Quantum Theory and the Electronic Structure of Atoms

1
Quantum Theory and the Electronic Structure of
Atoms
Chapter 7
2
Properties of Waves
Wavelength (l) is the distance between identical
points on successive waves.
Amplitude is the vertical distance from the
midline of a wave to the peak or trough.
7.1
3
Properties of Waves
Frequency (n) is the number of waves that pass
through a particular point in 1 second (Hz 1
cycle/s).
The speed (u) of the wave l x n
7.1
4
Maxwell (1873), proposed that visible light
consists of electromagnetic waves.
Electromagnetic radiation is the emission and
transmission of energy in the form of
electromagnetic waves.
Speed of light (c) in vacuum 3.00 x 108 m/s
All electromagnetic radiation l x n c
7.1
5
7.1
6
l x n c
l c/n
l 3.00 x 108 m/s / 6.0 x 104 Hz
l 5.0 x 103 m
l 5.0 x 1012 nm
7.1
7
Mystery 1, Black Body ProblemSolved by Planck
in 1900
Energy (light) is emitted or absorbed in discrete
units (quantum).
E h x n Plancks constant (h) h 6.63 x 10-34
Js
7.1
8
Mystery 2, Photoelectric EffectSolved by
Einstein in 1905
hn

• Light has both
• wave nature
• particle nature

KE e-
Photon is a particle of light
hn KE BE
KE hn - BE
7.2
9
E h x n
E h x c / l
E 6.63 x 10-34 (Js) x 3.00 x 10 8 (m/s) /
0.154 x 10-9 (m)
E 1.29 x 10 -15 J
7.2
10
7.3
11
7.3
12
Bohrs Model of the Atom (1913)
THIS CALCULATION HAS BEEN REMOVED

• e- can only have specific (quantized) energy
  values
• light is emitted as e- moves from one energy
  level to a lower energy level

n (principal quantum number) 1,2,3,
RH (Rydberg constant) 2.18 x 10-18J
7.3
13
7.3
14
THIS CALCULATION HAS BEEN REMOVED
Ephoton DE Ef - Ei
7.3
15
THIS CALCULATION HAS BEEN REMOVED
Ephoton 2.18 x 10-18 J x (1/25 - 1/9)
Ephoton DE -1.55 x 10-19 J
Ephoton h x c / l
l h x c / Ephoton
l 6.63 x 10-34 (Js) x 3.00 x 108 (m/s)/1.55 x
10-19J
l 1280 nm
7.3
16
De Broglie (1924) reasoned that e- is both
particle and wave.
2pr nl l h/mu u velocity of e- m mass
of e-
THIS CALCULATION HAS BEEN REMOVED
7.4
17
THIS CALCULATION HAS BEEN REMOVED
l h/mu
m in kg
h in Js
u in (m/s)
l 6.63 x 10-34 / (2.5 x 10-3 x 15.6)
l 1.7 x 10-32 m 1.7 x 10-23 nm
7.4
18
Chemistry in Action Element from the Sun
In 1868, Pierre Janssen detected a new dark line
in the solar emission spectrum that did not match
known emission lines
Mystery element was named Helium
In 1895, William Ramsey discovered helium in a
mineral of uranium (from alpha decay).
19
Chemistry in Action Laser The Splendid Light
Laser light is (1) intense, (2) monoenergetic,
and (3) coherent
20
Chemistry in Action Electron Microscopy
le 0.004 nm
STM image of iron atoms on copper surface
21
Schrodinger Wave Equation

• In 1926 Schrodinger wrote an equation that
  described both the particle and wave nature of
  the e-
• Wave function (Y) describes
• . energy of e- with a given Y
• . probability of finding e- in a volume of space
• Schrodingers equation can only be solved exactly
  for the hydrogen atom. Must approximate its
  solution for multi-electron systems.

7.5
22
QUANTUM NUMBERS

• The shape, size, and energy of each orbital is a
  function of 3 quantum numbers which describe the
  location of an electron within an atom or ion
• n (principal) --- energy level
• l (orbital) --- shape of orbital
• ml (magnetic) --- designates a particular
  suborbital
• The fourth quantum number is not derived from the
  wave function
• s (spin) --- spin of the electron
  (clockwise or counterclockwise ½ or ½)

23
Schrodinger Wave Equation
Y fn(n, l, ml, ms)
principal quantum number n
n 1, 2, 3, 4, .
distance of e- from the nucleus
7.6
24
7.6
25
Schrodinger Wave Equation
Y fn(n, l, ml, ms)
angular momentum quantum number l
for a given value of n, l 0, 1, 2, 3, n-1
l 0 s orbital l 1 p orbital l 2
d orbital l 3 f orbital
n 1, l 0 n 2, l 0 or 1 n 3, l 0, 1,
or 2
Shape of the volume of space that the e-
occupies
7.6
26
Types of Orbitals (l)
s orbital
p orbital
d orbital
27
7.6
28
p Orbitals

• this is a p sublevel with 3 orbitals
• These are called x, y, and z

There is a PLANAR NODE thru the nucleus, which is
an area of zero probability of finding an electron
3py orbital
29
p Orbitals

• The three p orbitals lie 90o apart in space

30
7.6
31
f Orbitals

• For l 3, f sublevel with 7 orbitals

32
Schrodinger Wave Equation
Y 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
7.6
33
ml -1
ml 0
ml 1
ml -2
ml -1
ml 0
ml 1
ml 2
7.6
34
Schrodinger Wave Equation
Y fn(n, l, ml, ms)
spin quantum number ms
ms ½ or -½
ms -½
ms ½
7.6
35
Schrodinger Wave Equation
Y fn(n, l, ml, ms)
Existence (and energy) of electron in atom is
described by its unique wave function Y.
Pauli exclusion principle - no two electrons in
an atom can have the same four quantum numbers.
Each seat is uniquely identified (E, R12,
S8) Each seat can hold only one individual at a
time
7.6
36
7.6
37
Schrodinger Wave Equation
Y fn(n, l, ml, ms)
Shell electrons with the same value of n
Subshell electrons with the same values of n
and l
Orbital electrons with the same values of n, l,
and ml
If n, l, and ml are fixed, then ms ½ or - ½
Y (n, l, ml, ½)
or Y (n, l, ml, -½)
An orbital can hold 2 electrons
7.6
38
If l 1, then ml -1, 0, or 1
2p
3 orbitals
If l 2, then ml -2, -1, 0, 1, or 2
3d
5 orbitals which can hold a total of 10 e-
7.6
39
Orbital Diagrams Energy of orbitals in a
multi-electron atom
Energy depends on n and l
7.7
40
Fill up electrons in lowest energy orbitals
(Aufbau principle)
Li 3 electrons
Be 4 electrons
B 5 electrons
C 6 electrons
Li 1s22s1
Be 1s22s2
B 1s22s22p1
H 1 electron
He 2 electrons
H 1s1
He 1s2
7.7
41
C 6 electrons
N 7 electrons
O 8 electrons
F 9 electrons
Ne 10 electrons
C 1s22s22p2
N 1s22s22p3
O 1s22s22p4
F 1s22s22p5
Ne 1s22s22p6
7.7
42
Order of orbitals (filling) in multi-electron atom
1s 5p
7.7
43
Why are d and f orbitals always in lower energy
levels?

• d and f orbitals require LARGE amounts of energy
• Its better (lower in energy) to skip a sublevel
  that requires a large amount of energy (d and f
  orbtials) for one in a higher level but lower
  energy
• This is the reason for the diagonal rule! BE SURE
  TO FOLLOW THE ARROWS IN ORDER!

44
Electron configuration is how the electrons are
distributed among the various atomic orbitals in
an atom.
1s1
Orbital diagram
H
7.8
45
Mg 12 electrons
1s
1s22s22p63s2
2 2 6 2 12 electrons
Abbreviated as Ne3s2
Ne 1s22s22p6
Cl 17 electrons
1s
1s22s22p63s23p5
2 2 6 2 5 17 electrons
Last electron added to 3p orbital
n 3
l 1
ml -1, 0, or 1
ms ½ or -½
7.8
46
Outermost subshell being filled with electrons
7.8
47
Paramagnetic
Diamagnetic
unpaired electrons
all electrons paired
7.8
48
7.8
49
Exceptions to the Aufbau Principle

• Remember d and f orbitals require LARGE amounts
  of energy
• If we cant fill these sublevels, then the next
  best thing is to be HALF full (one electron in
  each orbital in the sublevel)
• There are many exceptions, but the most common
  ones are
• d4 and d9
• For the purposes of this class, we are going to
  assume that ALL atoms (or ions) that end in d4 or
  d9 are exceptions to the rule. This may or may
  not be true, it just depends on the atom.

50
Exceptions to the Aufbau Principle

• d4 is one electron short of being HALF full
• In order to become more stable (require less
  energy), one of the closest s electrons will
  actually go into the d, making it d5 instead of
  d4.
• For example Cr would be Ar 4s2 3d4, but since
  this ends exactly with a d4 it is an exception to
  the rule. Thus, Cr should be Ar 4s1 3d5.
• Procedure Find the closest s orbital. Steal one
  electron from it, and add it to the d.

51
Try These!

• Write the shorthand notation for
• Cu
• W
• Au

Ar 4s1 3d10 Xe 6s1 4f14 5d5 Xe 6s1 4f14 5d10
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Exceptions to the Aufbau Principle

• The next most common are f1 and f8
• The electron goes into the next d orbital
• Example
• La Xe6s2 5d1
• Gd Xe6s2 4f7 5d1

53
Keep an Eye On Those Ions!

• Electrons are lost or gained like they always are
  with ions negative ions have gained electrons,
  positive ions have lost electrons
• The electrons that are lost or gained should be
  added/removed from the highest energy level (not
  the highest orbital in energy!)

54
Keep an Eye On Those Ions!

• Tin
• Atom Kr 5s2 4d10 5p2
• Sn4 ion Kr 4d10
• Sn2 ion Kr 5s2 4d10
• Note that the electrons came out of the highest
  energy level, not the highest energy orbital!