Silberberg - Ch. 7

1
Chapter 7 Quantum Theory and
Atomic Structure
7.1 The Nature of Light 7.2 Atomic Spectra 7.3
The Wave - Particle Duality of Matter and
Energy 7.4 The Quantum - Mechanical Model of the
Atom
2
Electromagnetic Radiation

• WAVELENGTH - The distance (in meters) between
  identical points on successive waves. ( ? )
• FREQUENCY - The number of waves (or cycles) that
  pass through a particular point per second. (?)
  ENERGY of radiation is function of frequency.

? ? ??
c

• AMPLITUDE - The vertical distance from the
  midline to a peak, or trough in the wave.

3
Fig. 7.1
4
Fig. 7.2
5
Fig. 7.3
6
The Spectrum of Electromagnetic Radiation

• The wavelength of visible light is between 400
  and 700 nanometers
• Radio, TV , microwave and infrared radiation have
  longer wavelengths (shorter frequencies), and
  lower energies than visible light.
• Gamma rays and X-rays have shorter wavelengths
  (larger frequencies), and higher energies than
  visible light!

7
Calculation of Frequency from Wavelength
Problem The wavelength of an x-ray is 1.00 x10
-9 m or 1 nm, what is the frequency of this
x-ray?
Plan Use the relationship between wavelength
and frequency to obtain the answer. wavelength x
frequency speed of light!
Solution l ? c therefore ? c / l
speed of light (m/s) wavelength(m)
frequency(cycles/sec)

3.00 x 108 m/s 1.00 x 10 - 9 m
frequency 3.00 x
1017 cycles/sec
8
Different Behaviors of Waves and Particles
Fig. 7.4
9
Demonstration of the Photoelectric Effect
Fig. 7.7
10
The Photoelectric Effect - I

• Below the threshold energy, nothing occurs !
• Above the threshold, the kinetic energy of the
  ejected electrons is proportional to the
  frequency of the light.
• Also, when above the threshold, as intensity of
  the light increases, so does the number of
  ejected electrons.
• All metals experience this effect, but each has a
  unique threshold frequency.

11
The Photoelectric Effect - II

• Albert Einstein
• Theorized Photons
• Won Nobel prize - 1921
• Photons have an energy equal to
• E h?
• h Planks Constant, and is equal to
• 6.6260755 x 10 - 3 4Jsec

12
Calculation of Energy from Frequency
Problem What is the energy of a photon of
electromagnetic radiation being emitted by radio
station KBSG 97.3 FM ( 97.3 x 108
cycles/sec)? What is the energy of a gamma ray
emitted by Cs137 if it has a frequency of 1.60 x
1020/s? Plan Use the relationship between
energy and frequency to obtain the energy of the
electromagnetic radiation (E hv). Solution
EKBSG hv (6.626 x 10 -34Js)(9.73 x 109/s)
6.447098 x 10 -24J
EKBSG 6.45 x 10 - 24 J
Egamma ray hv ( 6.626 x 10-34Js )( 1.60 x
1020/s ) 1.06 x 10 -13J
Egamma ray 1.06 x 10 - 13J
13
Light Has Momentum

• momentum p mu mass x velocity
• p Planks constant / wavelength
• or p mu h/wavelength
• wavelength h / mu de Broglies
  equation
• de Broglies expression gives the wavelength
  relationship of a particle traveling a velocity
  u !!

14
The de Broglie Wavelengths of Several Objects
Substance Mass (g) Speed (m/s)
? (m)
Slow electron 9 x 10 - 28
1.0 7 x 10 - 4 Fast
electron 9 x 10 - 28 5.9
x 106 1 x 10 -10 Alpha particle
6.6 x 10 - 24 1.5 x 107
7 x 10 -15 One-gram mass 1.0
0.01
7 x 10 - 29 Baseball 142
25.0 2
x 10 - 34 Earth 6.0 x 1027
3.0 x 104 4 x 10
- 63
Table 7.1 (p. 274)
15
de Broglie Wavelength Calc. - I
Problem Calculate the wavelength of an electron
traveling 1 of the speed of light ( 3.00 x
108m/s). Plan Use the de Broglie relationship
with the mass of the electron, and its speed.
Express the wavelength in meters and
nanometers. Solution
electron mass 9.11 x 10 -31 kg
velocity 0.01 x 3.00 x 108 m/s 3.00 x 106 m/s
h m x u
6.626 x 10 - 34Js ( 9.11 x 10 -
31kg )( 3.00 x 106 m/s )
wavelength

kg m2 s2
J
therefore
wavelength 0.24244420 x 10 - 9 m 2.42 x 10
-10 m 0.242 nm
16
Light and Atoms

• When an atom gains a photon, it enters an excited
  state.
• This state has too much energy - the atom must
  lose it and return back down to its ground state,
  the most stable state for the atom.
• An energy level diagram is used to represent
  these changes.

17
A desktop analogy for the H atoms energy
Fig. 7.11
18
Energy Level Diagram

• Energy
• Excited States
• photons path
• Ground State

Light Emission Light Emission
Light Emission
19
The Line Spectra of Several Elements
Fig. 7.8
20
Three Series of Spectral Lines of Atomic
Hydrogen
Fig. 7.9
21
Fig. 7.10
22
Heisenberg Uncertainty Principle

• It is impossible to know simultaneously both the
  position and momentum (mass X velocity) of a
  particle with certainty !

23
Quantum Mechanical Model of the Atom
Wave function called ORBITAL based upon
probability of location of electron at any given
moment in time.
ORBITAL given as a set of quantum numbers
No 2 electrons of same atom can have the same set
of 4 quantum numbers!!! (Pauli Exclusion
Principle)
24
A Radial Probability Distribution of Apples
25
Fig. 7.15
26
Quantum Numbers - I

• 1) Principal Quantum Number n
• Also called the energy quantum number,
  indicates the approximate distance from the
  nucleus .
• Denotes the electron energy shells around the
  atom, and is derived directly from the
  Schrodinger equation.
• The higher the value of n , the greater the
  energy of the orbital, and hence the energy of
  electrons in that orbital.
• Positive integer values of n 1 , 2 , 3 , etc.

27
Quantum Numbers - II

• 2) Azimuthal L
• Denotes the different energy sublevels within the
  main level n
• Also indicates the shape of the orbitals around
  the nucleus.
• Positive integer values of L are 0 (
  n-1 )
• n 1 , L 0 n 2 ,
  L 0 and 1
• n 3 , L 0 , 1 , 2

28
Quantum Numbers - III

• 3) Magnetic Quantum Number - mL Also called
  the orbital orientation quantum
• denotes the direction or orientation in a
  magnetic field - or it denotes the different
  magnetic geometries around the nucleus - three
  dimensional space
• values can be positive and negative (-L 0
  L)
• L 0 , mL 0 L 1 , mL
  -1,0,1
• L 2 , mL -2,-1,0,1,2

29
Quantum Numbers
Allowed Values
n
1 2 3
4
L
0 0 1 0 1
2 0 1 2 3
mL
0 0 -1 0 1 0 -1 0 1
0 -1 0 1
-2 -1
0 1 2 -2 -1 0 1 2
-3 -2
-1 0 1 2 3
30
Determining Quantum Numbers for an Energy Level
(Like S.P. 7.5)
Problem What values of the azimuthal (L) and
magnetic (m) quantum numbers are allowed for a
principal quantum number (n) of 4? How many
orbitals are allowed for n4? Plan We determine
the allowable quantum numbers by the rules given
in the text. Solution The L values go from 0 to
(n-1), and for n3 they are L
0,1,2,3. The values for m go from -L to zero to
L For L 0, mL 0 L 1,
mL -1, 0, 1 L 2, mL -2, -1,
0, 1, 2 L 3, mL -3, -2, -1, 0,
1, 2, 3 There are 16 mL values, so there are
16 orbitals for n4! as a check, the total
number of orbitals for a given value of n is n2,
so for n 4 there are 42 or 16 orbitals!
31
Fig 7.16
32
Radial probability Accurate
Stylized Combined
area distribution
representation of the 2p
of the three 2p
of the 2p
distribution orbitals 2px,
2py
distribution
and 2pz orbitals


Fig. 7.17
33
Fig. 7.18
34
Fig. 7.19
35
Quantum Numbers Noble Gases
Electron Orbitals
Number of Electrons Element
1s2
2
He
1s2 2s22p6
10
Ne
1s2 2s22p6 3s23p6
18 Ar
1s2 2s22p6 3s23p6 4s23d104p6
36 Kr
1s2 2s22p6 3s23p6 4s23d104p6 5s24d105p6
54 Xe
1s2 2s22p6 3s23p6 4s23d104p6 5s24d105p6
6s24f14 5d106p6 86 Rn
1s2 2s22p6 3s23p6 4s23d104p6 5s24d105p6
6s24f145d106p6 7s25f146d10?
36
The Periodic Table of the Elements
Electronic Structure
He
H
Ne
F
O
N
C
B
Li
Be
Ar
Cl
S
P
Si
Al
Na
Mg
Kr
Zn
Cu
Ni
Co
Fe
Mn
Cr
V
Ti
Sc
Br
Se
As
Ge
Ga
K
Ca
Xe
Cd
Ag
Pd
Rh
Ru
Tc
Mo
Nb
Zr
Y
I
Te
Sb
Sn
In
Rb
Sr
Rn
Hg
Au
Pt
Ir
Os
Re
W
Ta
Hf
La
At
Po
Bi
Pb
Tl
Cs
Ba
Ac
Rf
Ha
Fr
Ra
Sg
Ce
Pr
Nd
Pm
Sm
Eu
Gd
Tb
Dy
Ho
Er
Tm
Yb
Lu
Th
Pa
U
Np
Pu
Am
Cm
Bk
Cf
Es
Fm
Md
No
Lr
S Orbitals
P Orbitals f Orbitals
d Orbitals