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Atomic Structure
Chapter 7
Chapter 7
1
Electromagnetic Radiation
- Visible light is a small portion of the electromagnetic
spectrum
Chapter 7
2
Electromagnetic Radiation
Frequency (v, nu) – The number of
times per second that one complete
wavelength passes a given point.
Wavelength (l, lambda) – The
distance between identical points
on successive waves.
lv=c
c = speed of light, 2.997 x 108 m/s
Chapter 7
3
Electromagnetic Radiation
- When talking about atomic structure, a special type of
wave is important:
Standing Wave: A special type of wave with two or more
stationary point with no amplitude.
Chapter 7
4
Planck, Einstein, Energy and Photons
Planck’s Equation
- We can also say that light energy is quantized
- This is used to explain the light given-off by hot
objects.
- Max Planck theorized that energy released or
absorbed by an atom is in the form of “chunks” of
light (quanta).
E=hv
h = planck’s constant, 6.63 x 10-34J/s
- Energy must be in packets of (hv), 2(hv), 3(hv), etc.
Chapter 7
5
Planck, Einstein, Energy and Photons
The Photoelectric Effect
Chapter 7
6
Planck, Einstein, Energy and Photons
The Photoelectric Effect
- The photoelectric effect provides evidence for the
particle nature of light.
- It also provides evidence for quantization.
- If light shines on the surface of a metal, there is a
point at which electrons are ejected from the metal.
- The electrons will only be ejected once the
threshold frequency is reached .
- Below the threshold frequency, no electrons are
ejected.
- Above the threshold frequency, the number of
electrons ejected depend on the intensity of the
light.
Chapter 7
7
Planck, Einstein, Energy and Photons
The Photoelectric Effect
- Einstein assumed that light traveled in energy packets
called photons.
- The energy of one photon, E = hn.
Chapter 7
8
Bohr’s Model of the Hydrogen Atom
Line Spectra
Chapter 7
9
Bohr’s Model of the Hydrogen Atom
Line Spectra
Chapter 7
10
Bohr’s Model of the Hydrogen Atom
Line Spectra
Line spectra can be “explained” by the following equation:
1 1
 2.179 x10  2  2 
l
 n2 n1 
1
18
- this is called the Rydberg equation for hydrogen.
Chapter 7
11
Bohr’s Model of the Hydrogen Atom
Bohr’s Model
- Assumed that a single electron moves around the
nucleus in a circular orbit.
- The energy of a given electron is assumed to be
restricted to a certain value which corresponds to a
given orbit.
 kz
E 2
n
2
k = 2.179 x 10-18J
z = atomic number
n = integer for the orbit
Chapter 7
12
Bohr’s Model of the Hydrogen Atom
Bohr’s Model
- Assumed that a single electron moves around the
nucleus in a circular orbit.
- The energy of a given electron is assumed to be
restricted to a certain value which corresponds to a
given orbit.
2
n ao
radius 
z
n = integer for the orbit
ao = 0.0529 angstroms
z = atomic number
Chapter 7
13
Bohr’s Model of the Hydrogen Atom
Bohr’s Model – Important Features
- Quantitized energy and angular momentum
- The first orbit in the Bohr model has n = 1 and is
closest to the nucleus.
- The furthest orbit in the Bohr model has n close to
infinity and corresponds to zero energy.
- Electrons in the Bohr model can only move between
orbits by absorbing and emitting energy in quanta
(hn).
Chapter 7
14
Bohr’s Model of the Hydrogen Atom
Bohr’s Model – Line Spectra
Ground State – When an electron is in its lowest energy
orbit.
Excited State – When an electron gains energy from an
outside source and moves to a higher
energy orbit.
Chapter 7
15
Bohr’s Model of the Hydrogen Atom
Bohr’s Model – Line Spectra
E(light )  E2  E1
Chapter 7
16
Bohr’s Model of the Hydrogen Atom
Bohr’s Model – Line Spectra
E (light )  E2  E1
  kz2  kz2 
  2  2 
n1 
 n2
Chapter 7
17
Bohr’s Model of the Hydrogen Atom
Bohr’s Model – Line Spectra
E (light )  E2  E1
  kz  kz 
  2  2 
n1 
 n2
1 
2 1
  kz  2  2 
 n2 n1 
2
Chapter 7
2
18
Bohr’s Model of the Hydrogen Atom
Bohr’s Model – Line Spectra
E (light )  E2  E1
  kz2  kz2 
  2  2 
n1 
 n2
1
2 1
 kz  2  2 
 n2 n1 
 1 1 
  2.179 x10  2  2 
 n2 n1 
18
Chapter 7
19
Bohr’s Model of the Hydrogen Atom
Bohr’s Model
- Since the energy states are quantized, the light emitted
from excited atoms must be quantized and appear as
line spectra.
Chapter 7
20
Quantum Mechanical View of the Atom
- DeBroglie proposed that there is a wave/particle
duality.
- Knowing that light has a particle nature, it seems
reasonable to assume that matter has a wave nature.
- DeBroglie proposed the following equation to describe
the relationship:
h
l
mv
- The momentum, mv, is a particle property, where as l
is a wave property.
Chapter 7
21
Quantum Mechanical View of the Atom
The Uncertainty Principle
Heisenberg’s Uncertainty Principle - on the mass scale of
atomic particles, we cannot determine exactly the
position, speed, and direction of motion
simultaneously.
- For electrons, we cannot determine their momentum
and position simultaneously.
Chapter 7
22
Quantum Mechanical View of the Atom
- These theories (wave/particle duality and the
uncertainty principle) mean that the Bohr model
needs to be refined.
 Quantum Mechanics 
Chapter 7
23
Quantum Mechanics
Schrödinger’s Model
- The path of an electron can no longer be described
exactly, now we use the wavefunction(y).
Wavefunction (y) – A mathematical expression to
describe the shape and energy of an electron in an
orbit.
- The probability of finding an electron at a point in
space is determined by taking the square of the
wavefunction:
Probability density = y2
Chapter 7
24
Quantum Mechanics
Quantum Numbers
- The use of wavefunctions generates four quantum
numbers.
Principal Quantum Number (n)
Angular Momentum Quantum Number (l)
Magnetic Quantum Number (ml)
Spin Quantum Number (ms)
Chapter 7
25
Quantum Mechanics
Quantum Numbers
Principal Quantum Number (n)
- This is the same as Bohr’s n
- Allowed values: 1, 2, 3, 4, … (integers)
- The energy of an orbital increases as n increases
- A shell contains orbitals with the same value of n
Chapter 7
26
Quantum Mechanics
Quantum Numbers
Angular Momentum Quantum Number (l)
- Allowed values: 0, 1, 2, 3, 4, . , (n – 1) (integers)
- Each l represents an orbital type
l
orbital
0
s
1
p
2
d
3
f
Chapter 7
27
Quantum Mechanics
Quantum Numbers
Angular Momentum Quantum Number (l)
- Allowed values: 0, 1, 2, 3, 4, . , (n – 1) (integers)
- Each l represents an orbital type
- Within a given value of n, types of orbitals have slightly
different energy
s<p<d<f
Chapter 7
28
Quantum Mechanics
Quantum Numbers
Magnetic Quantum Number (ml).
- This quantum number depends on l.
- Allowed values: -l  +l by integers.
- Magnetic quantum number describes the orientation of the
orbital in space.
l
0
1
Orbital
s
p
2
d
ml
0
-1, 0, +1
-2, -1,
Chapter 7
0, +1, +2
29
Quantum Mechanics
Quantum Numbers
Magnetic Quantum Number (ml).
- This quantum number depends on l.
- Allowed values: -l  +l by integers.
- Magnetic quantum number describes the orientation of the
orbital in space.
- A subshell is a group of orbitals with the same value of n
and l.
Chapter 7
30
Quantum Mechanics
Quantum Numbers
Spin Quantum Number (ms)
- Allowed values: -½  +½.
- Electrons behave as if they are spinning about their own
axis.
- This spin can be either clockwise or counter clockwise.
Chapter 7
31
Quantum Mechanics
Quantum Numbers
Chapter 7
32
Representation of Orbitals
The s Orbitals
- All s-orbitals are spherical.
- As n increases, the s-orbitals get larger.
- As n increases, the number of nodes increase.
- A node is a region in space where the probability of
finding an electron is zero.
Chapter 7
33
Representation of Orbitals
The s Orbitals
Chapter 7
34
Representation of Orbitals
The p Orbitals
- There are three p-orbitals px, py, and pz. (The letters
correspond to allowed values of ml of -1, 0, and +1.)
- The orbitals are dumbbell shaped.
Chapter 7
35
Representation of Orbitals
The p Orbitals
Chapter 7
36
Representation of Orbitals
The d and f Orbitals
- There are 5 d- and 7 f-orbitals.
- Four of the d-orbitals have four lobes each.
- One d-orbital has two lobes and a collar.
Chapter 7
37
Representation of Orbitals
The d and f Orbitals
Chapter 7
38
Homework Problems
32, 34, 42
Chapter 7
39