The Electronic Structure of Atoms

1
Chapter 4

• The Electronic Structure of Atoms

2
Aim

• To learn how to write the electronic
  configuration of an atom and ion.
• Concept of shells and subshells as different
  energy levels.
• Sequence of these energy levels
• How the electronic configuration of an atom is
  related to its position in the Periodic Table.

3
Electronic Configuration
You have learned in cert. level that electrons in
an atom are moving around the nucleus in certain
orbits. The electron orbits are now called
electron shells.
The arrangement of electrons in the various
shells is known as the Electronic Configuration
of the atoms. How can this arrangement be found ?
4
Prediction of Electronic Structure from
Ionization Enthalpy
Ionization Enthalpy
M(g) ? M(g) e- ?H kJ mol-1
ve
Note This ionization energy can be found
experimentally.
5
Prediction of Electronic Structure from
Ionization Enthalpy
If the atom has more than 1 electron, there are
successive ionization enthalpies. e.g. He
First Ionization Energy of He He(g) ? He(g)
e- ?H 1st I.E.
What would be the equation representing the
second I.E. of He?
Second Ionization energy of He He(g) ?
He2(g) e- ?H 2nd I.E.
6
Prediction of Electronic Structure from
Ionization Enthalpy
I.E. increases in this order
1st I.E. 2nd I.E. 3rd I.E.
lt lt
Reasons
1. no. of shielding e- decreased, ?
electrostatic attraction by the nucleus is
increased.
For the time being, you may simply regard the
shielding electron as the repulsive forces
between electrons.
2. second e- is closer the nucleus than the
first one, the coulombic attraction is
greater.
7
Evidence of Shells
The scientists got ionization energies data from
an atom and then put the data into a graph. What
information can you get from the following graph?
8
Evidence of Shells
How many e- does this element contain?
11
Why are there sharp changes / rises in I.P.
between 1st 2nd ionization 9th 10th
ionization?
Probably the 2nd and the 10th electrons are
closer to the nucleus than The 1st and the 9th
electrons.
The plots of the successive ionization energies
suggested that the electrons are in different
quantum shells
1st electron being removed
2nd electron being removed with
greater difficulty, as it experiences stronger
attraction
Similarly, the 9th and 10th IE would differ
greatly
9
Evidence of Shells
A graph of successive ionization enthalpies of an
atom sheds light on how electrons are arranged in
an atom.
Refer to your handout P.8 There are four
occupied quantum shells in potassium. First
quantum shell (n1) are occupied by two
electrons. Second quantum shell (n2) are
occupied by 8 electrons, etc.
For the time being, just accept the words quantum
and quantum number or principal quantum
number. You probably get the picture that greater
the quantum number, further away the electron
from nucleus and thus higher energy.
10
Summary
Electron shell with principal quantum number n
3 Electron is furthest away from nucleus, thus
easiest to be removed
Electron shell with principal quantum number n
2
Electron shell with principal quantum number n
1 Electron is closest to the nucleus, thus most
difficult to be removed
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Get ready for new concept

• Do all electrons in the same shell (i.e. same
  principal quantum number) have same energy level
  ?
• Lets have closer inspection of ionization
  energies of potassium.
• Remember that the electronic configuration of K
  is 2,8,8,1.
• It was found that

12
Evidence of Sub-shell

• From 2nd to 9th ionization and 10th to 17th
  ionization, a similar pattern is observed

A sharper change in I.E. were observed somewhere,
in which electrons are being removed in the same
quantum shell.
8 electrons in the same shell are split into two
groups two subshells, which are also of
different energy.
13
Not a very correct representation
Third quantum shell, two subshells (shown here so
far) one higher (also called p subshell), one
lower (also called s subshell)
Second quantum shell, two subshells one higher
(called p subshell), one lower (called s
subshell).
First quantum shell, only one subshell
How about this quantum shell ? What do you expect
?
14
Evidence of Sub-shell
6
subshell of higher energy
This holds ___ e-.
Third quantum Shell (n3)
2
subshell of lower energy
This holds ___ e-.
6
subshell of higher energy
This holds ___ e-.
Second quantum Shell (n2)
2
subshell of lower energy
This holds ___ e-.
15
Closer look at the IE
1st and 2nd IE differ greatly
These six IE are similar as the electrons are in
the same subshell
7th and 8th IE also show sharper change
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Brief summary
2
8
18
32
s subshell can hold 2 electrons, p subshell can
hold 6 electrons, d subshell can hold 10
electrons, while f subshell can hold 14 electrons
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Basic concept of Orbital

• Its a volume of space within which the
  probability of finding an electron is very high
  (say, 95).
• Each orbital can accommodate (??) no more than 2
  electrons.
• Orbitals in different subshells would have
  different shapes.

18
Orbital vs. orbit

• In the beginning of 20th century, scientists
  thought that electrons move around the nucleus in
  fixed orbits, with a certain distance from the
  nucleus. Like the planets go around the sun
  solar system.
• However, scientists soon found out that electrons
  can not remain in a fixed distance from the
  nucleus.
• And, we cant accurately locate it. We can just
  describe it with complicated mathematical
  equations.
• These equations consist of different numbers
  which help to define the size and shape of a
  region within which we can find the electrons
  with great chance the orbital.

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Subshells

• It refers to the collection of all the orbitals
  within the same principal quantum number (n)
  which have the same energy level.

Example principal quantum number n2, the
second shell, it has s subshell,
with one s orbital, holding a max. of
2 electrons principal
quantum number n2, the second shell, it has
p subshell, with ______ p orbitals,
holding a max. of 6 electrons.
3
Therefore, the second shell can accommodate a
total of 8 electrons.
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Subshells

• Refer to your handout P.9
• p subshell is composed of three p orbitals
• namely Px, Py and Pz
• d subshell is composed of 5 d orbitals
• dxy, dyz, dxz,
• You will learn the differences between these s, p
  and d orbitals later. Sigh

21
Energy levels

• Generally, the shell with higher principal
  quantum number n would have higher energy level.
• i.e. K lt L lt M lt N
• In the same quantum shell, the energy level of
  the subshells is in this order
• s lt p lt d lt f
• Therefore 3s lt 3p lt 3d

22
What do you notice ?
Study the table 4-4 in P.122 yourself.
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Energy levels

• There is a reversal in energy level
• 4s lt 3d
• Similar pattern happens also in
• 5s lt 4d
• 6s lt 5d lt 4f !!!
• Do you really want me to explain this to you ?
• Now, try Q.5 in your handout P.10.

24
Electronic configuration

• 1. Aufbau Principle
• Electrons enter the orbitals in order of
  ascending energy, i.e. electrons fill in the
  lowest energy orbital first before the higher
  energy levels are filled.
• Order of energy levels of atomic orbitals
• Try Q.6 in P.12

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Order of energy levels
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Electronic configuration

• 2. Hunds rule
• Orbitals of the same energy must be occupied
  singly before pairing occurs.
• ___ ___ ___ ___ ___
• 1s 2s 2px 2py 2pz

This is because if the two electrons are in the
same orbital, it would cause a large repulsion.
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Electronic Configuration

• Pauli Exclusion Principle
• No orbital can accommodate more than 2 electrons.
  
• If two electrons occupy the same orbital, the
  electrons must have opposite spin.??

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Try some examples

• Try to write down the electronic configuration of
  carbon
• 1s2 2s2 2p2 OR 1s2 2s2 2px1 2py1
• Manganese (atomic number 25)
• 1s2 2s2 2p6 3s2 3p6 3d5 4s2 OR
• Ar 3d5 4s2

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Electronic configuration of isolated atoms or ions

• Q.8

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Electron-in-boxes diagram
1s 2s 2p 3s 3p
4s
K
3d 4s
Fe
Ar
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The Periodic Table

• In the Periodic Table, elements are arranged in
  increasing order of their atomic numbers. As the
  atomic number increases, the number of electrons
  in the atoms also increases. Hence, how
  electrons are arranged in an atoms is closely
  related to the position of the element in the
  Periodic Table.
• You may take the Periodic Table as a building
  with different blocks. If an element has it
  last-filled electron in s-orbital, its a s-block
  element. For example sodium 1s2 2s2 2p6 3s1.

32
The Periodic Table
s-block
p-block
2s
d-block
3s
3d
4s
4d
5s
5d
6s
6d
7s
4f 5f
f-block
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The Periodic Table

• Horizontal rows (Periods)
• Each period starts with the elements with their
  outermost electron occupying s orbitals.
• Vertical column (Groups)
• Groups consists of elements having similar
  chemical properties, because elements possess
  same number of outermost shell electrons / same
  outermost shell configuration.

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Brief summary of different blocks of elements

• s-block
• Group IA and Group IIA
• Alkali metals and alkaline earth metals
• Reactive metals
• p-block
• Group III to Group VIII(0)
• Chemical properties differ widely from reactive
  metals to noble gases
• Trends within a group are not too clear

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Brief summary of different blocks of elements

• d-block
• There are three transition series
• Transition metals differ greatly from main group
  metals, including both physical and chemical
  properties
• E.g. coloured ions, variable oxidation states,
  etc
• Would be discussed in S7
• f-block
• Also called inner transition series / metals

36
Try Q.9

• Check up the order of energy levels in P.12 in
  your handout.
• Also check up the Periodic Table in your textbook.

37
Q.9

• Period I
• First shell being filled. This s orbital can
  accommodate 2 electrons only.
• Period II
• Fill up the second shell. Since it comes to s
  orbital, it should start a new period in the
  Periodic Table. This shell can accommodate 8
  electrons, hence there are 8 elements in this
  period.

38
Q.9

• Period III
• The third shell can accommodate 18 electrons
  (with subshell 3s, 3p and 3d).
• However, after filling in 3s and 3p, electrons
  fill in 4s rather than 3d subshell because 4s is
  of lower energy than 3d.
• As filling of 4s electron should start a new
  period in the Periodic Table (Why?), Period III
  only comprise of 8 elements.
• This gives rise to transition elements in the
  next period.

39
Q.9

• Period IV
• First two elements 4s orbital
• From scandium (atomic no. 21) to zinc (atomic no.
  30), fill in 10 3d electrons.
• This is the first transition series.
• After zinc, fills up 4p orbital with 6 more
  electrons.
• How many elements are there in this period ?

40
Q.9

• Period V
• Fill up 5s, 4d (the second transition series) and
  5p orbitals
• Also contains 18 elements
• 4f orbitals not yet filled.
• Period VI
• Fill up 6s, 5d (the third transition series) and
  4f (the inner transition series) and finally 6p
  orbitals.
• Total 32 elements.

41
Continuous and Line Spectra
Continuous Spectrum
If white light is analyzed in a spectroscope, a
continuous sequence of colour is obtained.
42
Continuous and Line Spectra
Continuous spectrum
43
Continuous and Line Spectra
Line Spectrum (Emission Spectrum)
When flames which emit coloured light (e.g.
sodium vapour lamp or from a gas discharged) is
analyzed in the same way, the spectrum given out
is made up of one or more coloured lines
separated by dark spaces.
44
Continuous and Line Spectra
Press
Emission Line Spectrum
45
The Emission Spectrum of Atomic Hydrogen
When hydrogen gas discharged, the spectrum of
hydrogen gas consists of several groups or series
of discrete lines.
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The Emission Spectrum of Atomic Hydrogen
Lyman series Near ultra-violet region Balmer
series Visible light region Paschen series
Infra-red region Brackett series Far
infra-red region
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Interpretation of the Atomic Hydrogen Spectrum
For each series, the lines come closer together
(or converge) at higher frequency, until they
merge into a continuum.
48
Interpretation of the Atomic Hydrogen Spectrum
Electrons are moving around the nucleus in
circular orbits. Each orbit is associated with a
definite amount energy.
It is called quantum theory.
49
Basic assumptions of the quantum theory
1. An electron in an atom can only exist in
certain states characterized by definite energy
levels. The energy of an electron can only
change by some definite whole number multiple of
a unit called the quantum. 2. As the energy of an
electron is quantized, the radius of the orbit
should also be quantized. Different orbits
represent different energy levels.
50
Basic assumptions of the quantum theory
3. When an electron moves from one orbit to
another, it must emit or absorb a definite amount
of energy to bring it to that orbit.
?E E2 - E1 h?
Press
where E2 and E1 are the energy of the two
orbitals, E2 is higher energy than E1. h is the
Plancks constant (6.626 x 10-34 Js) ? is the
frequency of the light emitted.
51
Basic assumptions of the quantum theory
If the electron absorbed energy, it can jump from
a lower energy state to higher energy state.
This process is called excitation.   Electron is
unstable at higher state so it will fall back to
a lower energy level. Excess energy is emitted
as radiation.
52
Basic assumptions of the quantum theory
As the energy difference between higher and lower
energy levels can only have certain fixed values,
this explains why discrete lines of fixed
frequencies are found in the spectrum.   By using
Plancks equation, an electron moving in a
stationary state of energy E2 to another state of
energy E1 (of lower energy) will emit energy
which is in the form of a radiation of frequency
53
Basic assumptions of the quantum theory
n?
n4
Energy Levels of a hydrogen atom
n3
n2
Press
n1
a
b
c
54
Convergence Limits and Ionization
Each series of the line spectrum converges to a
continuum because the difference in energy levels
become smaller. The line at continuum related to
the electron at infinity (i.e. n ?) moved back
to a certain level.
For hydrogen atom, there is only one electron in
its atom. When the electron is at its lowest
energy level, it is at its ground state (n1).
If the electron is excited to an energy level in
which the nucleus exerts no attraction on the
electron (n?), the atom is ionized.
55
Convergence Limits and Ionization
The convergence limit corresponds to the energy
needed for the transition of electron from n 1
to n ?, i.e. the energy required to ionize a
hydrogen atom. This is known as the ionization
enthalpy of hydrogen. (N.B. The convergence
limit is a value of wavelength, so you should use
the equation to calculate the ionization energy.)
This equation shows the energy required to excite
one electron to infinity.
56
Convergence Limits and Ionization
The definition of ionization energy is the energy
to remove 1 mole of electrons from 1 mole of
substance. Therefore, you should apply the
following equation
57
The Uniqueness of Atomic Emission Spectra
No other element gives same spectrum, i.e. this
spectrum is unique to hydrogen.
Different element will have different atomic
emission spectrum. (Why?) Do you know why the
scientists know what kinds of elements in the
sun?
Try to do the questions in P.114 (New P.100)
58
Quantum Numbers
Orbitals are specified with a set of numbers so
that a clearer picture about the energy status of
an electron could be obtained.
Four quantum numbers are used to describe the
various atomic orbitals. They are principal
quantum number (n), subsidiary quantum number
(l), magnetic quantum number (m), spin quantum
number (s)
59
Quantum Numbers
Principal quantum number (n) This number is used
to describe the average distance of an electron
from the nucleus. This determines the size and
energy of the orbitals. It is start from n1
and so on. It is equal to the no. of electron
shell you learned it before. e.g.
60
Quantum Numbers
Subsidiary quantum number (l) This number is used
to determines the shape of the orbitals. The
energy of the subshell increases as the value of
l increases. It can have values of 0 to
n-1. i.e. l 0, 1, 2, ....., n 1
The symbols given for these orbitals are s, p, d,
f, etc.,
The number of orbitals in a subshell is 2l1.
61
Atomic Orbitals
s orbitals e.g. 1s, i.e. n1, l 0
The electron are mostly concentrated at the area
near the nucleus. This suggest that the
probability of finding an electron is the
greatest around the nucleus, but it drops off
rapidly as the distance from the nucleus
increases.
62
Atomic Orbitals
s orbitals are spherical in shape.
Probability
Distance from nucleus
63
Atomic Orbitals
The radial probability distribution can also be
used to represent the total probability of
finding an electron in successive spherical
shells against the distance from nucleus.
1s orbital
2s orbital
Radial probability
Radial probability
nodal surface
64
Atomic Orbitals
2s orbital comparing with 1s orbital
Difference 2s orbital possesses higher energy
and so the electron has a greater probability of
being found further away from the nucleus.
Similarity Both 1s and 2s orbitals are spherical
in shape.
The diagram in your textbook P.125 shows more
detail of 1s, 2s and 3s orbitals.
65
Atomic Orbitals
p orbital e.g. n2, l1
nodal plane
It is not spherically symmetrical, but
directional. It has a dumb-bell shape.
66
Quantum Numbers
Magnetic quantum number (m)
Orbitals may lie up in different spatial
orientations. The magnetic quantum number m
determines the different spatial orientation of
the orbital in the magnetic field. m -l, .....,
0, ......, l
This gives the number of orbitals in a subshell.
For s orbital, m 0. For p orbital, m -1, 0,
1. For d orbital, m -2, -1, 0, 1, 2.
67
Atomic Orbitals
The three 2p orbitals are labelled according to
the xyz axes along which the lobes lie.
68
Quantum Numbers
Spin quantum number (s) Electrons are found in
pairs in orbitals. The spin quantum number
describe the spin property of the electron,
either clockwise or anti-clockwise.
69
(No Transcript)
70
Evidence of Sub-shell
The following graph is the first ionization
enthalpy against the atomic numbers of the first
20 elements.
Can you get any information from the following
graph?
71
Evidence of Sub-shell
The First Period The I.E. is relative high in H
and He. Reason Electron are at the nearest
shell. Experiences the greatest nuclear
attraction.
72
Evidence of Sub-shell
The Second Period Sharp decrease from He to
Li ? Li and He are not in the same
shell.   Steady increase from Li to Ne ? They
are in a same shell but get a greater nuclear
attraction force.   The 1st I.E. of Be gt B and N
gt O ? Be and N is abnormally more stable than B
and O. (Or B and O is abnormally unstable than Be
and N.)
73
Evidence of Sub-shell
The Third Period Similarly to the second period.
74
Bohr's Atomic Model and its Limitations
Limitations 1. There is still no experimental
evidence that proved electrons are moving around
the nucleus of an atom in fixed orbitals. 2. It
cannot explain the more complicated spectral
lines observed in spectra other than hydrogen.
75
Wave Nature of Electrons
So far, an electron has been regarded as a tiny
and negatively charged particles.
Some times later, scientists found that the
electron beam can be diffracted by a gold foil,
which is similar to the X-ray beam diffracted by
gold crystal.
76
Wave Nature of Electrons
This shows that electrons possess wave-like
properties. Electrons can behave either as
particles or as waves, like visible
light. Electrons have a dual wave-particle
nature.   Later, an other scientist developed the
wave-mechanical model of the atom. In this
model, electrons are treated as both particles
and waves, complex mathematical equations being
used to describe the arrangement and motion of
electrons in atoms.
77
Wave Nature of Electrons
This model suggests that electrons are not
localized in fixed orbitals. Within each energy
level, we can only describe the location of an
electron in terms of the probability of finding
it in a certain position at any time. The term
orbital is used to define such region of space.
The shapes of orbitals are defined by the
probability distribution of electrons.
78
Quantum Numbers
Orbitals are spatial regions in an atom where
there is a high probability of finding the
electron. There are several types of orbitals
which may be of different distances from the
nucleus and have different shapes.
79
Atomic Orbitals
An atomic orbital is a representation of a region
within which there is a high probability (about
90) of finding an electron. In the
wave-mechanical model, an electron is treated as
a wave but not a particle.
For complicated atoms, electrons can occupy
different orbitals according to their energy
status. e.g. e- in the principal quantum shell (n
1 shell has lower energy than n 2 shell,
etc.,). But there are different sub-shell in n
2 (s and p). These sub-shell is used to
designates the shape of the orbital.
80
Atomic Orbitals
Ex. Give the name, magnetic quantum no., no. of
orbitals and the maximum no. of e- for each
sub-shell with the following quantum
numbers a. n 2, l 1 b. n 4, l 2 c. n
3, l 0 d. n 5, l 3
81
Atomic Orbitals
3p orbital comparing with 2p orbital
Difference 3p orbital possesses more energy and
so the electron has a greater probability of
being found further away from the nucleus.
Similarity Both 2p and 3p orbitals are dumb-bell
shape.
Try to do the questions in P.126