Table of Contents
Chapter 7 - Atomic Structure
I.
ELECTROMAGNETIC RADIATION: ............................................................................. 2
THE ELECTROMAGNETIC SPECTRUM .............................................................................................. 2
II.
HOW DOES THIS AFFECT OUR STUDY OF CHEMISTRY? .................................... 4
III.
EARLY QUANTUM THEORY .......................................................................................... 4
MAX PLANCK (1858-1947), A GERMAN PHYSICIST, ....................................................................... 4
LIGHT AS PARTICLES – PHOTOELECTRIC EFFECT. ........................................................................... 5
WAVE PROPERTIES OF MATTER: LOUIS DE BROGLIE (1892-1987) ................................................. 6
HYDROGEN LINE SPECTRA & THE BOHR MODEL OF THE ATOM .................................................... 7
Johann Balmer (1825-1898) and Johannes Rydberg (1854-1919)............................................ 7
Niels Bohr (1885-1962) A Danish Scientist ............................................................................... 7
IV.
THE WAVE MODEL OF THE ATOM ............................................................................. 9
HEISENBERG UNCERTAINTY PRINCIPLE .......................................................................................... 9
Warner Heisenberg (1901-1976) ............................................................................................... 9
Max Born (1882-1970) ............................................................................................................... 9
SCHRÖDINGER WAVE EQUATION (1926) ........................................................................................ 9
Erwin Schrödinger (1887-1961), an Austrian Scientist ............................................................. 9
V.
QUANTUM NUMBERS .................................................................................................... 10
Orbitals..................................................................................................................................... 11
Orbital Shapes (based on 2nd QN, l) ....................................................................................... 11
Shells and Subshells ................................................................................................................. 12
Practice with Quantum Numbers ............................................................................................. 12
Page 7-1
Chapter 7 - Atomic Structure
There are periodic trends that can be explained by atomic structure, for which we
need to understand a little physics.
I. Electromagnetic Radiation:
- Energy transport in the form of _______
- James Maxwell described radiation in terms of oscillating electro-magnetic fields
- EMR encompasses radio waves, microwaves, IR radiation, visible light, UV
radiation, X-rays, -rays; visible tight is a form of _______________
The Electromagnetic Spectrum
In EMR visible light of different v or  correspond to different colors.
Wave motion characterized by frequency or wavelength, and the wave velocity.
____________, , is the number of waves or cycles per second that pass a given
point in space
Units: s-1 or cycles per sec or Hz
____________, , is the distance from crest to crest in a wave
Units: nm (10-9m) or Å (angstroms = 10-8cm or 10-10m)
Page 7-2
v and  are inversely proportional to each other
(as one goes up the other goes down)
c  λ ν
Since all EMR travels at the same speed,
- If you have a short  (like a short step) you
need to take steps more frequently to keep up (have a higher frequency).
- Conversely, if you have a long wavelength, you need to have a smaller
frequency (take fewer steps).
For EMR,- velocity in--vacuum is
c = 2.9979 x 108 m/s, ____________________
Intensity is proportional to the _____________.
Energy is inversely proportional to the _____________.
Short wavelengths have high energy.
Long wavelengths have low energy.
There are two types of waves:
- ______________ waves
like waves in the ocean – any number of cycles are possible
- ______________ waves
like a guitar string – only whole numbers of cycles are possible.
(This is the type that is applicable to our studies of the atom.)
All forms of Electromagnetic Radiation:
- Travel at the __________________ (2.9979 x 108 m/s)
- Have an ______________ component
- Have a ____________ component
- Have a dual __________ and ________ nature
Lecture Problem #1.
What is the frequency of light which has a  of 100. nm?
Page 7-3
II. How Does This Affect Our Study of Chemistry?
Some properties of matter could not be explained by Rutherford’s model of the atom:
(Dense positively charged nucleus with e- freely occupying the non-dense
exterior.)
1. The presence of ______________
rather than a complete spectrum
when elements were heated.
2. The “Ultraviolet Catastrophe”
When matter is heated, (stove coils for
example) they give of different colors at
different temperatures
(called: black body radiation)
The intensity of the radiation did not
continue to increase as the frequency
increased the way that classical physics
of the time predicted.
III. Early Quantum Theory
Max Planck (1858-1947), a German Physicist,
Attempted to explain these phenomena.
In 1900 he theorized that black body radiant energy was __________, and could only
have _________________.
He then made the assumption that atoms/molecules absorb or emit energy in small
packages or ___________.
Page 7-4
Plank’s Equation for the energy of _____________: E  h 
Since c  λ  ν
ν
c
λ
therefore
E
hc
λ
Where  = _____________ of the radiation
h = 6.626x10-34J·sec (Planck’s Constant)
Lecture Problem #2.
How many photons are in 4.00 x 10-17 J of energy produced from orange light
with a wavelength of 600. nm?
Light as Particles – Photoelectric Effect.
Discovered by Albert Einstein in 1905.
- If you shine light on a metal, it
will give off an _____________.
- It has to be light of sufficient
____________.
(You cannot substitute a lot of
(high intensity) low energy/long
wavelength particles for a fewer
high energy/short wavelength
particles.
(Just like you can’t substitute a bunch of ping-pong balls for a bowling ball!!!)
Einstein explained the photoelectric effect by extending Planck’s idea of quantized
black body radiation to all _______.
Page 7-5
Examples of:
Quantized
_____________
_____________
Not Quantized
_____________
_____________
Wave Properties of Matter: Louis de Broglie (1892-1987)
- In 1925 de Broglie thought: if light, which is a wave, can have a particle
nature, then why can’t __________ (especially electrons) have a
___________________?
- He used Einstein’s and Planck’s equations to derive a relationship between the
mass (in kg) of a particle and its wavelength (in m) at a certain velocity (in
m/s).
hc
λ
from Planck
hc
 mc 2
λ
 λ
E
E  mc 2
hc
h

2
mc
mc
fromEinstein
this is only true
for ___________ 
If we substitute c with the velocity of the particle:
De Broglie' s Equation : λ 
h
mv Good for the  of moving ________.
Lecture Problem #3.
What is the De Broglie wavelength (in nm) of a hydrogen molecule (m=3.35x10-27 kg)
moving at a velocity of 1.84x103m/s ?
We know that a J 
kg  m 2
s2
and
h is in units of J·sec
Page 7-6
Hydrogen Line Spectra & The Bohr Model of the Atom
Johann Balmer (1825-1898) and Johannes Rydberg (1854-1919)
- examined the four visible lines in the spectrum of the hydrogen atom.
- played around with these numbers and eventually figured out that all four
wavelengths fit into the Rydberg Equation:
1
1 1 
 R 2  2 
λ
2 n 
Where R=1.097x107/m (Rydberg Constant)
and n=3, 4, 5…(for a 1 e- system)
From this they concluded that for:
n=3
red
n=4
blue-green
n=5
blue
n=6
indigo
(656.3 nm)
(486.1 nm)
(434.0 nm)
???
Lecture Problem #4.
Calculate the wavelength of light emitted (in nm) when an electron falls from the n=6
to the n=2 level in the hydrogen atom.
Niels Bohr (1885-1962) A Danish Scientist
- In 1913 he proposed a new model of the atom that attempted to better explain
atomic line spectra and disproved J.J. Thompson’s “Plum Pudding” model.
- Electrons move in circular ____________ around the nucleus.
- The closer the orbit to the nucleus, the lower its ______________.
- Each orbit has a specific energy that has a _______________ value (n).
- The lowest energy orbit is called the _____________________.
- Electrons can move from one orbit to another.
Going to a higher energy orbit ______________ energy.
Returning to a lover energy orbit ___________ energy.
Emitted energy is usually in the form of _________.
Page 7-7
The lines studied by Rydberg and
Balmer all ended in n=___ for a
reason.
For nf=2 the E for the transition put
the emitted EMR in the _________
portion of the spectra. These were
called the ____________ series.
For nf=1 the E for the transition put
the emitted EMR in the _________
portion of the spectra (large E
means small ). These were called
the _____________series.
For nf=3 the E for the transition put
the emitted EMR in the _________
portion of the spectra (small E
means long ). These were called
the _____________series.
Beyond the Paschen series is the Bracket series (nf=4) and Pfund series (nf=5).
Bohr calculated the energy of any given level as: E  
Rhc
n2
Rhc=1312 kJ/mol
The energy difference between any two levels is given by:
 1
1 
ΔE  Rhc  2  2  If you know the ____________________ involved.
 nf ni 
ΔE 
hc
λ
If you know the _______________ of the emission.
Unfortunately, Bohr’s model only successfully explained the spectrum of the H atom.
Efforts were made to modify his theory (e.g., elliptical orbits) but were unsuccessful.
We had to move to a whole new theory.
Page 7-8
IV. The Wave Model of the Atom
Heisenberg Uncertainty Principle
Warner Heisenberg (1901-1976)
In studying the works of Bohr and DeBroglie concerning the wave nature of the
electron stated that:
Because matter has a particle and wave properties, it is impossible to determine
the exact _____________ and the exact ______________ (or energy, velocity)
of a particle ___________________.
To see something, we must shine light on it, but small particles change position and
energy when struck by photons of light.
Heisenberg related the uncertainty in the position (x) to the uncertainty in the
momentum (p) as follows:
Δx Δp  
h
4π
where h  Planck' s constant;
and
π  3.14159
Δp  Δm  v  mΔΔ
Max Born (1882-1970)
Interpreted Heisenberg’s Uncertainty Principle as:
If we choose to know the __________of an electron in an atom with only a small
uncertainty, we must accept a relatively large uncertainty in its ___________ in
the space around an atom’s ____________.
This means that we can only develop areas of high ________________ of finding an
electron of a given energy in a certain ____________ of space.
Schrödinger Wave Equation (1926)
Erwin Schrödinger (1887-1961), an Austrian Scientist
Developed a mathematical wave function (H)(psi) to describe the ____________
for finding a given electron for the hydrogen atom in certain regions of space.
The equation is long and complex, but includes _________ important variables:
Page 7-9
V. Quantum Numbers
The three variables that come out of the wave equation are: n, l, ml
n
l
ml
These - are quantum variables
- have a restricted set of allowed values
-known as quantum numbers .
Different solutions were attempted for the wave equation and allowed values were
found to be:
QN
n
l
ml
Dependence
independent
dependent on ___
Possible Values
1, 2, 3, etc. in integers
0 to (n-1) in integers
dependent on ___
- l to + l in integers
There are “sets” of possible quantum numbers
Lecture Problem #5.
Try writing the possible sets of n, l, and ml that can be obtained when n=3.
n
l
ml
The solutions to the wave equation (2) were plotted to see what the affect of the
different variables was on the probability distribution.
Symbol Name
n
primary QN
l
angular momentum
QN
ml
magnetic QN
Affect
The ______of the probability region (the energy level)
The __________of the probability region
The _____________in space of the probability region
Page 7-10
Orbitals
The density of the probability points varies with
the distance from the nucleus.
- The density is not homogeneous.
- The probability region extends to infinity (but
probability gets very small).
- We enclose the 90% probability area in a surface
known as _____________.
Orbital Shapes (based on 2nd QN, l)
When l =0 the orbital is _________________
Known as an ___ orbital.
- There are ___ nodal planes.
- There is ___ lobe
When l =1, the orbital looks like a _____________
Known as a ___ orbital.
- There is ___ nodal plane.
- There are ___ lobes
When l =2, the orbital looks like a double dumbbell or a dumbbell with a doughnut.
Known as a ___ orbital.
- There are ___ nodal plane.
- There are ___ lobes
(or 2 lobes and a
doughnut)
When l =3 (see bottom
right for shape)
Known as a ___ orbital.
- There is ___ nodal
plane.
- There are ___ lobes
(after f comes g, h, i, etc)
Page 7-11
Shells and Subshells
A shell is a grouping of orbitals with the same values ____ .
A subshell is a grouping of orbitals with the same values of ________.
e.g. 3p (a set of 3 orbitals) or 4d (a set of 5 orbitals)
Within each shell there are ____ subshells.
e.g. when n=1 there is 1 subshell (1s)
n=2 there are 2 subshells (2s, 2p)
n=3 there are 3 subshells (3s, 3p, 3d)
n=4 there are 4 subshells (_______________)
Practice with Quantum Numbers
When n=4 what are the possible values of l?
When l=2, what are the possible values of ml?
For a 4s orbital, what are the possible values of n, l, ml?
For a 3f orbital, what are the possible values of n, l, ml?
What is wrong with each set of QNs?
n=2, l=2, ml=0
n=3, l=0, ml=-2
n=0, l=0, ml=-1
Page 7-12