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Chapter 7 Quantum Theory and the Electronic Structure of Atoms
7.1 From Classical Physics to Quantum Theory
7.3 Bohr’s Theory of the Hydrogen Atom
7.6 Quantum Numbers
7.7 Atomic Orbital's
7.8 Electron Configurations
7.9 The Building-Up Principle
p312: 7.3, 7.8, 7.16, 7.18
p313: 7.32, 7.34, 7.120
p314: 7.56, 7.58, 7.62, 7.66, 7.70
p315: 7.76, 7.78, 7.79, 7.84, 7.88, 7.90, 7.124
Dr Laila Al-Harbi
Properties of Waves
Wavelength ( λ) 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
Frequency ( ν) 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
All electromagnetic radiation
l x n = c
Speed of light (c) in vacuum = 3.00 x 108 m/s
Electromagnetic radiation is the emission and transmission of energy in the form of electromagnetic waves.
All electromagnetic radiation travels at the same velocity: the speed of light (c),
The wave length of the green light from a traffic signal is centered at 522nm . What is the frequency of this radiation?
c = l x n
n = c/ l
= 3 x108 / 522 x10-9
= 5.57 x1014 Hz
What is the l in meter (m) of an electromagnetic waves whose frequncy is 3.64 x107Hz?
l = c/ n
= 3 x108 / 3.64 x107
= 7.25 m
Planck’s Quantum Theory
E = h x n
E = h x c/l
Planck’s constant (h)
h = 6.63 x 10-34 J•s
Energy (light) is emitted or absorbed in discrete units (quantum).
When copper is bombarded with high-energy electrons, X rays are emitted. Calculate the energy (in joules) associated with the photons if the wavelength of the X rays is 0.154 nm.
E = h x c / l
E = 6.63 x 10-34 (J•s) x 3.00 x 10 8 (m/s) / 0.154 x 10-9 (m)
E = 1.29 x 10 -15 J
Line Emission Spectrum of
7.3Bohr’s Theory of the Hydrogen Atom
Emission Spectra of the Hydrogen atom
En = -RH
Bohr’s Model of
the Atom (1913)
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
ni = 3
ni = 2
nf = 2
DE = RH
Ef = -RH
Ei = -RH
nf = 1
Ephoton = DE = Ef - Ei
When photon is emitted
ni > nf
DE is negative
Energy is lost to the surrounding
When photon is absorbed
ni < nf
DE is positive
Energy is gained from the surrounding
7.6 Quantum Numbers
Electrons in multi-electron atoms can be classified into a series of:
shells → subshells → orbitals
Three quantum numbers are required to describe the distribution of electrons in hydrogen and other atoms.
A fourth quantum the spin quantum number –describe the behavior of a specific electron and completes the description of electron in the atoms
Principal Quantum Number, n
The principal quantum number, n, describes the energy level on which the orbital resides and to distance from nucleus (size)
The maximum number of electrons in principle quantum number n = 2n2
The values of n are integers ≥ 0.
possible values of n = 1, 2, 3, 4, .....
Angular momentum Quantum Number, ℓ
related to shape of various subshells within a given shell
Allowed values of ℓ are integers ranging from 0 to n − 1.
We use letter designations to communicate the different values of ℓ and, therefore, the shapes and types of orbitals.
Value of ℓ
Type of orbital
Magnetic Quantum Number, mℓ
Describes the three-dimensional orientation of the orbital.
Values are integers ranging from - ℓ to ℓ :
−ℓ ≤ ml ≤ ℓ.
The number of orbitals in each subshell ℓ equal =2 ℓ +1
mℓ =2 ℓ +1
Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc
Spin Quantum Number, ms
In the 1920s, it was discovered that two electrons in the same orbital do not have exactly the same energy.
The “spin” of an electron describes its magnetic field, which affects its energy.
No two electrons in the same atom can have exactly the same energy.
For example, no two electrons in the same atom can have identical sets of quantum numbers.
The spin quantum number has only 2 allowed values:
ms = +1/2 and −1/2.
7.7 Atomic orbitals
Value of ℓ= 0.
Spherical in shape.
Radius of sphere increases with increasing value of n.
Value of ℓ = 1.
Have two lobes with a node between them.
mℓ =2 ℓ +1 = 2×1+1 = 3
Value of mℓ = 1,0,-1 ( Px , Pz , Py)
Value of ℓ is 2.
mℓ =2 ℓ +1 = 2×2+1 = 5
Value of mℓ = 2,1,0,-1,-2
( dxy , dzy , dxz ,d z2 d x2- y2)
Four of the five orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center.
Energies of Orbitals
For a one-electron hydrogen atom, orbitals on the same energy level have the same energy.
That is, they are degenerate.
The energies of H orbitals increase as follows
As the number of electrons increases, though, so does the repulsion between them.
Therefore, in many-electron atoms, orbitals on the same energy level are no longer degenerate.
Order of orbitals (filling) in multi-electron atom
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s
number of electrons
in the orbital or subshell
quantum number ℓ
7.8 Electron configuration
is how the electrons are distributed among the various atomic orbitals in an atom.
The four quantum numbers n, ℓ, mℓ and ms enable us to label completely an electron in any orbital in any atom.
The value of ms has no effect on the energy ,size, shape , or orintation of an orbital, but it determines , how electron are arranged in an orbital.
Each box represents one orbital.
Half-arrows represent the electrons.
The direction of the arrow represents the spin of the electron.
The Pauli exclusion principle
“No two electrons in the same atom can have identicalvalues for all four of their quantum numbers”.
i.e.: no more than two electrons can occupy the sameorbital, and that two electrons in the same orbital must have opposite spins
Diamagnetism and paramagnetism
all electrons paired
repelled by magnet
attracted by a magnetic
The Shielding Effect (many electron atoms)
Electrons in the smaller orbitals (lower energy) are closerto nucleus (e.g., 1s) than electrons in larger orbitals (e.g., 2p, 3s)
Thus they are "shielded" from the attractive forces of the nucleus.
This causes slight increase in energy of the more distant electrons.
thus 4s orbital is lower in energy than the 3d orbital .
The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins
The Aufbau principle dictates that as protons are added one to the nucleus to build up the elements, electrons are similarly added to the atomic orbitals.
alkali metals and alkaline earth metals fill the s orbitals last main group elements fill the p orbitals last transition metals fill the d orbitals last lanthanides (4f) and actinides (5f) fill the f orbitals last
Elements in same group have same valence shell econfigurations
e.g., group V:
7N 2s2 2p3
15P 3s2 3p3
33As 4s2 4p3
51Sb 5s2 5p3
83Bi 6s2 6p3
Dr. Laila Al-Harbi
Short-hand notation -- show preceding inert gas configuration plus the additional electrons
Some irregularities occur when there are enough electrons to half-fill s and d orbitals on a given row.
For instance, the electron configuration for copper 29Cu is
[Ar] 4s1 3d 10 rather than the expected [Ar] 4s2 3d 9.
the electron configuration for 24Cr is
[Ar] 4s1 3d 5 rather than the expected [Ar] 4s2 3d 4.
alkali metals and alkaline earth metals fill the s orbitals last main group elements fill the p orbitals last transition metals fill the d orbitals last lanthanides (4f) and actinid