Download I. Waves & Particles

Ch. 6 – Electronic Structure
of Atoms
I. Waves & Particles
Properties of Waves
 Many of the properties of light may be
described in terms of waves even
though light also has particle-like
characteristics.
 Waves are repetitive in nature
A. Waves
Wavelength () - length of one complete
wave; units of m or nm
Frequency () - # of waves that pass a
point during a certain time period
hertz (Hz) = 1/s
Amplitude (A) - distance from the origin to
the trough or crest
A. Waves

crest
A

greater
amplitude
origin
(intensity)
A
trough
greater
frequency
(color)
Electromagnetic Radiation
 Electromagnetic radiation: (def) form of
energy that exhibits wavelike behavior as
it travels through space
Types of electromagnetic radiation:
 visible light, x-rays, ultraviolet (UV),
infrared (IR), radiowaves, microwaves,
gamma rays
Electromagnetic Spectrum
 All forms of electromagnetic radiation
move at a speed of about 3.0 x 108
m/s through a vacuum (speed of light)
Electromagnetic spectrum: made of all
the forms of electromagnetic radiation
B. EM Spectrum
H
I
G
H
E
N
E
R
G
Y
L
O
W
E
N
E
R
G
Y
B. EM Spectrum
H
I
G
H
L
O
W
E
N
E
R
G
Y
red
R O Y
G.
orange
green
yellow
B
blue
I
indigo
V
violet
E
N
E
R
G
Y
B. EM Spectrum
Frequency & wavelength are inversely
proportional
c = 
c: speed of light (3.00  108 m/s)
: wavelength (m, nm, etc.)
: frequency (Hz)
B. EM Spectrum
EX: Find the frequency of a photon with a
wavelength of 434 nm.
GIVEN:
WORK:
=c
=?

 = 434 nm
= 4.34  10-7 m  = 3.00  108 m/s
-7 m
8
4.34

10
c = 3.00  10 m/s
 = 6.91  1014 Hz
C. Quantum Theory
 Photoelectric effect: emission of
electrons from a metal when light
shines on the metal
 Hmm… (For a given metal, no electrons
were emitted if the light’s frequency was
below a certain minimum – why did light
have to be of a minimum frequency?)
C. Quantum Theory
Planck (1900)
Observed - emission of light from hot
objects
Concluded - energy is
emitted in small, specific
amounts (quanta)
Quantum - minimum amount of energy
change
C. Quantum Theory
Planck (1900)
vs.
Classical Theory
Quantum Theory
C. Quantum Theory
Einstein (1905)
Observed - photoelectric effect
C. Quantum Theory
The energy of a photon is proportional to
its frequency.
E = h
E: energy (J, joules)
h: Planck’s constant (6.626  10-34 J·s)
: frequency (Hz)
C. Quantum Theory
EX: Find the energy of a red photon with a
frequency of 4.57  1014 Hz.
GIVEN:
WORK:
E=?
E = h
 = 4.57  1014 Hz
E = (6.6262  10-34 J·s)
h = 6.6262  10-34 J·s
(4.57  1014 Hz)
E = 3.03  10-19 J
C. Quantum Theory
Einstein (1905)
Concluded - light has properties of both
waves and particles
“wave-particle duality”
Photon - particle of light that carries a
quantum of energy
Ch.66.3. Bohr Model of the Atom
Excited and Ground State
Ground state: lowest energy state of
an atom
Excited state: an atom has a higher
potential energy than it had in its
ground state
When an excited atom returns to its
ground state, it gives off the energy it
gained as EM radiation
A. Line-Emission Spectrum
excited state
ENERGY IN
PHOTON OUT
ground state
B. Bohr Model
 2) e- exist only in orbits with specific
amounts of energy called energy levels
 When e- are in these orbitals, they
have fixed energy
 Energy of e- are higher when they are
further from the nucleus
B. Bohr Model
Therefore…Bohr model leads
us to conclude that:
e- can only gain or lose
certain amounts of energy
only certain photons are
produced
B. Bohr Model
65
4
3
2
1
Energy of photon
depends on the
difference in energy
levels
Bohr’s calculated
energies matched
the IR, visible, and
UV lines for the H
atom
Each element has a unique bright-line
emission spectrum.
“Atomic Fingerprint”
Helium
Bohr’s calculations only worked for
hydrogen! 
Ch. 6 - Electrons in Atoms
III. Wave
Behavior of
Matter
A. Electrons as Waves
Louis de Broglie (1924)
Applied wave-particle theory to ee- exhibit wave properties
QUANTIZED WAVELENGTHS
A. Electrons as Waves
EVIDENCE: DIFFRACTION PATTERNS
VISIBLE LIGHT
ELECTRONS
A. Electrons as Waves
Diffraction: (def) bending of a wave as it
passes by the edge of an object
 Interference: (def) when waves overlap
(causes reduction and increase in energy in
some areas of waves)
Chapter 6
6.5: Quantum Model
A. Quantum Mechanics
Heisenberg Uncertainty Principle
Impossible to know both the velocity
and position of an electron
A. Quantum Mechanics
Schrödinger Wave Equation (1926)
finite # of solutions  quantized energy
levels
defines probability of finding an e-
Ψ 1s 

1 Z 3/2 σ
π a0
e
B . Quantum Mechanics
 Schrodinger wave equation and
Heisenberg Uncertainty Principle laid
foundation for modern quantum theory
Quantum theory: (def) describes
mathematically the wave properties of
e- and other very small particles
B. Quantum Mechanics
Orbital (“electron cloud”)
Region in space where there is 90%
probability of finding an e-
Orbital
Radial Distribution Curve
C. Quantum Numbers
Four Quantum Numbers:
Specify the “address” of each electron
in an atom
UPPER LEVEL
C. Quantum Numbers
1. Principal Quantum Number ( n )
 Main energy level
Size of the orbital
n2 = # of orbitals in
the energy level
C. Quantum Numbers
2. Angular Momentum Quantum # ( l )
Energy sublevel
Shape of the orbital (# of possible shapes equal
to n)
 values from 0 to n-1
s
p
d
f
C. Quantum Numbers
If l equals…
Then orbital shape is…
0
s
1
p
2
d
3
f
Principle quantum # followed by letter of sublevel
designates an atomic orbital
C. Quantum Numbers
3. Magnetic Quantum Number ( ml )
Orientation of orbital
Specifies the exact orbital
within each sublevel
C. Quantum Numbers
 Values for ml:
m = -l… 0… +l
C. Quantum Numbers
px
py
pz
C. Quantum Numbers
Orbitals combine to form a spherical
shape.
2px
2py
2s
2pz
C. Quantum Numbers
4. Spin Quantum Number ( ms )
Electron spin  +½ or -½
An orbital can hold 2 electrons that spin
in opposite directions.
C. Quantum Numbers
Pauli Exclusion Principle
No two electrons in an atom can have
the same 4 quantum numbers.
Each e- has a unique “address”:
1. Principal #
2. Ang. Mom. #
3. Magnetic #
4. Spin #




energy level
sublevel (s,p,d,f)
orbital
electron
C. Quantum Numbers
n = # of sublevels per level
n2 = # of orbitals per level
Sublevel sets: 1 s, 3 p, 5 d, 7 f
Wrap-Up
Quantum # Symbol What it
describes
Principle
n
main E level,
quantum #
size of orbital
Possible
values
n = positive
whole
integers
Angular
Momentum
Quantum #
l
sublevels and
their shapes
0 to (n-1)
Magnetic
Quantum #
Spin
Quantum #
ml
orientation of
orbital
electron spin
-l … 0 … +l
ms
+1/2 or -1/2
Feeling overwhelmed?
Read
Section 4-2!