Transcript AP Notes Chapter 7

AP Notes Chapter 6
Atomic Structure
Describe
properties of electromagnetic radiation
Light & relationship to atomic structure
Wave-particle duality
Basic ideas of quantum mechanics
Quantum numbers & atomic structure
Electromagnetic Spectrum
Light
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Made up of electromagnetic radiation.
Waves of electric and magnetic fields at
right angles to each other.
Parts of a wave
Wavelength
l
Frequency (n) = number of cycles in one second
Measured in hertz 1 hertz (hz) = 1 cycle/second
EMR - Wave Nature
c = ln
where
c = Speed of light
l = wavelength
n = frequency
l
cycles
1
n:
 sec  Hertz (Hz)
sec
EMR - Particle Nature
(Quantized)
Planck: E = hn
E = energy
h = Planck’s constant =
6.626 x 10- 34 J. s
n= frequency
Reminder
kg  m
1J  1
2
s
2
Kinds of EM waves
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There are many different l and n
Radio waves, microwaves, x rays and
gamma rays are all examples.
Light is only the part our eyes can detect.
Gamma
Rays
Radio
waves
The speed of light
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in a vacuum is 2.998 x 108 m/s
=c
c = ln= wavelength x frequency
What is the wavelength of light with a
frequency 5.89 x 105 Hz?
What is the frequency of blue light with a
wavelength of 484 nm?
In 1900(s)
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Matter and energy were seen as different
from each other in fundamental ways.
Matter was particles.
Energy could come in waves, with any
frequency.
Max Planck found that as the cooling of
hot objects couldn’t be explained by
viewing energy as a wave.
Energy is Quantized
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Planck found DE came in chunks with size
hn
DE = nhn or nhc/l
where n is an integer.
and h is Planck’s constant
h = 6.626 x 10-34 J s
these packets of hn are called quantum
Einstein is next
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Said electromagnetic radiation is quantized
in particles called photons.
Each photon has energy = hn = hc/l
Combine this with Einstein’s E = mc2
You get the apparent mass of a photon.
m = h / (lc)
Neils Bohr (1885 –1962)
Bohr Model
of the
Hydrogen
Atom
Energy
Bohr model of the atom
In the Bohr
model,
electrons can
only exist at
specific energy
levels (orbit).
The Bohr Ring Atom
n=4
n=3
n=2
n=1
Bohr Model of Atom
Postulates
-
P1: e revolves around the
nucleus in a circular
orbit
Bohr Model of Atom
Postulates
P2:Only orbits allowed are
those with angular
momentum of integral
multiples of:
h
2
Bohr Model of Atom
Postulates
P3: e- does not radiate
energy in orbit, but
gains energy to go to
higher level
allowed orbit & radiates
energy when falling to
lower orbit
Photo Absorption and
Emission
The Bohr Model
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n is the energy level
for each energy level the energy is
Z is the nuclear charge, which is +1 for
hydrogen.
E = -2.178 x 10-18 J (Z2 / n2 )
n = 1 is called the ground state
when the electron is removed, n =
E=0

We are worried about the
change
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When the electron moves from one energy level
to another.
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DE = Efinal - Einitial

DE = -2.178 x 10-18 J Z2 (1/ nf2 - 1/ ni2)
 1 1
DE  k 2  2 
 nf ni 
Rotating Object Balance
 Centrifugal
Force =
electrical attraction of
positive nucleus and
negative e
Centrifugal Force = Electrostatic Attraction
2
2
mv
e

2
r
 0r
where  0  1.112  10
2
e
v 
 0mr
2
10
Definition
 Angular
 By
P2:
Momentum = mvr
h
mvr  n 
2
By rearrangement:
nh
v
2mr
By rearrangement:
nh
v
2mr
2 2
n
h
2
v 
2
2 2
4 m r
2
2
2
e
nh


2
2 2
 0mr 4  m r
n h 0
r 
2
2
4  me
2
2
For H-atom [n = 1]
r = 5.29 x 10
-11
m
or
52.9 pm = 0.529
Angstoms
In general, when
n = orbit
a0 = radius of H-atom
for n = 1
& Z = atomic #
2
n a0
r
Z
e
To keep
in orbit,
must balance
kinetic energy and
potential energy
1
E  2
n
1
E  -k 2
n
where
k = Rydberg constant
-18
k = 2.179 x 10 J
For the transition of an e- from an
initial energy level (Ei) to a final
energy level (Ef), we can write
D E  E f  Ei

1  
1
DE    k 2     k 2 
n
n
f
i 

 
 1
1 
DE  k 2  2 
ni 
 nf
Examples
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Calculate the energy need to move an
electron from its to the third energy
level.
Calculate the energy released when an
electron moves from n= 4 to n=2 in a
hydrogen atom.
Calculate the energy released when an
electron moves from n= 5 to n=3 in a
He+1 ion
When is it true?
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Only for hydrogen atoms and other
monoelectronic species.
Why the negative sign?
To increase the energy of the electron you
make it closer to the nucleus.
the maximum energy an electron can have
is zero, at an infinite distance.
The Bohr Model
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Doesn’t work.
Only works for hydrogen atoms.
Electrons don’t move in circles.
The quantization of energy is right, but
not because they are circling like planets.
Which is it?
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Is energy a wave like light, or a particle?
Yes

Concept is called the Wave-Particle duality.
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What about the other way, is matter a wave?
Yes
The Quantum Mechanical Model
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A totally new approach.
De Broglie said matter could be like a
wave.
De Broglie said they were like standing
waves.
The vibrations of a stringed instrument.
Matter as a wave
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Using the velocity v instead of the
wavelength n we get.
De Broglie’s equation l = h/mv
Can calculate the wavelength of an object.
Examples
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The laser light of a CD is 7.80 x 102 m.
What is the frequency of this light?
What is the energy of a photon of this
light?
What is the apparent mass of a photon
of this light?
What is the energy of a mole of these
photons?
What is the wavelength?
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Of an electron with a mass of
9.11 x 10-31 kg traveling at 1.0 x 107 m/s?
Of a softball with a mass of 0.10 kg
moving at 125 mi/hr?
Diffraction
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Diffraction Grating splits light into its
components of light of different
frequencies or wavelengths.
When light passes through, or reflects off,
a series of thinly spaced lines, it creates a
rainbow effect
Because the waves interfere with each
other.
A wave
moves toward
a slit.
Comes out as a curve
with two holes
with two holes
Two Curves
with two holes
Two Curves
Interfere with
each other
with two holes
Two Curves
Interfere with
each other
crests add up
Several waves
Several waves
Several Curves
Several
Severalwaves
waves
Several Curves
Interference
Pattern
Louis de Broglie
(1892-1987)
Electrons should
be considered
waves confined
to the space
around an
atomic nucleus
deBroglie “connected” the wave &
particle natures of matter
c  ln

c
l
n
c  ln

E  hn

c
l
n
ch
l
E
c  ln

E  hn

E  mc
2
c
l
n
ch
l
E
c
c  ln  l 
n
ch
E  hn  l 
E
h
2
E  mc  l 
mc
deBroglie & Bohr consistent
deBroglie started with
h
l
mv
But, for constructive
interference of a body
orbiting in a circle
2r  nl
nh
then, 2r 
mv
nh
mvr 
2
Which is Bohr
Postulate #2
n=2
n=3
n=5
Schroedinger Equation
h        
 2  2  2   V  E
2
8 m  x
y
z 
2
2
2
2
Where:
V = potential energy of electron
E = total energy of electron
 = wave function of electron
For electron in ground
state of hydrogen atom:
(as a 1st approximation)
  Ae
r
ao
Where:
r = distance electron from nucleus
ao = Bohr radius
A
1
a
3
O
1
2
3
2
1
0 node
1 node
2
2
2 node
2
3
nucleus
r
52.9 pm
2

50 100 150 200
Distance from nucleus (pm)
2

100 200 300 400 500 600
Distance from nucleus (pm)
Heisenberg
Uncertainty Principle
h
Dx  D mv  
4
Electron Probability
Space &
Quantum Numbers
Quantum #s or QN
___, ___, ___, ___
n  ml ms
Principal QN = n
n
= 1, 2, 3, . . .
==> size and energy of orbital
==> relative distance of ecloud from nucleus
 for
H:
1
E  k 2
n
Principal QN = n
 for
all other:
2
z
E  k 2
n
where z = nuclear charge
-18
k = +2.179 x 10 joule
Angular Momentum QN =

  0 , 1, 2, ... (n - 1)
 Shape
of e- cloud
corresponds/defines
sub-level
Angular Momentum QN =

n
1
2
3
4
l
0
0,1
# sub
1
2
spectral
s
s, p

Magnetic (orbital) QN = ml (m)
m   ... 0...  
l
0
ml
0
s-orbital
s - orbital
Magnetic (orbital) QN = ml (m)
m   ... 0...  
l
0
1
ml
0
-1,0,+1
s-orbital
(3) p-orbitals
py
pz
px
px
pz
py
(3)
p - orbital
px , py , p z
Magnetic (orbital) QN = ml (m)
m   ... 0...  
l
0
1
2
ml
0
s-orbital
-1,0,+1
(3) p-orbitals
-2,-1,0,+1,+2 (5) d-orbitals
(3)
(1)
dxy , dyz , dxz
dx 2  y2
d - orbitals
(1)
dz 2
Spin QN = ms (s)
1
ms  
2
-
spin of e on own axis
max e
n=1
-
n=1 s
n=2
max e
2
-
n=1 s
n=2 s 2
p 6
n=3
max e
2
8
-
n=1 s
n=2 s 2
p 6
n=3 s 2
p 6
d 10
max e
2
8
18
-
-
n=1 s
n=2 s 2
p 6
n=3 s 2
p 6
d 10
max e = 2n2
2
8
18
Pauli Exclusion Principle
n
l
1
1
2
2
2
2
2
2
2
2
0
0
0
0
1
1
1
1
1
1
ml
0
0
0
0
-1
-1
0
0
1
1
s
+1/2
-1/2
+1/2
-1/2
+1/2
-1/2
+1/2
-1/2
+1/2
-1/2
Orbital
1S
2s
2p
Pauli Exclusion Principle
2 e- in same atom can
have the same set of four
quantum numbers
 No
Electron Probability
Space &
Quantum Numbers
Quantum #s
___, ___, ___, ___
n 
ml ms
Principal QN = n
n
= 1, 2, 3, . . .
==> size and energy of orbital
==> relative distance of ecloud from nucleus
 for
H:
1
E  k 2
n
Principal QN = n
 for
all other:
2
z
E  k 2
n
where z = nuclear charge
-18
k = +2.179 x 10 joule
Angular Momentum QN =

  0 , 1, 2, ... (n - 1)
 Shape
of e- cloud
corresponds/defines
sub-level
Angular Momentum QN =

n
1
2
3
4
l
0
0,1
# sub
1
2
spectral
s
s, p

Magnetic (orbital) QN = ml (m)
m   ... 0...  
l
0
ml
0
(1) s-orbital
Magnetic (orbital) QN = ml (m)
m   ... 0...  
l
0
1
ml
0
-1,0,+1
(1) s-orbital
(3) p-orbitals
Magnetic (orbital) QN = ml (m)
m   ... 0...  
l
0
1
2
ml
0
(1) s-orbital
-1,0,+1
(3) p-orbitals
-2,-1,0,+1,+2 (5) d-orbitals
Magnetic (orbital) QN = ml (m)
m   ... 0...  
l
0
1
2
3
ml
0
-1,0,+1
-2,-1,0,+1,+2
-3,-2,-1,0,+1,+2,+3
(1) s-orbital
(3) p-orbitals
(5) d-orbitals
(7) f-orbitals