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UNIT 2 – STRUCTURE & PROPERTIES
Origins of Quantum Theory
 Kirchhoff’s work on “blackbodies” was start of quantum theory but
Planck was credited with starting quantum theory
 “blackbody” used to describe an ideal perfectly black object i.e.
does not reflect any light & emits various forms of light as a result
of temperature
Planck’s Quantum Hypothesis
 when an object is heated it was observed that it will glow
 initially it will glow red, then white, these changes do not depend
on the composition of the solid
 if we look at the intensity of the different colours we get a bell
shaped curve
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 scientists couldn’t explain why the bell curve didn’t follow what
was expected “the classical theory” until Planck came up with an
equation to explain this (1900)
 Planck’s theory was that the energies of the atoms in the solids
were multiples of small quantities of energy i.e. energy was not
continuous
 Einstein continued this work by pointing out that Planck’s
hypothesis led to the conclusion that light emitted by a hot solid is
also “quantized” i.e. sent out as bursts of energy
 Each of these bursts were referred to as a quantum of energy
(read money analogy in text on page 169)
 lead to thinking that as temperature increased, the proportion of
each larger quantum becomes greater
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The Photoelectric Effect
 Maxwell proposed that light was an electromagnetic wave
composed of electric and magnetic fields that could exert forces
on charged particles (classical theory of light)
 Hertz discovered photoelectric effect which involved the effect of
electromagnetic radiation or light on substances
 classical theory said that the intensity (brightness) shining on the
metal would determine the kinetic energy of the freed electrons i.e.
the brighter the light, the greater the energy of the emitted
electrons
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 further work showed that this was incorrect and that it was the
frequency (colour/energy) of the light that was the most important
characteristic of the light to produce this effect
 Einstein won the Nobel Prize (1905) for using Planck’s ideas to
explain this effect
 Einstein proposed the idea that light consisted of a stream of
packets of energy or quanta which were later called photons
 a photon of red light contained less energy that a photon of UV
light
 Einstein used idea that energy of photon could be transferred to
the electron and that some of the energy was used to by the
electron to break free with the rest being left over as kinetic
energy in the ejected electron
 The electron could not break free of the atom unless a certain
quantity of energy is absorbed from a single photon
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(see marble in bowl explanation)
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The Bohr Atomic Theory
BOHR MODEL (approx 1913)
The Bohr model of the atom was based on the line spectra of the
Hydrogen atom. The model also incorporated the concept developed
by Einstein regarding the particle behaviour of light during emission
or absorption (photon or quanta of energy).
Postulates:
1. Energy Levels
 an electron can only have specific energy values in an atom
 the path followed by the electrons is a circular orbit (spherical
in 3-D)
 these energies are called energy levels given the name Principal
Quantum Number, n
 the orbit closest to the nucleus is given n=1, with
the lowest energy
 as one moves outward the energies get larger and
“n” increases (n=1,2,3,4,...)
 an electron can only circle in one of the allowed orbits
WITHOUT a loss of energy
2.
Transition Between Energy Levels
 an electron in an atom can only change energy by going from
one energy level to another level, i.e. NOT in-between
 light is emitted when an electron falls from a higher energy
level to a lower energy level
 an electron generally remains in its ground state – the
lowest energy level possible (n=1 for hydrogen)
 when an electron is given energy it can be bumped to a
higher energy level called the excited state
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 as the electron drops from the excited state down to lower
energy levels it emits light
 Bohr was able to show that his model was able to match the
Balmer series (Visible light, drop to n=2) and predict the
Paschen series ( IR light , drop to n=3) and the Lyman series
(UV light, drop to n=1)
Although the Bohr model could explain the behaviour of the
hydrogen atom, it could not fully explain the behaviour of other
atoms
QUANTUM NUMBERS
During and subsequent to Bohr’s work, others continued to probe the
behaviour of light emitted or absorbed by the atom. As a result,
additional components were added to Bohr’s model to improve its
ability to explain the behaviours observed. This led to the
introduction of quantum numbers, in addition to Bohr’s Principle
Quantum Number.
Principal Quantum Number, n




Goes back to Bohr model which labeled the shells
Today called Principal Quantum Number, i.e. n=1,2,3……etc.
n=1 is closest to the nucleus with the lowest energy
Relates primarily to the main energy of an electron
e.g. Fig. 1 “energy staircase” where energy levels are like
unequal steps
Secondary Quantum Number, l
 Michelson found that the spectrum of H was composed of more
than one line (experimental observation using spectrometry
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




indicated that main lines of hydrogen spectra composed of
more than one line – line splitting (Michelson, 1891)
Sommerfeld (1915) used elliptical orbits to extend the
knowledge of the time by explaining Michelson’s work
He introduced the concept of there being additional electron
subshells (or sublevels) that formed part of the energy levels
and used the concept of the secondary quantum number to
describe this concept
I.e. each energy “step” was a group of several little steps
“l” relates to the shape of the electron orbit and the number of
values for l equals the volume of n
i.e. if n=3, then l=0,1,2
as letters: l = s, p, d, f, g
Magnetic Quantum Number, ml
 it was observed that if a gas discharge tube was placed near a
strong magnet, some single lines split into new lines
 called normal Zeeman effect after Zeeman who 1st observed
this (1897)
 this was explained by Sommerfeld & Debye (1916) who
thought that orbits may exist at varying angles and that the
energies may be different when near strong magnets
 for each value of l, ml can vary from –l to +l (each value
represents a different orientation)
 i.e. if l=1 then ml can be –1,0 or +1
if l=2 then ml can be –2,-1,0,+1, or +2
Summary: The magnetic quantum number ml , relates to the
direction of the orbit of the electrons. The number of values of ml
represents the number of orientations of the orbits that we can
have.
Spin Quantum Number, ms
 needed to explain additional spectral line-splitting & different
kinds of magnetism
 ferromagnetism-associated with substances containing Fe, Co &
Ni
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 paramagnetism-weak attraction to strong magnets (individual
atoms vs. collection of atoms)
 paramagnetism couldn’t be explained until Wolfgang Pauli
suggested that electrons spin on their axis (1925)
 could spin only 2 ways (clockwise vs. counterclockwise) and he
used only 2 numbers to describe this:
ms = +1/2 (clockwise) or –1/2 (counterclockwise)
 opposite pairs of electron spins represent a stable arrangement
 when electrons are paired – spin in opposite directions – the
magnetic field is neutralized, while an individual electron spin
can be affected by a magnet
Homework:
Nelson 12: Page 184 #’s 1-7
ATOMIC STRUCTURE & THE PERIODIC TABLE
 using the quantum numbers gives an ordered description of the
electrons in a particular atom
 the secondary quantum number, l, is presented as s, p, d, and f
to represent the shape of the orbitals
Value of l
Letter designation
Name designation
0
s
sharp
1
p
principal
2
d
diffuse
3
f
fundamental
Electron orbitals
 4 quantum numbers apply equally for the electron orbits
(paths), as well as, electron orbitals (clouds) [see Fig. 1 &
Table 2 on p. 185]
 1st 2 quantum numbers (n & l) describe electrons that have
different energies under normal circumstances in multi-electron
atoms
 the last 2 quantum numbers describe electrons that have
different energies under special conditions (e.g. strong
magnetic fields
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 we use a number for the main energy level and a letter for the
energy sublevel
 simpler to use 1s than n=1, l=0 and 2p is n=2, l=1…etc
 if we needed the third quantum number ml we would need
another designation, 2px, 2py, 2pz
Value of l
0
1
2
3
Sublevel symbol
s
p
d
f
Number of orbitals
1
3
5
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Creating Energy-Level Diagrams
 these diagrams indicate which orbital energy levels are
occupied by electrons for an atom or ion
 In fig.2 on p. 187, as atoms become larger & the main energy
levels come closer, some sublevels may overlap
 Generally the sublevels for a particular value of n, increase in
energy in the order of s<p<d<f.
There are also some rules that apply to creating an energy-level
diagram
 Pauli Exclusion Principle - states that no 2 electrons in an
atom have the same 4 quantum numbers (usually you place 1
electron with  and the other electron )
 Aufbau Principle – an energy sublevel must be filled before
moving into the next higher energy sublevel
 Hund’s Rule – one electron is placed into each of the
suborbitals before doubling up any pair of electrons
 These are the “rules” that are followed until all the electrons
have been placed in their proper place
(see Fig. 6 p. 188 for order diagram.
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1s, 2s, 2p,3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p,
6f, 7d, 7f.
Order of filling sub-shells:
7s
6s
5s
4s
3s
2s
1s
7p
6p
5p
4p
3p
2p
7d
6d
5d
4d
3d
7f
6f
5f
4f
7g
6g
5g
The filling of sub-shells can also be shown on an energy level
diagram as follows:
6s
5p 5p
5p
4p 4p
4p
3p 3p
3p
2p 2p
2p
4d
4d 4d
4d
4d
3d
3d 3d
3d
3d
5s
4s
3s
2s
1s
This method allows one to see the different energy levels in diagram
form – energy is on the vertical axis. Each underline (orbital) can
take up to 2 electrons – one electron  (clockwise spin) and the other
electron  (counterclockwise spin)
Sample problem 4:
O = 8 electrons
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6s
5p 5p
5p
4p 4p
4p
4d
4d 4d
4d
4d
3d
3d 3d
3d
3d
4d
4d 4d
4d
4d
3d
3d 3d
3d
3d
5s
4s
3s

2s

1s
3p 3p
 
2p 2p
3p

2p
5p 5p
5p
Fe = 26 electrons
6s
5s
4p 4p
4p
4s
3s
3p 3p
3p
2p 2p
2p
2s
1s
Creating Energy-Level Diagrams for Anions
 Are done the same way except add the extra electrons that
corresponds to the ion charge to the total number of electrons
before showing the distribution of electrons
e.g. S has 16 electrons but S-2 has 18 electrons
Creating Energy-Level Diagrams for Cations
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 Draw the energy-level diagram for the neutral atom first, then
remove the number of electrons needed (for the correct ion
charge) from the orbitals with the highest principal quantum
number
Homework:
Nelson 12 p. 191 #’s 1-4
Electron Configuration
 Provide the same information in a more concise format
Examples:
 O: 1s2 2s2 2p4
 S-2: 1s2 2s2 2p6 3s2 3p6
 Fe: 1s2 2s2 2p6 3s2 3p6 4s2 3d6
Sample Problems p.192 & 193
Shorthand Form of Electron Configurations
 There is an internationally accepted form of shorthand that can
be used where the core electrons are expressed by the
preceding noble gas and just adding the electrons beyond the
noble gas
 E.g. Cl: 1s2 2s2 2p6 3s2 3p5 becomes [Ne] 3s2 3p5
Homework:
Nelson 12 p. 194 #’s 6-11
Explaining the Periodic Table
Period
Period
Period
Period
Period
1
2
3
4-5
# of elements
2
8
18
18
Electron Distribution:
Groups: 1-2 13-18 3-12
Orbitals: s
p
d
2
2
6
2
6
10
2
6
10
f
14
Period 6-7
32
2
6
10
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 Can use the filling of the subshells to explain the Periodic Table
 Noble gases all have ns2 np6 in the outer shell of electrons
 These types of patterns of configuration are seen in the
representative elements
 Transition elements can be explained as elements filling the d
elements therefore the transition elements are sometimes
referred to as the d block of elements
 Lanthanides and actinides are explained by the filling of the f
orbitals
Explaining Ion Charges
 Zn: [Ar] 4s2 3d10 has 12 outer electrons but Zn+2: [Ar] 3d10 and
it is unlikely that Zn would give up 10 electrons to go to 4s
sublevel
 Pb: [Xe] 6s2 4f14 5d10 6p2 lead can either lose 2 6p electrons to
become Pb2+ or lose 4 electrons from the 6s and 6p orbitals to
form Pb4+
Explaining Magnetism
 To explain magnetism we can draw the electron configuration
of a ferromagnetic element, e.g. Fe [Ar] 4s2 3d6 = 1 pair + 4
unpaired= unpaired electrons cause the magnetism?
 Ruthenium which is right under iron is only paramagnetic
(weakly magnetic)
 Result occurs probably because the atoms form groups called
domains that cause this type of magnetism
 “Ferromagnetism is based on the properties of a collection of
atoms, rather than just one atom”
Anomalous Electron Configurations
 List on p.196 shows some anomalies in predictions of electron
configurations
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 evidence suggests that half-filled and filled subshells are more
stable (lower energy) than unfilled subshells
 i.e. Cr: [Ar] 4s2 3d4 expected but in fact it is [Ar] 4s1 3d5
 appears more important for d subshells and in the case of
chromium an s electron is promoted to the d subshell to create
two half-filled subshells
 the justification is that the overall energy state is lower after
the promotion of the electron
Homework:
Nelson 12 p. 197 #’s 1-14
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PROBABILITY MODEL
(WAVE MECHANICAL MODEL or
QUANTUM MECHANICAL MODEL)
DeBroglie (1924)
 Proposed that moving electrons could be considered to behave like
waves
 experimentation showed that electrons can exhibit diffraction
patterns like light – a key part of the wave model of light
 derived expression relating wave properties to particle
properties
vm/h = ‫ג‬
where: fo htgnelevaw = ‫ג‬
particle wave
h = Planck’s Constant
m = mass of particle
v = speed of particle
for a baseball of m= 0.145 g with v=27 m/s
01 = ‫ג‬-34 m
for an electron of m = with v=3.00x108 m/s
01 x 001 = ‫ג‬-12 m (100 pm)
visible light has a wavelength range of 400 to 750 nm
Schrodinger’s Theory (1926)
 extended wave properties of electrons to their behaviour in atoms
and molecules
 consider Bohr’s Model – electron orbits nucleus like the earth
around the sun in a continuous path
 in quantum mechanics – electron does NOT have a precise
orbit in an atom
 using principle of standing waves (wave theory) and the quantum
numbers, Schrodinger was able to devise an expression, called the
wave equation, that could identify the space an electron will
occupy
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Heisenberg’s Uncertainty Principle (1927)
 Heisenberg claimed that it was impossible to know at the same
time (absolutely), both the position and momentum of an electron
in an atom
(Δx)(Δpx) ≥ h/4
where: Δx = uncertainty in position
Δpx = uncertainty in momentum
 another way of saying this is:
“if you know where a particle is, you cannot know where it is
going”
 because of the interaction of photons of light with electrons,
once one identifies where the electron is, then the light will
excite the electron and send to a place unknown
 nonetheless, one can make a statistical statement about where
an electron is in an atom – one can indicate the probability of
finding an electron at a certain point in an atom
 to do this we can employ the wave equation
 suggests that the atom does not have a definite boundary –
unlike the Bohr model
probability
of finding
particle at
position r
for 1s
orbital
50
100
150
r (pm) – distance from nucleus