#### Transcript AP Chemistry Notes Quantum Theory and Atomic Structure

```Quantum Theory and Atomic
Structure
AP Chemistry
Late 1880s…physicists
thought they knew
everything…discouraged
students from studying
physics in college
CLASSICAL THEORY OF PHYSICS
MATTER
ENERGY
-particulate
-massive
-continuous
-wavelike
Background: WAVES
Waves
A disturbance traveling
through a medium by which
energy is transferred from one
particle of the medium to
another without causing any
permanent displacement of the
medium itself.
Parts of A Wave
node
peak/crest
trough
wavelength
distance between two consecutive peaks or troughs in a wave
symbol: lambda, l
units: meters (m)
frequency
the number of waves passing a point in a given amount of time
symbol: nu, n
units: cycles/sec, 1/sec, sec-1, Hertz (Hz)
Figure 7.1
Frequency
and
Wavelength
c=ln
Figure 7.2
Amplitude (Intensity)
of a Wave
Speed of radiation = wavelength ·
frequency
c=l•n
where c = 3 X 108 m/s
(speed of light, all EM radiation in a vacuum)
Electromagnetic
The Electromagnetic Spectrum
Sample Problem 7.1
Interconverting Wavelength and Frequency
PROBLEM: A dental hygienist uses x-rays (l= 1.00A) to take a series of dental
radiographs while the patient listens to a radio station (l = 325cm)
and looks out the window at the blue sky (l= 473nm). What is the
frequency (in s-1) of the electromagnetic radiation from each source?
(Assume that the radiation travels at the speed of light,
3.00x108m/s.)
Energy as a Wave
Diffraction of Light
Change in the directions and
intensities of a group of waves after
passing by an obstacle or through an
aperture (slit) whose size is
approximately the same as the
wavelength of the waves
Figure 7.4
Different
behaviors
of waves
and
particles.
Prism used to separate light into wavelengths
A single point source and the resulting wave fronts
The diffraction pattern caused by light passing through two adjacent slits.
Figure 7.5
Wave interference pattern produced by two point sources
Constructive Interference
Destructive Interference
Young’s Double Slit Exp. (1802)
Confirms that light is an electromagnetic wave
Energy as a PARTICLE
• Heat a solid and it starts to glow
Hot coals ~1000 K
Electric heating coil ~1500 K
Lightbulb filament~2000 K
• Why does the wavelength change with Temp?
Max Planck (1903) - black body radiation
Black body: a perfect absorber of radiation; object appears
Black when cold and emits a temperature dependent spectrum of light Observations:
Energy is gained
and lost in whole
numbers
Intensity and
frequency (color)
depend on
temperature
Snow is a black body for IR radiation, but not for visible
Energy as a PARTICLE
• Heat a solid and it starts to glow
Hot coals ~1000 K
Electric heating coil ~1500 K
Lightbulb filament~2000 K
• Why does the wavelength change with Temp?
• If an atom can only absorb certain
wavelengths of energy, then it can only emit
certain wavelengths
Planck’s Quantum theory of EM waves
Light energy is transmitted in discrete “packets”
(photons) called quanta (singular is quantum)
The energy of one quantum:
E=hn
h = Planck’s constant
6.63 x 10-34 J·s
Niels Bohr and Max Planck at MIT
“Photoelectric Effect” Einstein (1905)
When EM radiation above a certain frequency is shined
on the device, an electric current registers on the meter
As frequency increases, the current increases
BUT – below the cutoff frequency, no current is
obtained, even at very high intensities!!
Conclusion: Photon is a “particle” of light with energy E=hn
Sample Problem 7.2
Calculating the Energy of Radiation from Its
Wavelength
PROBLEM: A cook uses a microwave oven to heat a meal. The wavelength of
the radiation is 1.20cm. What is the energy of one photon of this
Planck and Einstein at Nobel Conference
Dual Nature of Light
Light has both:
wave nature
particle nature
ATOMIC THEORY
Determination of the Structure of the Atom
1897- J.J. ThompsonCathode Ray Tube
Determined the charge/mass
ratio of an electron.
Suggested plum pudding
model for atom
1911- Ernest RutherfordGold Foil Experiment
Suggested presence of a
positively charged nucleus
Rutherford and Geiger.
Figure 7.8
The line spectra
of several
elements
Colors of “neon” lights
Red = Ne
Others = Ar, Hg, phosphor
Continuous Spectrum
vs.
Line Spectrum
Niels Bohr’s Model of the Atom (1913)
•
e- can only have specific
(quantized) energy values
•
The e-’s energy
correspond to orbits
around the nucleus. Outer
orbits have higher energy
•
Photon
E=hn
light is emitted as e- moves
from higher energy level to
lower energy level
Ground State: n =
Excited State: n
Ionized:
n=
1
>1
∞
Figure 7.10
Quantum staircase
E = hn
E = hn
Problem – model does not work for atoms with more than 1 e- !!!
Rydberg equation
1
l
=
R
1
n12
1
n22
R is the Rydberg constant = 1.09 × 107m-1
Figure 7.9
Three series of spectral lines of atomic hydrogen
for the visible series, n1 = 2 and n2 = 3, 4, 5, ...
Figure 7.11
The Bohr explanation of the three series of spectral lines.
Figure B7.1
Flame tests
strontium 38Sr
Figure B7.2
copper 29Cu
Emission and absorption spectra of sodium atoms.
Bright Line Spectra of Several Elements
7.3
En = -RH (
En = -RH (
Z2
n2
1
n2
)
)
n (principal quantum number) = 1,2,3,…
Z = Atomic Number (Hydrogen, Z = 1)
RH = 2.18 x 10-18J
Sample Problem 7.3
A hydrogen atom absorbs a photon of visible light and its electron transitions
from the n = 1 to n = 4 energy level. Calculate
(a) The change of energy of the atom, and
(b) The wavelength (in nm) of the photon
Figure B7.3
The main components of a typical spectrophotometer
Lenses/slits/collimaters
narrow and align beam.
in region of interest. Must
be stable and reproducible.
In most cases, the source
emits many wavelengths.
Sample in compartment
absorbs characteristic
amount of each incoming
wavelength.
Monochromator
(wavelength selector)
disperses incoming
of component
wavelengths that are
scanned or individually
selected.
Computer converts
signal into displayed
data.
Detector converts
into amplified electrical
signal.
Louis De Broglie (1924)
Q: Why is e- energy quantized?
1802 - T. Young
1905 - A. Einstein
1899 – J.J. Thomson
- Light is a wave
- Light is also a particle
- e- is a particle
- Maybe e- is also a wave!!!
only certain
frequencies
can work in a
circle with
a particular
l = h/mu
Wave-like
Properties
Particle-like
Properties
u = velocity of em = mass of e-
Sample Problem 7.4
Find the deBroglie wavelength of an electron
with a speed of 1.00x106m/s (electron mass =
9.11x10-31kg; h = 6.626x10-34 kg*m2/s).
l = h /mu
Table 7.1
The de Broglie Wavelengths of Several Objects
Substance
Mass (g)
Speed (m/s)
l (m)
slow electron
9x10-28
fast electron
9x10-28
5.9x106
1x10-10
alpha particle
6.6x10-24
1.5x107
7x10-15
one-gram mass
1.0
0.01
7x10-29
baseball
142
25.0
2x10-34
6.0x1027
3.0x104
4x10-63
Earth
1.0
7x10-4
G.P. Thomson (1925)
The e- is also a wave!
Exhibits properties similar to
those of x-rays
Thomson’s diffraction
apparatus
Figure 7.15
CLASSICAL THEORY
Matter
particulate,
massive
Energy
continuous,
wavelike
Summary of the major observations
theory to quantum theory.
Since matter is discontinuous and particulate
perhaps energy is discontinuous and particulate.
Observation
Theory
Planck:
photoelectric effect
Energy is quantized; only certain values
allowed
Einstein: Light has particulate behavior (photons)
atomic line spectra
Bohr:
Energy of atoms is quantized; photon
emitted when electron changes orbit.
Figure 7.15 continued
Since energy is wavelike perhaps matter is wavelike
Observation
Davisson/Germer:
electron diffraction
by metal crystal
Theory
deBroglie: All matter travels in waves; energy of
atom is quantized due to wave motion of
electrons
Since matter has mass perhaps energy has mass
Observation
Compton: photon
wavelength increases
(momentumdecreases)
after colliding with
electron
Theory
Einstein/deBroglie: Mass and energy are
equivalent; particles have wavelength and
photons have momentum.
QUANTUM THEORY
Energy same as Matter
particulate, massive, wavelike
Heisenberg Uncertainty Principle
Werner Heisenberg, 1926
Investigates limitations in pinpointing the
position of an e-
DxDp > h/4p
AP Chemistry
DxmDu > h/4p
Bohr, Heisenberg, and Pauli
POSITION of the e- is determined,
"The more precisely the _____________
the less precisely the _________________
MOMENTUM is known"
Uncertainty Principle
A photon of “light” strikes an electron and is reflected (left).
In the collision the photon transfers momentum to the
electron. The reflected photon is seen through the
microscope, but the electron is out of focus (right). Its exact
position cannot be determined.
Erwin Schroedinger (1926) Once at the end of a colloquium I heard
Debye saying something like:
Attempts to incorporate statistics
with DeBroglie’s and Heisenberg’s
work
“Schroedinger, you are not working right
now on very important problems… why
don’t you tell us some time about that
thesis of de Broglie’s…
In one of the next colloquia,
Schroedinger gave a beautifully clear
account of how de Broglie associated a
wave with a particle, and how he could
obtain the quantization rules…
When he had finished, Debye casually
remarked that he thought this way of
talking was rather childish… To deal
properly with waves, one had to have a
wave equation.
Felix Bloch, Address to the American
Physical Society, 1976
In the span of about two weeks, Schroedinger
develops his wave equation
  ( x, t )
 ( x, t )

 V ( x, t ) ( x, t ) = ih
2
2m x
t
2
2
“ epoch-making work” M. Planck
“true genius” A. Einstein
Schroedinger visits the University of Wisconsin, Madison to deliver a series of lectures in
January and February 1927, introducing his his work on wave mechanics to American
physicists and chemists
: “Wave Function”
2:
-A region in space in which there is a 90% chance
of finding an electron
ORBITAL
-Also called an _______________
The Schrödinger Equation
H = E
wave function
d2
dx2
+
d2
dy2
mass of electron
+
d2
dz2
how  changes in space
potential energy at x,y,z
8p2mQ
+
(E-V(x,y,z)(x,y,z) = 0
2
h
total quantized energy of
the atomic system
Figure 7.16
Electron probability in the
ground-state H atom
Where 90% of the
e- density is found
for the 1s orbital
e- density (1s orbital) falls off rapidly
as distance from nucleus increases
“Anyone who is not shocked by
quantum theory does
not understand it”
--Niels Bohr, 1897
“No one understands
quantum theory”
--Richard Feynman, 1967
Schrodinger Wave Equation
 = fn(n, l, ml, ms)
Existence (and energy) of electron in atom is described
by its unique wave function .
No two electrons in an atom
can have the same four quantum numbers.
Each seat is uniquely identified
(Camp Randall, E, R12, S8)
Each seat can hold only one individual at a time
Quantum Numbers and Atomic Orbitals
An atomic orbital is specified by three quantum numbers.
n the principal quantum number - a positive integer
l the angular momentum quantum number - an integer from 0 to n-1
ml the magnetic moment quantum number - an integer from -l to +l
Principal Quantum Number (Shell)
 = fn(n, l, ml, ms)
principal quantum number = n
n = 1, 2, 3, 4, ….
distance of e- from the nucleus
n=1
n=2
n=3
Figure 7.17
1s
2s
3s
Angular Momentum Quantum Number
(Subshell)
 = fn(n, l, ml, ms)
angular momentum quantum number l
for a given value of n, l = 0, 1, 2, 3, … n-1
n = 1, l = 0
n = 2, l = 0 or 1
n = 3, l = 0, 1, or 2
l=0
l=1
l=2
l=3
s orbital
p orbital
d orbital
f orbital
Shape of the “volume” of space that the e- occupies
l=0
l=1
l=2
l=3
s orbital
p orbital
d orbital
f orbital
Figure 7.18
The 2p orbitals
Figure 7.15
A Cross Section of the Electron Probability
Distribution for a 3p Orbital
Figure 7.19
The 3d orbitals
Figure 7.19 continued
Figure 7.20
One of the seven
possible 4f orbitals
Magnetic Quantum Number
 = fn(n, l, ml, ms)
magnetic quantum number ml
for a given value of l
ml = -l, …., 0, …. +l
if l = 1 (p orbital), ml = -1, 0, or 1
if l = 2 (d orbital), ml = -2, -1, 0, 1, or 2
orientation of the orbital in space
Quantum Numbers and Atomic Orbitals
An atomic orbital is specified by three quantum numbers.
n the principal quantum number - a positive integer
l the angular momentum quantum number - an integer from 0 to n-1
ml the magnetic moment quantum number - an integer from -l to +l
Table 7.2 The Hierarchy of Quantum Numbers for Atomic Orbitals
Name, Symbol
(Property)
Allowed Values
Quantum Numbers
Principal, n
Positive integer
(size, energy)
(1, 2, 3, ...)
1
Angular
momentum, l
0 to n-1
(shape)
0
0
0
0
Magnetic, ml
-l,…,0,…,+l
(orientation)
2
3
1
0
1
2
0
-1 0 +1
-1 0 +1
-2
-1
0
+1 +2
Sample Problem 7.5
Determining Quantum Numbers for an Energy Level
PROBLEM: What values of the angular momentum (l) and magnetic (ml)
quantum numbers are allowed for a principal quantum number (n) of
3? How many orbitals are allowed for n = 3?
PLAN: Follow the rules for allowable quantum numbers found in the text.
l values can be integers from 0 to n-1; ml can be integers from -l
through 0 to + l.
SOLUTION: For n = 3, l = 0, 1, 2
For l = 0 ml = 0
For l = 1 ml = -1, 0, or +1
For l = 2 ml = -2, -1, 0, +1, or +2
There are 9 ml values and therefore 9 orbitals with n = 3.
Sample Problem 7.6
Determining Sublevel Names and Orbital Quantum
Numbers
PROBLEM: Give the name, magnetic quantum numbers, and number of orbitals
for each sublevel with the following quantum numbers:
(a) n = 3, l = 2
(b) n = 2, l = 0
(c) n = 5, l = 1 (d) n = 4, l = 3
PLAN: Combine the n value and l designation to name the sublevel.
Knowing l, we can find ml and the number of orbitals.
SOLUTION:
n
l
sublevel name possible ml values # of orbitals
(a)
3
2
3d
-2, -1, 0, 1, 2
5
(b)
2
0
2s
0
1
(c)
5
1
5p
-1, 0, 1
3
(d)
4
3
4f
-3, -2, -1, 0, 1, 2, 3
7
Sample Problem 7.6
Determining Sublevel Names and Orbital Quantum
Numbers
PROBLEM: Give the name, magnetic quantum numbers, and number of orbitals
for each sublevel with the following quantum numbers:
(a) n = 3, l = 2
(b) n = 2, l = 0
(c) n = 5, l = 1 (d) n = 4, l = 3
PLAN: Combine the n value and l designation to name the sublevel.
Knowing l, we can find ml and the number of orbitals.
SOLUTION:
n
l
sublevel name possible ml values # of orbitals
(a)
3
2
3d
-2, -1, 0, 1, 2
3
(b)
2
0
2s
0
1
(c)
5
1
5p
-1, 0, 1
3
(d)
4
3
4f
-3, -2, -1, 0, 1, 2, 3
7
Sample Problem 7.8: Identifying
Incorrect Quantum Numbers
What is wrong with each
of the following
quantum number
designations and/or
sublevel names?
n
l
ml Name
a) 1
1
0
b) 4
3
+1 4d
c) 3
1
-2
1p
3p
Energy of orbitals in a multi-electron atom
Energy depends on n and l
n=3 l = 2
n=3 l = 0
n=2 l = 0
n=1 l = 0
n=3 l = 1
n=2 l = 1
Writing Orbital Diagrams and Electron
Configurations
Aufbau Principle:
Electrons fill from lowest to highest energy levels
Hund’s Rule:
Each orbital must half fill before it completely fills
Pauli Exclusion Principle:
No 2 e-s can have the same quantum numbers
Each orbital can hold 2 electrons with opposite spin
NOT
Practice: Write Electron Configurations
for:
1s22s22p63s23p1
[Ne]3s23p1
[He]2s22p6
OR
Al
22s22p6
1s
OR
3+
Al
24p5
22s22p63s23p64s23d104p5
[Ar]4s
1s
OR
Br
2
6
Br- 1s22s22p63s23p64s23d104p6 OR [Ar]4s 4p
[Ar]4s13d5
Cr
Cu
[Ar]4s13d10 Why does 4s fill before 3d?
Cu1+ [Ar]3d10
Zn2+ [Ar]3d10
Outermost subshell being filled with electrons
Terms
– Isoelectronic:
• Atoms/Ions that have the same electron
configurations
– Core electrons:
• Electrons in the lower energy levels
– Valence electrons:
• Electrons in the outer energy level
Quantum Numbers
A series of numbers that describe the
properties of an orbital
Spin Quantum Number
 = fn(n, l, ml, ms)
spin quantum number ms
ms = +½ or -½
ms = +½
ms = -½
7.6
Para/Diamagnetism
• Paramagnetism
attracted to a magnetic field
unpaired electrons
• Diamagnetism
repelled by a magnetic field
paired electrons
Paramagnetic
unpaired electrons
2p
Diamagnetic
all electrons paired
2p
7.8
Determining Para/Diamagnetism
Substance is placed between
electromagnets.
If the substance appears heavier, it is
attracted in the magnetic field, and is
paramagnetic.
If the substance appears lighter, it is
diamagnetic.
Magnet Video
These links need to be fixed
Nitrogen Video
Oxygen Video
Write electron configuration for each and predict para- or dia-magnetic
Na+
Para or Dia?
1s22s22p6
Dia
1s22s22p63s23p6
Dia
1s22s22p63s23p6
Dia
1s22s22p63s23p63d10
Dia
1s22s22p63s23p63d9
Para
1s22s22p63s23p63d5
Para
1s22s22p63s23p63d3
Para
1s22s22p63s23p6
Dia
NaCl
ClCaSO4
Ca2+
ZnSO4
Zn2+
CuSO4
Cu2+
MnSO4 Mn2+
MnO2
KMnO4
+4
?
Mn
?
Mn+7
```