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Chapter 7: Periodicity and
Atomic Structure
Renee Y. Becker
Valencia Community College
CHM 1045
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Light and Electromagnetic Spectrum
• Several types of electromagnetic radiation make
up the electromagnetic spectrum
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Light and Electromagnetic Spectrum
Frequency, : The number of wave peaks that
pass a given point per unit time (1/s)
Wavelength, : The distance from one wave
peak to the next (nm or m)
Amplitude: Height of wave
Wavelength x Frequency = Speed
(m) x (s-1) = c (m/s)
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Light and Electromagnetic Spectrum
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The Planck Equation
E=h
E = hc / 
h = Planck’s constant, 6.626 x 10-34 J s
1 J = 1 kg m2/s2
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Example1: Light and Electromagnetic Spectrum
• The red light in a laser pointer comes from a
diode laser that has a wavelength of about
630 nm. What is the frequency of the light? c
= 3 x 108 m/s
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Atomic Spectra
• Atomic spectra: Result from excited atoms
emitting light.
• Line spectra: Result from electron transitions
between specific energy levels.
• Blackbody radiation is the visible glow that
solid objects emit when heated.
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Atomic Spectra
• Max Planck (1858–1947): proposed the energy is
only emitted in discrete packets called quanta.
The amount of energy depends on the
frequency:
E = energy
 = frequency
 = wavelength c = speed of light
h = planck’s constant
E = h =
hc

h = 6.626  10 -34 J  s
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Atomic Spectra
Albert Einstein (1879–1955):
Used the idea of quanta to explain the photoelectric
effect.
• He proposed that light behaves as a stream of
particles called photons
• A photon’s energy must exceed a minimum
threshold for electrons to be ejected.
• Energy of a photon depends only on the frequency.
E=h
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Atomic Spectra
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Example 2: Atomic Spectra
• For red light with a wavelength of about 630
nm, what is the energy of a single photon and
one mole of photons?
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Wave–Particle Duality
• Louis de Broglie (1892–1987): Suggested
waves can behave as particles and particles
can behave as waves. This is called wave–
particle duality.
m = mass in kg p = momentum (mc) or (mv)
h
h
For Light :  =
=
mc
p
For a Particle
:  =
h
mv
=
h
p
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Example 3: Wave–Particle Duality
• How fast must an electron be moving if it has
a de Broglie wavelength of 550 nm?
me = 9.109 x 10–31 kg
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Quantum Mechanics
• Niels Bohr (1885–1962): Described atom as
electrons circling around a nucleus and
concluded that electrons have specific energy
levels.
• Erwin Schrödinger (1887–1961): Proposed
quantum mechanical model of atom, which
focuses on wavelike properties of electrons.
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Quantum Mechanics
• Werner Heisenberg (1901–1976): Showed
that it is impossible to know (or measure)
precisely both the position and velocity (or the
momentum) at the same time.
• The simple act of “seeing” an electron would
change its energy and therefore its position.
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Quantum Mechanics
• Erwin Schrödinger (1887–1961): Developed
a compromise which calculates both the
energy of an electron and the probability of
finding an electron at any point in the
molecule.
• This is accomplished by solving the
Schrödinger equation, resulting in the wave
function
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Quantum Numbers
• Wave functions describe the behavior of electrons.
• Each wave function contains four variables called
quantum numbers:
• Principal Quantum Number (n)
• Angular-Momentum Quantum Number (l)
• Magnetic Quantum Number (ml)
• Spin Quantum Number (ms)
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Quantum Numbers
• Principal Quantum Number (n): Defines the
size and energy level of the orbital. n = 1, 2,
3, 
– As n increases, the electrons get farther
from the nucleus.
– As n increases, the electrons’ energy
increases.
– Each value of n is generally called a shell.
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Quantum Numbers
• Angular-Momentum Quantum Number (l):
Defines the three-dimensional shape of the
orbital.
• For an orbital of principal quantum number n,
the value of l can have an integer value from
0 to n – 1.
• This gives the subshell notation:
l = 0 = s orbital
l = 3 = f orbital
l = 1 = p orbital
l = 2 = d orbital
l = 4 = g orbital
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Quantum Numbers
• Magnetic Quantum Number (ml): Defines
the spatial orientation of the orbital.
• For orbital of angular-momentum quantum
number, l, the value of ml has integer values
from –l to +l.
• This gives a spatial orientation of:
l = 0 giving ml = 0
l = 1 giving ml = –1, 0, +1
l = 2 giving ml = –2, –1, 0, 1, 2,
on…...
and so
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Quantum Numbers
• Magnetic Quantum Number (ml): –l to +l
S orbital
0
P orbital
-1
0
1
-2
-1
0
1
2
-2
-1
0
1
D orbital
F orbital
-3
2
3
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Quantum Numbers
• Spin Quantum
Number: ms
• The Pauli Exclusion
Principle states that no
two electrons can have
the same four quantum
numbers.
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Quantum Numbers
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Example 4: Quantum Numbers
• Why can’t an electron have the following
quantum numbers?
(a) n = 2, l = 2, ml = 1
(b) n = 3, l = 0, ml = 3
(c) n = 5, l = –2, ml = 1
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Example 5: Quantum Numbers
•
Give orbital notations for electrons with
the following quantum numbers:
(a)n = 2, l = 1
(b) n = 4, l = 3
(c) n = 3, l = 2
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Electron Radial Distribution
• s Orbital Shapes: Holds 2 electrons
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Electron Radial Distribution
• p Orbital Shapes: Holds 6 electrons,
degenerate
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Electron Radial Distribution
• d and f Orbital Shapes: d holds 10
electrons and f holds 14 electrons,
degenerate
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Effective Nuclear Charge
• Electron shielding leads to energy differences
among orbitals within a shell.
• Net nuclear charge felt by an electron is
called the effective nuclear charge (Zeff).
• Zeff is lower than actual nuclear charge.
• Zeff increases toward nucleus
ns > np > nd > nf
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Effective Nuclear Charge
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