Transcript Chapter 1: Matter and Measurement

Atomic structure
Dr. Ayman H. Kamel
Office:33
Contents
9-1
9-2
9-3
9-4
9-5
9-6
9-7
Electromagnetic Radiation
Atomic Spectra
Quantum Theory
The Bohr Atom
Two Ideas Leading to a New Quantum Mechanics
Wave Mechanics
Quantum Numbers and Electron Orbitals
Contents
9-8
9-9
Quantum Numbers
Interpreting and Representing Orbitals of the
Hydrogen Atom
9-9 Electron Spin
9-11 Electron Configurations
9-12 Electron Configurations and the Periodic Table
9-1 Electromagnetic Radiation
• Electric and magnetic fields
propagate as waves through
empty space or through a
medium.
• A wave transmits energy.
EM Radiation
Low 
High 
Frequency, Wavelength and Velocity
• Frequency () in Hertz—Hz or s-1.
• Wavelength (λ) in meters—m.
• cm
m
nm

(10-2 m)
(10-6 m) (10-9 m)
pm
(10-10 m) (10-12 m)
• Velocity (c)—3x 108 m s-1.
c = λ
λ = c/
= c/λ
Electromagnetic Spectrum
Red
Orange
Yellow
700 nm
450 nm
Green
Blue
Indigo
Violet
Prentice-Hall © 2002
General Chemistry: Chapter 9
Slide 8 of 50
9-3 Quantum Theory
Blackbody Radiation:
Heated bodies emit light
Blackbody Radiation
Iαλ
Classical theory predicts continuous increase of intensity
with wavelength.
1900, Max Planck made the revolutionary proposal
that ENERGY, LIKE MATTER, IS DISCONTINUOUS.
Introduces the concept of QUANTA of energy.
Max Planck, 1900:
Energy, like matter, is discontinuous.
E = h
, h = 6.62607 x 10-34 J s.
The Photoelectric Effect
• Light striking the surface of certain metals
causes ejection of electrons.
•  > o
• e-  I
• ek  
threshold frequency
• Photon strikes a bound electron which absorbs the energy, if
binding energy (known as the work function) is less than photon
energy, the e- is ejected.
The Bohr Atom
-RH
E= 2
n
RH = 2.179  10-18 J
The Bohr Atom
• Electrons move in circular orbits about the
nucleus.
• Motion described by classical physics.
• Fixed set of stationary states (allowed orbits).
– Governed by angular momentum: nh/2π, n=1,
2, 3….
• Energy packets (quanta) are absorbed or emitted
when electrons change stationary states.
• The integral values are allowed are called quantum
numbers.
Energy-Level Diagram
-RH -RH
– 2
ΔE = Ef – Ei =
2
nf
ni
1
1
–
= RH ( 2
) = h = hc/λ
2
ni
nf
• In spite of its accomplishments, there
are weaknesses in Bohr theory. Can’t
explain
1. Spectra of species with more than one
electron.
2. Effect of magnetic fields on emission
spectra.
• Modern quantum theory replaced
Bohr theory in 1926.
Emission and Absorption Spectroscopy
Two Ideas Leading to a New Quantum
Mechanics
• Wave-Particle Duality.
– Einstein suggested particle-like properties of
light could explain the photoelectric effect.
– But diffraction patterns suggest photons are
wave-like.
• deBroglie, 1924
– Small particles of matter may at times display
wavelike properties.
deBroglie and Matter Waves
If matter waves exist for small particles, then
beams of particles such as electrons should
exhibit the characteristic properties of waves:
diffraction.
E = mc2
h = mc2
h/c = mc = p
p = h/λ
λ = h/p = h/mu
X-Ray Diffraction
1927 Davisson aand Germer – Diffraction of slow electrons from a Ni crystal.
1927 Thomson- diffraction from thin metal foil
Nobel prize shared by Davisson and Thomson in 1937.
The Uncertainty Principle
• Werner Heisenberg: It is difficult to
determine the position and velocity of the
electron in the same time.
h
Δx Δp ≥
4π
Schroedinger equation:
• *Wave functions,  are introduced to
describe the allowed shapes and
•
Energies of electron waves (each is called
orbital to distinguish it from Bohr’s orbits).
• For the hydrogen atom, the square of the
function ,2, is directly proportional to the
probability of finding the electron in any
point.
•
To understand this, see the figure, the depth of
colour is proportional to the probability of
finding the electron at a given point. The
closer to the nucleus the higher the
probability of finding the electron.
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Quantum numbers
• When schrodinger equation was solved, many wave functions
(orbitals) were found to satisfy it. Each of these orbitals is
characterized by a series of numbers called quantum numbers,
which describes various properties of the orbital.
The principal quantum number (n)
n has integral value 1, 2, 3, ….
The principal quantum number is related to the size and energy of the
orbital. As n increases, the orbital becomes larger and the electrons
spread more time further from the nucleus. An increase in n also
means higher energy, because the electron is less tightly bound to the
nucleus and the energy is less negative.
An electron for which n=1 is said to be in the first principal level. If n=
2, we are dealing with the 2nd principal level and so on.
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Wave Mechanics
• Standing waves.
– Nodes do not undergo displacement.
2L
λ=
, n = 1, 2, 3…
n
Wave Functions
• ψ, psi, the wave function.
– Should correspond to a
standing wave within the
boundary of the system being
described.
• Particle in a box.
ψ 
2
 n x 
sin

L
 L 
Probability of Finding an Electron
Wave Functions for Hydrogen
• Schrödinger, 1927
Eψ = H ψ
– H (x,y,z) or H (r,θ,φ)
ψ(r,θ,φ) = R(r) Y(θ,φ)
R(r) is the radial wave function.
Y(θ,φ) is the angular wave function.
Quantum numbers (cont.)
The angular momentum quantum number (ℓ)
Has integral values from 0 to n-I for each value of n.
ℓ = 0, 1, 2, …(n-1)
This quantum number is related to the shape of atomic orbitals. The
value of ℓ for a particular orbital is commonly assigned a letter: ℓ
=0 is called s, ℓ = 1 is called p; ℓ = 2 is called d; ℓ = 3 is called
f…….
If n= 1, there is only one possible value of ℓ namely 0. This means
that in the first principal level there is only one sublevel (s).
If n=2, two values of ℓ are possible, 0 and 1. (s, p)
If n= 3, ℓ = 0, 1, 2 (three sublevels) (s, p, d)
If n=4, ℓ = 0, 1, 2, 3 (four sublevels) (s, p, d, f)
In general, in the nth principal level, there are n different
sublevels.
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Quantum numbers (cont.)
The magnetic orbital quantum number (mℓ)
Has integral values between ℓ and -ℓ, including zero.
mℓ = ℓ,….,+1, 0, -1,…., - ℓ
The value of mℓ is related to the orientation of the orbital in space
relative to the other orbitals in the atom.
For s sublevel (ℓ=0), mℓ can have only one value 0. This means that
an s sublevel contains only one orbital referred to as an s orbital.
For p sublevel (ℓ=1), mℓ =1, 0, -1. This means that the p sublevel has
three orbitals .
For d sublevel (ℓ=2), mℓ = 2, 1, 0, -1, -2 (five orbitals)
For f sublevel (ℓ=3), mℓ = 3, 2, 1, 0, -1, -2, -3 (seven orbitals)
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Quantum numbers (cont.)
Magnetic spin quantum number (ms)
• This is related to electron spin. An electron has magnetic
properties that correspond to those of a charged particle spinning
on its axis. Either of two spin is possible cw or ccw.
• This quantum number is not related to any of the previous ones but
it can only have one of two values
ms = +1/2 or –1/2
• Electrons that have the same value of ms are said to have parallel
spin and those of different values of ms are said to be of opposed
spins.
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29
Pauli exclusion principal
• Principal that relates the four quantum numbers to each other. It states
that, no two electrons in an atom can have the same set of
four quantum number.
• It requires that only two electrons can fit into an orbital. Since there
are only two values of ms. Moreover, if two electrons occupy the
same orbital, they must have opposed spins. Otherwise they would
have the same set of four quantum numbers.
• Example Consider the following sets of quantum numbers (n, ℓ,
mℓ , ms ). Which ones could not occur? For the valid identify the
orbital involved.
3, 1, 0, +1/2
Valid, 3p
1, 1, 0, -1/2
not valid, ℓ cannot equal n
2, 0, 0, +1/2
Valid, 2s
4, 3, 2, +1/2
Valid, 4f
2, 1, 0, 0
not valid, ms cannot be zero
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Atomic orbitals, shapes and sizes
P orbitals
S orbitals
D orbitals
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F orbitals
Electron configuration in atoms
• Given the rules stated before , it is possible to assign quantum
numbers to each electron in an atom. Electrons can be assigned to
specific principal level, sublevels and orbitals.
• The simplest way to describe the arrangement of electrons in an atom
is to give its electronic configuration, which shows the number of
electrons, indicated by a superscript, in each sublevel.
• Remember that, electrons enter the available sublevels in order of
increasing sublevel energy. Ordinarily, a sublevel is filled to capacity
before the next one starts to fill. The order of increasing energy for
the sublevels is
This means that the order of filling
orbitals is
1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 4f
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5d 5f….. and so on
Orbital Filling
)n=1( Complete shell
Hund’s Rule:
When several
orbitals of equal
energy are available,
electrons enter singly
with parallel spins.
)n=2( Complete shell
complete
subshell (n=3)
Exception to
Hund’s Rule
(half filled d
subshell)
Exception to
Hund’s Rule
filled d
subshell)
Filled subshell
)n=4(
Compact form of electron configuration
)n=1( ‫غالف مكتمل‬
)n=2( ‫غالف مكتمل‬
Ar (Z=18) 1s22s22p63s23p6
3s
3p
‫تحت غالف مكتمل‬
)n=3(
Hund’s rule of orbital filling (cont.)
• Based on Hund’s rule, it is possible to determine the
number of unpaired electrons in an atom.
• With solids, this is done by studying their behaviour in a
magnetic field.
• If there are unpaired electrons present, the solid will
be attracted into the field. Such a substance is said to be
paramagnetic.
• If the atoms in the solid contain only paired electrons,
it is slightly repelled by the field and is called
diamagnetic.
• With gaseous atoms, the atomic spectrum can be also
used to establish the presence and number of
unpaired electrons.
38
Aufbau Process and Hunds Rule
Filling p Orbitals
Electon Configurations of Some Groups of
Elements
Electron Configurations and the Periodic Table