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Atomic Structure
Wave/Particle Concept

Atomic H Spectrum

Quantization

Bohr Model

Quantum Mechanics

Heisenberg Uncertainty

Quantum Numbers

Applications
Electron Configuration
Electron Affinity
Ionization Energy
Electronegativity
Size

Energy Levels

The Wave Nature of Light
• All waves have a characteristic wavelength, λ, and
amplitude, A
...

• Speed of a wave, c, is given by its frequency multiplied
by its wavelength:

c = λ ⋅ν

• For light, speed = c = 3
...

• A Brief History of Time

The Wave Nature of Light

The Wave Nature of Light

The Wave Nature of Light

X – rays
Wavelength: λ (m)
Frequency: ν (s-1)
Energy: E (J)

Microwaves

1
...
00x10-2 m

Comment(s)

Quantized Energy and Photons
• Planck: energy can only be absorbed or released from
atoms in certain amounts called quanta
...
626 × 10-34 J s )
...

• The energy of one photon is:

E = h ⋅ν

Nature of Waves: Quantized Energy and Photons
X – rays
Wavelength: λ (m)
Frequency: ν (s-1)
Energy: E (J)

Microwaves

1
...
00x10-2 m

Comment(s)

Line Spectra and the Bohr Model

•
•
•
•

Line Spectra
Radiation composed of only one wavelength is called
monochromatic
...

White light can be separated into a continuous spectrum
of colors
...


Line Spectra and the Bohr Model
Bohr Model
• Colors from excited gases arise because electrons move between energy states in
the atom
...

• After lots of math, Bohr showed that
E n = (− 2
...
e
...


Line Spectra and the Bohr Model
Bohr Model

∆E = E f − Ei = hν

E n = (− 2
...
178 × 10

• When ni > nf, energy is emitted
...
626 ⋅ 10

− 34

Red Line :

∆ E i
...
f

8

J⋅ s

c := 3
...
178 ⋅ 10

− 18


J⋅ 

− 18

2

m



ni 

2

1
1 
 2 − 2
3 
2

∆ E 3to2

n i := 4

∆ E 4to2 := − 2
...


n f := 2

∆ E 3to2 := − 2
...
626 ⋅ 10

∆ E 3to2 = − 3
...
00 ⋅ 10 ⋅ m ⋅ s

− 1

− 19

)

∆ E 3to2

= 3
...
1 nm

J

n f := 2

− 18

J⋅ 

1
1 
 2 − 2
4 
2

λ 4to2 :=

6
...
084 × 10

− 34

(

8

⋅ J ⋅ s ⋅ 3
...
8 nm

Line Spectra and the Bohr Model: Balmer Series Calculations

Line Spectra and the Bohr Model
Limitations of the Bohr Model
• Can only explain the line spectrum of hydrogen
adequately
...

• Cannot explain multi-lines with each color
...

• Electrons can have both wave and particle properties
...

• Using Einstein’s and Planck’s equations, de Broglie
h
showed:
λ=
mv
• The momentum, mv, is a particle property, whereas λ is a
wave property
...


The Wave Behavior of Matter
The Uncertainty Principle
• Heisenberg’s Uncertainty Principle: on the mass scale
of atomic particles, we cannot determine exactly the
position, direction of motion, and speed simultaneously
...

• If ∆x is the uncertainty in position and ∆mv is the
uncertainty in momentum, then
h
∆x·∆mv ≥
4π

Energy and Matter
Size of Matter

Particle Property

Wave Property

Large –
macroscopic

Mainly

Unobservable

Intermediate –
electron

Some

Some

Small – photon

Few

Mainly

E = m c2

Quantum Mechanics and Atomic Orbitals

• Schrödinger proposed an equation that contains both
wave and particle terms
...

• The wave function gives the shape of the electronic
orbital
...
]
• The square of the wave function, gives the probability of
finding the electron ( electron density )
...
’
These orbitals provide
the electron density
distributed about the
nucleus
...


Quantum Mechanics and Atomic Orbitals
Orbitals and Quantum Numbers
• Schrödinger’s equation requires 3 quantum numbers:
1
...
This is the same as Bohr’s
n
...
( n = 1 , 2 , 3 , 4 , …
...
Angular Momentum Quantum Number,
...
The values of
begin at
0 and increase to (n - 1)
...
Usually we refer to the s, p, d
and f-orbitals
...
Magnetic Quantum Number, m
...
The magnetic quantum number has integral
values between and +
...


Quantum Numbers of Wavefuntions
Quantum #

Symbol

Values

Description

Principal

n

1,2,3,4,…

Size & Energy of orbital

0,1,2,…(n-1)
for each n

Shape of orbital

Angular
Momentum
Magnetic

m

- …,0,…+
for each

Relative orientation of orbitals within
same

Spin

ms

+1/2 or –1/2

Spin up or Spin down

Angular Momentum Quantum #
(

Name of Orbital

)
0

s (sharp)

1

p (principal)

2

d (diffuse)

3

f (fundamental)

4

g

Quantum Mechanics and Atomic Orbitals
n

ℓ

Orbital Name

mℓ (“sub-orbitals)

Comment

Quantum Mechanics and Atomic Orbitals
Orbitals and Quantum Numbers

Representations of Orbitals
The s-Orbitals

Representations of Orbitals
The p-Orbitals

d-orbitals

Orbitals and Their Energies
Orbitals CD

ManyMany-Electron Atoms

ManyMany-Electron Atoms
Electron Spin and the Pauli Exclusion
Principle

ManyMany-Electron Atoms
Electron Spin and the Pauli Exclusion
Principle
• Since electron spin is quantized, we define ms = spin
quantum number = ± ½
...

•

Therefore, two electrons in the same orbital must have
opposite spins
...
27

Orbitals CD

Figure 6
...
28

Orbitals CD

Orbitals and Their Energies
Orbitals CD

ManyMany-Electron Atoms

Electron Configurations
Species

Electron Configuration

Box Orbital

Comment

Electron Configurations
Species

Electron Configuration

Box Orbital

Comment

Metals, Nonmetals, and Metalloids
Metals

Figure 7
...


Figure 7
...
6

Figure 7
...
9

Electron Affinities
• Electron affinity is the opposite of ionization energy
...
11: Electron Affinities

Group Trends for the Active Metals
Group 1A: The Alkali Metals

Group Trends for the Active Metals
Group 2A: The Alkaline Earth Metals

Group Trends for Selected Nonmetals
Group 6A: The Oxygen Group

Group Trends for Selected Nonmetals
Group 7A: The Halogens

Group Trends for the Active Metals

•
•

•
•

Group 1A: The Alkali Metals
Alkali metals are all soft
...

Alkali metals react with water to form MOH and
hydrogen gas:
2M(s) + 2H2O(l) → 2MOH(aq) + H2(g)

Group Trends for the Active Metals
Group 2A: The Alkaline Earth Metals
• Alkaline earth metals are harder and more dense than the
alkali metals
...

Mg(s) + Cl2(g) → MgCl2(s)
2Mg(s) + O2(g) → 2MgO(s)
• Be does not react with water
...
Ca onwards:
Ca(s) + 2H2O(l) → Ca(OH)2(aq) + H2(g)

Atomic Structure
c = λ ⋅ν

Wave/Particle Concept

Atomic H Spectrum

E =

h ⋅c

λ

( per

photon

Heisenberg Uncertainty

[ n , l , ml , ms ]

Quantization

)

Bohr Model

Quantum Mechanics

Quantum Numbers

Applications

Energy Levels

∆Ei −> f

 1 1
= −2

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