PRINCIPLES OF CHEMISTRY I CHEM 1211 CHAPTER 7
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PRINCIPLES OF CHEMISTRY I
CHEM 1211
CHAPTER 7
DR. AUGUSTINE OFORI AGYEMANAssistant professor of chemistryDepartment of natural sciences
Clayton state university
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CHAPTER 7
ELECTRONIC STRUCTURE OF ATOMS
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ELECTROMAGNETIC RADIATION
- Also known as radiant heat or radiant energy
- One of the ways by which energy travels through space
- Consists of electric and magnetic fields which are perpendicularto each other and to the direction of propagation
Examples
heat energy in microwaveslight from the sun
X-ray radio waves
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- Light properties is a key concept for understandingelectronic structure
- Studies of atomic structure has come from observations of the interaction of visible light and matter
- To study the properties of electrons in atoms, it is helpful to understand waves and electromagnetic radiation
ELECTROMAGNETIC RADIATION
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Three Characteristics of Waves
Wavelength (λ) - Distance for a wave to go through a complete cycle
(distance between two consecutive peaks or troughs in a wave)
Frequency (ν)- The number of waves (cycles) per second that pass
a given point in space
Speed (c)- All waves travel at the speed of light in vacuum (3.00 x 108 m/s)
ELECTROMAGNETIC RADIATION
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one second
λ1
λ3
λ2
ν1 = 4 cycles/second
ν2 = 8 cycles/second
ν3 = 16 cycles/second
amplitude
peak
trough
ELECTROMAGNETIC RADIATION
node
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- Inverse relationship between wavelength and frequency
λ α 1/ν
c = λ ν = 3.00 x 108 m/s
λ = wavelength (m)
ν = frequency (cycles/second = 1/s = s-1 = hertz = Hz)
c = speed of light (3.00 x 108 m/s)
ELECTROMAGNETIC RADIATION
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Gamma rays
X rays Ultr-violet
Infrared Microwaves Radio frequency FM Shortwave AM
Vis
ible
Visible Light: VIBGYORViolet, Indigo, Blue, Green, Yellow, Orange, Red
400 – 750 nm
- White light is a blend of all visible wavelengths
- Can be separated using a prism
Wavelength (m)
Frequency (s-1)
10-11 103
1020104
ELECTROMAGNETIC RADIATION
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An FM radio station broadcasts at 90.1 MHz. Calculate the wavelength (in m, nm, Ǻ) of the corresponding radio waves
c = λ ν
λ = ?ν = 90.1 MHz = 90.1 x 106 Hz = 9.01 x 107 Hz
c = 3.00 x 108 m/s
λ = c/ ν = [3.00 x 108 m/s]/[9.01 x 107 Hz]
= 3.33 m = 3.33 x 109 nm = 3.33 x 1010 Ǻ
ELECTROMAGNETIC RADIATION
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Max Planck’s Postulate
- Energy can be gained or lost by whole-number multiples
- Change in energy (E) = nhν
n = an integer (1, 2, 3, …..)
h = Planck’s constant (6.626 x 10-34 joule-second, J-s)
ν = frequency of electromagnetic radiation absorbed or emitted
QUANTIZATION OF ENERGY
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Max Planck’s Postulate
- Energy is quantized and can occur only in discrete units of size, hν
- Matter is allowed to emit or absorb energy only in whole-number multiples
- Each of these small quantities (packets) of energy is the quantum
- Many scientists dismissed Planck’s idea
QUANTIZATION OF ENERGY
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Albert Einstein’s Proposal
- Electromagnetic radiation is itself quantized
- Electromagnetic radiation can be viewed as a stream of‘tiny particles’ called photons
h = Planck’s constant (6.626 x 10-34 joule-second, J-s)ν = frequency of the radiation
λ = wavelength of the radiation
QUANTIZATION OF ENERGY
λ
hchνEphoton
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Photoelectric Effect
- A phenomenon in which electrons are emitted from the surface of a solid metal when light strikes
Eo = hνo
Eo = minimum energy required to remove an electron
νo = threshold frequency below which electrons are not emitted
by a given metal
QUANTIZATION OF ENERGY
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Photoelectric Effect
Below νo - No electrons are emitted irrespective of the light intensity
Above νo - Number of electrons emitted increases with light intensity
- Kinetic energy increases linearly with frequency
QUANTIZATION OF ENERGY
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o2
)k(electron hνhνmv2
1E
m = mass of electron (kg)
v = velocity of electron (m/s)
hν = energy of incident electron (J)
hνo = energy required to remove electron from metal’s surface (J)
Photoelectric Effect
QUANTIZATION OF ENERGY
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E = mc2
E = energy
m = mass
c = speed of light
Einstein’s Equation
QUANTIZATION OF ENERGY
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λc
h
c
hc/λ
c
Em
22
The Dual Nature of Light- Electromagnetic radiation exhibits wave properties and
particulate properties
Einstein’s Equation
QUANTIZATION OF ENERGY
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λv
h
λc
hm
mv
hλ
For a particle with velocity, v
- Particles have wavelength associated with them- Wavelength is inversely proportional to mass
- In conclusion, matter and energy are not distinct
De Broglie’s Equation
QUANTIZATION OF ENERGY
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mv
hλ
Calculate the wavelength of an electron of mass 8.81 x 10-31 kg,traveling at a speed of 1.5 x 107 m/s
λ = ? v = 1.5 x 107 m/s m = 8.81 x 10-31 kg
λ = (6.626 x 10-34 j-s)/[(8.81 x 10-31 kg)(1.5 x 107 m/s)]
= 5.0 x 10-11 m
De Broglie’s Equation
QUANTIZATION OF ENERGY
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THE ATOMIC SPECTRUM
SpectrumIntensity of light as a function of wavelength
Transmission- Electromagnetic radiation (EM) passes through matter
without interaction
Absorption- An atom (or ion or molecule) absorbs EM and
moves to a higher energy state (excited)
Emission- An atom (or ion or molecule) releases energy and
moves to a lower energy state
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THE ATOMIC SPECTRUM
- The excited atoms release energy by emitting light
- The emitted light has various wavelengths called emission spectrum
- The emission spectrum of an atom is called line spectrum
- Lines corresponding to discrete wavelengths are seen when passed through a prism
- Implies electron energy levels are quantized
- The emission spectrum of the sun (white light) is a continuous spectrum when passed through a prism (ROYGBIV-rainbow)
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RYDBERG EQUATION
- A study of the wavelengths from the line spectra of the hydrogen atom
22
21
H n
1
n
1R
λ
1
RH = Rydberg constant = 1.097 x 107 m-1
n1 and n2 are positive integers
n1 < n2
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THE BOHR MODEL
- An electron in a hydrogen atom moves around the nucleus in certain allowed circular orbits
- Negatively charged electrons are attracted to the positively charged nucleus
- Electrons are charged particles under acceleration and hence radiate energy (emit light and lose energy)
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2
218
n
ZJ10x2.178E
n = integer (the larger the n value, the larger the orbital radius)Z = nuclear charge (Z = 1 for hydrogen, one photon)
- If n is infinitely large (n = ∞), E = 0
As the electron gets closer to the nucleus- E becomes more negative
- Energy is released from the system
THE BOHR MODEL
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- Energy required to excite the H electron from one level to another level
(Z = 1)
E = Efinal – Einitial
= energy level n2 – energy level n1
21
22
18
n
1
n
1J10x2.178E
THE BOHR MODEL
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Limitations
- Bohr’s model does not work for any other atoms apart from H
- Electrons do not move in circular orbits around the nucleus
THE BOHR MODEL
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Calculate the energy required to excite the hydrogen electronfrom level n = 1 to level n = 3. Calculate the wavelength oflight that must be absorbed by a H atom in its ground state
to reach its excited state
THE BOHR MODEL
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21
22
18
n
1
n
1J10x2.178E
J10x1.9361
1
3
1J10x2.178ΔE 18
2218
m10x1.03J)10x(1.936
m/s)10xs)(3.00J10x(6.626
ΔE
hcλ 7
18
834
THE BOHR MODEL
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QUANTUM MECHANICS
- Developed by Heisenberg, de Broglie, and Schrödinger
- An electron bound to a nucleus seems to be a standing wave (stationary waves such as those from guitar strings)
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QUANTUM MECHANICS
Schrödinger’s Equation
Ĥψ = Eψ
ψ = wave function (coordinates x, y, z function)
ψ2 = probability of finding an electron at a given point in space
Ĥ = operator
E = total energy of atom (sum of potential and kinetic energies)
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THE WAVE FUNCTION
- A specific wave function is called the orbital
- It is difficult to know precisely the pathway (position and momentum) of an electron in a given time
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THE WAVE FUNCTION
Heisenberg Uncertainty Principle
4π
hΔ(mv)Δx
x = uncertainty in a particle’s position
(mv) = uncertainty in a particle’s momentum
Momentum = product of mass and velocity of an object
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QUANTUM NUMBERS
- Describes various properties of the orbital
Principal Quantum Number (n)- Called the electron shell
- Related to the size and energy of the atomic orbital- Has integral values 1, 2, 3, ……
- Orbital becomes larger as n increases (electron is farther from the nucleus)
- Electron energy increases with increasing n (electron is less tightly bound and energy is less negative)- Orbitals with the same energy (same n value) are said to
be degenerate
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- Describes various properties of the orbital
Angular Momentum (Azimuthal) Quantum Number (l)- Called electron subshell
- Related to the shape of the atomic orbitals- Has integral values 0, 1, 2, 3, ……, n-1 (for each value of n)
- The values of l are assigned letters
Value of l 0 1 2 3 4
Letter used s p d f g
QUANTUM NUMBERS
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- Describes various properties of the orbital
Magnetic Quantum Number (ml)- Related to the orientation of the orbital in space relative to
the other orbitals in the atom- Has integral values between l and –l, including 0 (ml = 2l + 1)
Value of l 0 1 2 3 4
Letter used s p d f g
# of orbitals (ml) 1 3 5 7 9
QUANTUM NUMBERS
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- Describes various properties of the orbital
Electron Spin Quantum Number (ms)
- Can have only one of the two values +1/2 and -1/2
- Electrons can spin in one of two opposite directions
- Two electrons with the same spin are parallel
- Two electrons with different spins are paired(one +1/2 and the other -1/2)
QUANTUM NUMBERS
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Shell 1 1 subshell 1s 2 electrons
Shell 2 2 subshells
3 subshells
4 subshells
Shell 3
Shell 4
2s2p
2 electrons6 electrons10 electrons14 electrons
2 electrons 6 electrons2 electrons6 electrons10 electrons
3s3p3d
4s4p4d4f
- The value of n and the letter for l are used to designate orbitals
n l
0
01
012
0123
Orbitaldesignation
ml
0
0-1,0,+1
0-1,0,+1
-2,-1,0,+1,+2
0-1,0,+1
-2,-1,0,+1,+2-3,-2,-1,0,+1,+2,+3
# of subshells
# ofelectrons
QUANTUM NUMBERS
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For shell n
- The number of orbitals = n2
- The maximum number of electrons = 2n2
QUANTUM NUMBERS
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n
1
2
3
4
Subshell
s
s, p
s, p, d
s, p, d, f
Number of orbitals
1
1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16
Maximum numberof electrons
2
8
18
32
QUANTUM NUMBERS
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PAULI EXCLUSION PRINCIPLE
- In a given atom, no two electrons can have the same set of four quantum numbers (n, l, ml, and ms)
- Electrons in the same orbital has the same n, l, and ml
- These electrons should have different values of ms
- Implies an orbital can hold a maximum of two electrons
- The two electrons in any orbital must have opposite spins
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ORBITAL SHAPES AND ENERGIES
- An orbital is a region of space within an electron subshell
- The electron with a specific energy has a high probability of being found
- An orbital can accommodate a maximum of 2 electrons
- The orbitals contain areas of high probability separated by areas of low probability
- The areas of low probability are called nodes
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The s orbital
- The number of nodes for s orbitals = n-1
- The s orbital is spherical
- Its function always has a positive sign
ORBITAL SHAPES AND ENERGIES
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The p orbital
- Note that there are no 1p orbitals
- p orbitals have 2 lobes separated by a node at the nucleus
- Labeled according to the xyz cordinate axis system 2p orbital with lobes centered along the x-axis is 2px orbital 2p orbital with lobes centered along the y-axis is 2py orbital 2p orbital with lobes centered along the z-axis is 2pz orbital
- The p orbital has positive and negative signs (phases)
- Size of lobes increase with increasing n
ORBITAL SHAPES AND ENERGIES
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The d orbital
- Note that there are no 1d nor 2d orbitals
- The d orbitals have two different fundamental shapes
- dxy, dxz, dyz, dx2-y2: four lobes centered in the indicated planes- dz2: two lobes along the z axis and a belt centered in the xy plane
- Size of lobes increase with increasing n
ORBITAL SHAPES AND ENERGIES
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The f orbital
- Note that there are no 1f, 2f, nor 3f orbitals
- Shapes are more complex than the d orbitals
ORBITAL SHAPES AND ENERGIES
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POLYELECTRONIC ATOMS
- Atoms with more than one electron
Three energy contributions- The kinetic energy of the electrons as they move around the
nucleus- The potenital energy of attraction between the nucleus and the
electrons- The potenital energy of repulsion between the electrons
- Electron repulsion cannot be calculated exactly since electron pathways are not exactly known (electron correlation problem)
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- Orbitals in a given principal quantum level for H atoms are degenerate
- No orbitals are degenerate in polyelectronic atoms
- Order of increasing energy levels s < p < d < f
POLYELECTRONIC ATOMS
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ELECTRON CONFIGURATION
- Elements in the periodic table are arranged in order of increasing atomic number (number of protons)
- Similar to protons, electrons are added one by one to the nucleus to build up elements (Aufbau Principle)
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Rules for assigning electrons
- Electron subshells are filled in order of increasing energy (s, p, d, f)
- All orbitals of a subshell acquire single electrons before any orbital acquire a second electron (Hund’s rule)
- All electrons in singly occupied orbitals must have the same spin
- A maximum of 2 electrons can exist in a given orbital and must have opposite spins (Pauli principle)
ELECTRON CONFIGURATION
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- Ordering of electron subshells is often complicated due to overlapsFor instance, the 3d subshell has higher energy than the 4s subshell
- Use of mnemonic for subshell filling is essential
1s
2s 2p
3s 3p 3d
4s
5s
4p 4d 4f
5p 5d 5f
6s
7s
6p 6d
7p
The (n+1)s orbitals alwaysfill before the nd orbitals
ELECTRON CONFIGURATION
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- Subshells containing electrons are designated using the sunshell numbers and letters (types)
- The number of electrons in a given subshell is indicated by a superscript
Carbon has 6 electrons: 1s22s22p2
Nitrogen has 7 electrons: 1s22s22p3
Sodium has 11 electrons: 1s22s22p63s1
ELECTRON CONFIGURATION
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ORBITAL DIAGRAMS
Hydrogen has electronic configuration written as 1s1
The orbital diagram is
H:
1s
Helium has electronic configuration written as 1s2
The orbital diagram is1s
He:
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Lithium has electronic configuration written as 1s22s1
The orbital diagram is Li:1s
Boron has electronic configuration written as 1s22s22p1
The orbital diagram is1s
B:
Beryllium has electronic configuration written as 1s22s2
The orbital diagram is
2s
2s1s
2p2s
Be:
ORBITAL DIAGRAMS
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Carbon has electronic configuration written as 1s22s22p2
The orbital diagram is C:
1s
Sodium has electronic configuration written as 1s22s22p63s1
The orbital diagram is1s
Na:
Nitrogen has electronic configuration written as 1s22s22p3
The orbital diagram is
2p2s
2s1s 2p
2p2s 3s
N:
ORBITAL DIAGRAMS
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Neon has electronic configuration written as 1s22s22p6
The orbital diagram is Ne:
1s 2p2s
The electron configuration for sodium (Na) can be abbreviated as
[Ne]3s1
Magnesium (Mg) is abbreviated as [Ne]3s2
ABBREVIATED ELECTRON CONFIGURATION
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Chromium (Cr) is expected to be [Ar]4s23d4
But is [Ar]4s13d5
Copper (Cu) is expected to be [Ar]4s23d9
But is [Ar]4s13d10
Tungsten (W) is expected to be [Xe]6s24f145d4
But is [Xe]6s14f145d5
Gold (Au) is expected to be [Xe]6s24f145d9
But is [Xe]6s14f145d10
ANOMALOUS ELECTRON CONFIGURATION