
h Plancks constant 6.63 x 10-34 Js
IR
longer l, lower n, lower E
UV
shorter l, higher n, higher E
1905, Albert Einstein photons packets of energy
E(photon) hn
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• Electromagnetic Spectrum

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• Electromagnetic Spectrum

KRCC broadcasts at 91.5 MHz. What is the
wavelength of this light? The most prominent
line in the spectrum of mercury is at 253.6 nm.
Other lines are at 365.0, 404.7, 435.8, and
1014.0 nm. a. Which of these is the most
energetic? The least? b. What is the frequency
of the most prominent line? What is the energy of
a photon of this wavelength?
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• Bohr Model of the Atom
• Line spectra Rydberg equation

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• Bohr Model of the Atom
• Line spectra Rydberg equation

Rydberg equation for the H atom (empirical)
where R (Rydberg constant) 1.0974 x 107 m-1 n1,
n2 1, 2, 3 ? and n2 n1
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• Bohr Model of the Atom
• Line spectra Rydberg equation

Calculate the wavelength of light emitted when an
electron changes from n 3 to n 1 in the H
atom. In what region of the spectrum is this
found?
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• Bohr Model of the Atom
• Bohr model

orbits n quantum number
-Rhc n2
n 1, 2, 3
En
R Rydberg constant h Plancks constant c
speed of light
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• Bohr Model of the Atom
• Bohr model

excited states
photon, DE hn
ground state
excitation (absorption)
de-excitation (emission)
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• Bohr Model of the Atom
• Bohr model

Planck/Einstein
or
Bohr predicted the Rydberg equation (empirical)
from a model (theoretical)! (But the equation
works only for single-electron species H,
He,Li2)
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• Quantum Mechanical Model Atomic Orbitals
• Wave properties of electrons

photons have both wave and particle
properties electrons have both wave and particle
properties
wave-particle dualism
Planck (1900)
(energy of a photon)
(effective mass of a photon)
Einstein (1908)
(for a photon)
DeBroglie (1929)
(for particles such as electrons)
velocity
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• Quantum Mechanical Model Atomic Orbitals
• Wave properties of electrons

standing waves quantized energy levels guitar
string
0 nodes
increasing energy
1 node
2 nodes
general
, only integral number of half-wavelengths
allowed ? quantized energy levels
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• Quantum Mechanical Model Atomic Orbitals
• Heisenberg uncertainty principle
• Schrödinger model of the atom

Heisenberg (1925) it is impossible to know
simultaneously both the exact momentum and exact
location of an electron.
?Can only determine the probability of finding an
electron within a given region of space.
Wave function (?) describes the standing wave
for the electron around an atom ?2 probability
of finding an electron in a given region of
space describes the orbital within which
an electron exists
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• Quantum Mechanical Model Atomic Orbitals
• Quantum numbers
• principal quantum number, n

Schrödingers wave functions (orbitals) described
by 3 quantum numbers principle quantum number,
n determines a. main energy level or shell b.
size of orbitals within each shell n 1, 2, 3,
4 ?
second shell, etc.
first shell
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• Quantum Mechanical Model Atomic Orbitals
• Quantum numbers
• angular momentum quantum number, l

angular momentum quantum number,
l determines shape (type) of orbital
(subshell) l 0, 1, 2 (n-1), inclusive
value of l 0 1 2 3 4 5 orbital
type s p d f g h (subshell)
fundamental
diffuse
no meaning!
principal
sharp
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• Quantum Mechanical Model Atomic Orbitals
• Quantum numbers
• magnetic quantum number, ml

magnetic quantum number, ml determines orientatio
n of orbital ml 0, ? 1, ? 2 ? l, inclusive
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• Quantum Mechanical Model Atomic Orbitals
• Quantum numbers

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• Quantum Mechanical Model Atomic Orbitals
• Shapes of orbitals s, p, d, f

s orbitals
p orbitals
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• Quantum Mechanical Model Atomic Orbitals
• Shapes of orbitals s, p, d, f

d orbitals
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Review
1. Light is given off by an excited atom when
electrons move from orbitalsof ______ energy to
orbitals of ______ energy. 2. Which transition
in the hydrogen atom would give off shorter
wavelengthlight, from n 3 to n 1, or from n
4 to n 2? 3. The quantum number n describes
the ______ of an orbital, and the quantumnumber
l describes the ______ of an orbital. 4. When n
3, the possible values of l are 5. What type of
orbital corresponds to l 3? 6. For a 4d
orbital, n ___, l ___, and the values of ml
are ____________. 7. What is the maximum number
of orbitals that can be associated with eachof
the following sets of quantum numbers? a. n 2
and l 1 b. n 3 c. n 4, l 2, and ml 0 8.
What type of orbital is each of the following?
How many nodes does eachhave?