Electrons in atoms

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Electrons in atoms
KTT 111/3 Inorganic Chemistry I
Dr. Farook Adam
August 2005
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Chapter 8 The Quantum Mechanical
Atom

• By the late 1800s it was clear that classical
  physics was incapable of describing atoms and
  molecules.
• Experiments showed that electrons acted like tiny
  charged particles in some experiments and waves
  in others.
• The physics that describes objects with
  wave/particle duality is called quantum mechanics
  or quantum theory.

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• Energy can be transferred between things as light
  or radiation
• Radiation carries energy through space as waves
  or oscillations moving outward from a disturbance
  
• Electromagnetic waves (radiation) may be
  characterized by their height or amplitude and
  the number that occur per second or frequency (v)

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• The units of frequency are the hertz (Hz)
• The minimum and maximum amplitude of
  electromagnetic radiation are evenly spaced
• The peak-to-peak distance is called the wavelength

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• The product of frequency and wavelength give the
  speed of light (c)
• Electromagnetic radiation comes in a broad range
  of frequencies called the electromagnetic
  spectrum
• The electromagnetic spectrum is divided into
  regions according to the wavelengths of radiation

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• What we call light is a small slice of the
  electromagnetic spectrum with wavelengths between
  about 400 and 700 nm
• This is called the visible region because we can
  see these wavelengths of the electromagnetic
  spectrum
• Gamma rays, X rays, and ultraviolet radiation
  have wavelengths shorter than the visible region
• Microwaves, infrared radiation, and radio waves
  have wavelengths longer than visible light

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• The way a substance absorbs electromagnetic
  radiation can be used to characterize it.
• For example, each substance absorbs a uniquely
  different set of infrared frequencies.
• A plot of wavelengths absorbed versus the
  absorption is called an infrared absorption
  spectrum.
• It can be used to identify a substance.

9
Infrared absorption spectrum of wood alcohol
(methanol).

• The oscillating magnetic and electric fields of
  an electromagnetic wave interact with particles
  that it passes
• A charged particle can pick up energy at the
  expense of the radiation source

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• The energy transfer is not described correctly by
  classical physics.
• In 1900 the German scientist Max Planck proposed
  that the electromagnetic radiation could be
  viewed as a stream of tiny energy packets or
  quanta we now call photons.
• Photons travel at the speed of light.
• Planck proposed, and Einstein confirmed, that the
  energy of a photon is proportional to its
  frequency.

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• This means that both electrons and
  electromagnetic radiation can be represented as
  either waves or particles.
• The visible spectrum is a continuous spectrum
  because it contains a continuous distribution of
  light of all colours.
• Excited atoms can emit light.

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• The atomic spectrum or emission spectrum is a
  series of individual lines called a line spectrum
• Atomic spectra are unique for each element

Light emitted by excited atoms is comprised of a
few narrow beams with frequencies characteristic
of the element.
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Comparison of line spectra and a continuous
spectrum
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• In general, the line spectrum of an element is
  rather complicated
• The line spectrum of hydrogen, with a single
  electron, is the simplest
• The Rydberg equation can be used to calculated
  all the spectral lines of hydrogen
• n1 and n2 are positive integers.
• NO ONE knew what these integers stood for.

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• The Rydberg constant, RH, is an empirical
  constant with a value of 109,678 cm-1.
• Atomic line spectra tells us that when an excited
  atom loses energy, not just any arbitrary amount
  can be lost. Only certain amounts of energy are
  lost!
• This is possible if the electron is restricted to
  certain energy levels.
• The energy of the electron is said to be
  quantized.

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Niels Bohr Structure of the atom
Ref J. D. Lee, Concise inorganic chemistry, 4th
Ed., Chapter. 1.
Was awarded the Nobel Prize for Physics in 1922
for his work on the structure of the atom.

• In 1896 Thomson had shown that electrons are
  present in the atom.
• Rutherford suggested (from ? particle scattering)
  that an atom
• consisted of a heavy positively charged nucleus,
  and
• enough number of negatively charged particles
  (electrons) around it to make it
  electrically neutral.
• Several problems arise from this concept!

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http//www.bcpl.net/7Ekdrews/bohr/bohr.html

• These problems are
• The electrons might be expected to slow down
  gradually.
• Why should electrons move in an orbit around the
  nucleus?
• Since the electrons and the nucleus have opposite
  charges, they should attract each other. Thus one
  would expect the electrons to collide with the
  nucleus.

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To explain these problems, Bohr made the
following proposals(1913)

• Electrons did not radiate energy if it stayed in
  one orbit and therefore did not slow down!
• When an electron moved from one orbit to another
  it either radiated or absorbed energy. If it
  moved towards the nucleus
• it will radiate energy and if it moved away
  from the nucleus it would absorb energy.
• For and electron to remain in its orbit the
  electrostatic attraction between the electron and
  the nucleus which tends to pull the electron
  towards the nucleus must be equal to the
  centrifugal force which tends to throw the
  electrons out of its orbit.

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Continuous (a) and discrete (b) potential energy
of a tortoise. The potential energy of the
tortoise in (b) is quantized.
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Derivation of Bohrs equation
For an electron of mass m, moving with a velocity
v in an orbit of radius r, centrifugal
force If the charge on the electron is e, the
number of charges on the nucleus Z and the
permittivity of vacuum is ?o, then Columbic
attractive force There fore
Then,
(1)
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According to Plancks quantum theory, energy is
not continuous but is discrete. This means that
energy occurs in packets called quanta, of
magnitude h/2?, where h is the Plancks
constant. The energy of an electron in orbit,
i.e. its angular momentum mvr, must equal to a
whole number n of quanta! (WHY?)
(1)
(2)
Combining equation (1) and (2), we get
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(3)
The atoms will only radiate energy when the
electrons jumps from one orbit to another. The
kinetic energy of an electron is
½ m v2
Incorporating this into equation (1)
(1)
Substituting for r from equation (3),
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If an electron jumps from an initial orbit i, to
a final orbit f, the change in energy ?E is
(4)
The energy is related to the wavelength by,
Equation (4) can be written as
Why do this?
(5)
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If you can recall, the Rydberg equation was given
as
(6)
Comparing equation (5) and (6),
The experimental value of R obtained by Rydberg
was 1.097373 x 107 m-1
The calculated value using Bohrs derived
equation for the hydrogen atom is
1.096776 x 107 m-1 !!!!!
This validates Bohrs theory of the atom and it
explains all the observed atomic spectral lines
of the hydrogen atom just like Rydbergs equation
did!!
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Bohrs model of an atom
nucleus
Electrons in orbits
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• Bohr proposed that the electrons moved around the
  nucleus in fixed paths or orbits much like the
  planets move around the sun.
• The orbits, labeled with the integer n, have
  energy.
• This equation allows the calculation of the
  energy of any orbit

NOW n has a meaning!
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n is also called the quantum number because it
determines the total energy an electron will
have at a particular orbit.
If we define,
A

e charge on the electron, m mass of the
electron, Z atomic number and h Planks
constant
And,
ao

ao Bohr radius i.e. the radius of the hydrogen
atom when the electron is at the ground state, n
1.
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Example Calculate the energy of the photon when
the electron drops to the fifth orbit to the
second orbit. Calculate also the frequency and
the wavelength of the photon in nm.
Solution
E -A/n2, A 2.18 x 10-18 J
For two orbits n1 and n2 which has different
energy,
E1 -A/n12 E2 -A/n22
The energy change when the electron falls from n1
to n2
?E E1 E2
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A
A
-
-
-
?E
n12
n22
1
1
-
A

n12
n22
If n1 5 and n2 2
1
1
-
?E
2.18 x 10-18
4.58 x 10-19 J
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4
?E h?
4.58 x 10-19 J
?E
?

6.91 x 1014 Hz
h
6.63 x 10-34 Js
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? . ? c
c
?
?
3.00 x 108 ms-1

6.91 x 1014 s-1
1 nm
4.34 x 10-7 m
10-9 m
434 nm
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Absorption and emission of energy by the hydrogen
atom. An electron that absorbs energy is raised
to a higher energy level. A particular frequency
of light is emitted when an electron falls to a
lower energy level.

• The lowest energy state of an atom is called the
  ground state (an electron with n 1 for a
  hydrogen atom)

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• An electron that escapes from the nucleus has
  infinity for its quantum number.
• Bohrs (theoretical) equation explains the
  (empirical) Rydberg equation

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• The combination of constants, b/hc, has a value
  which differs from the experimentally derived
  value of RH by only 0.05.
• Bohrs efforts to develop a general theory of
  electronic structure was eclipsed by the
  wave/particle duality of electrons.
• De Broglie suggested that the wavelength of a
  particle of mass m moving at speed v is

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• This relation provides the link between the
  description as a particle and as a wave.
• Heavy objects have very short wavelengths so
  their matter waves and the wave properties go
  un-noticed.
• Tiny particles with small masses have long
  wavelengths so their wave properties are an
  important part of their behavior.
• Waves combine in two ways.

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(a) Waves in phase interfere constructively. (b)
Out of phase waves produce destructive
interference. (c) Waves passing through holes fan
out and produce an interference pattern.

• The constructive and destructive interference is
  called diffraction.
• Electrons produce similar patterns.

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Heisenbergs uncertainty principle
In 1927,
Heisenberg deduced that it is not possible to
determine with accuracy of both the position and
the velocity of an electron at the same time
His statement can be represented mathematically as
gt
A small change in the position of the electron
A small change in the momentum of the electron
(mv).
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Standing waves

• There are two types of waves traveling and
  standing
• A standing wave is produced when a guitar string
  is plucked the center of the string vibrates,
  but the ends remain fixed.
• Points of zero wave amplitude are called nodes.

The wind produces traveling waves on the surfaces
of lakes and oceans.
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Standing waves on a guitar string.

• For guitar strings the only waves are those for
  which a half-wavelength is repeated exactly a
  whole number of times.
• For a string of length L with n an integer this
  can be written.

Lets see this in a bit more detail
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What ar the values of wavelengths that are
possible on the guitar string?
If the guitar string is L, then
L
n
n integer
Therefore, the allowed wavelength on the guitar
string will be
2L
?

n
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Standing waves
It is because both ends of the guitar are tied
both ends must be a node!! You should see that
this results in the generation of integral whole
numbers of half-wavelengths!! This is repeated
all along the guitar string no matter what
wavelength occurs on the string if at all it
occurs! However do not forget that only certain
specific wavelengths will allow the generation of
integral values of half-wavelengths to be set
upon the guitar string.
The integral whole number (n) is now generated
automatically!!!!!!
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• These results can be used to show how quantum
  theory unites the wave and particle description
  of a bound electron
• Consider the classical particle model of the
  bead on a wire
• If the electron (particle) has mass m and speed v
• The kinetic energy of the moving electron is

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(a) A classical model of the electron as a bead
on a wire. Any energy is possible and position is
exactly known. (b) Classical model of the
electron as a standing wave. (c) Quantum
mechanical model combines (a) and (b). Dark areas
indicate probable electron positions.

• The De Broglie relation connects models (a) and
  (b)

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• The electron energy is quantized because it
  depends on the integer n
• The lowest energy allowed is for n1 or Eh2/8mL2
  (the energy cannot be zero)

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• Electrons trapped on a wire have some residual
  kinetic energy, just like electrons trapped in
  atoms

The spacing between levels is proportional to
1/L2. (a) A long wire. (b) A short wire. The
longer the wire, the smaller the spacing between
allowed energy levels.
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• The wave that corresponds to the electron is
  called a wave function.
• The amplitude of the wave function at a given
  point can be related to the probability of
  finding the electron there.
• According to quantum mechanics there are regions
  of the wire where the electrons will not be
  found.
• Regions of zero wave function amplitude are
  called nodes.

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• It is generally true that the more nodes an
  electron has, the higher its energy.
• Erwin Schrödinger was the first to successfully
  apply the concept of the wave nature of matter to
  electronic structure
• He developed an equation that can be solved to
  give wave functions and energy levels for
  electrons trapped in them
• Wave functions for electrons in atoms are called
  orbitals

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Wave function in an atom
A set of wave functions were obtained that
describes very specifically the shape of the
electron wave and the allowed energy for it!! In
general, this wave function is simply represented
by
Is the radial function (radius) it only depends
on the radius of the electron form the centre, r.
This is the angular function it depends on the
direction and the orientation of the wave does
not depend on the distance.
Any wave that is allowed is called an ORBITAL.
(Cf. ORBIT from Bohrs theory)
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Wave function in an atom
Each orbital in an atom has a specific energy and
is understood as a volume of space around the
nucleus where an electron can be found. Remember
that electron is the wave and not a particle!!!
Every wave function that describes an orbital can
be represented by three fundamental numbers
called quantum numbers. These numbers were the
result of the solution of the wave equation.
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Wave function in an atom
How are the electrons arranged in an atom? We can
answer this question by understanding the meaning
of these quantum numbers. Remember these quantum
numbers came about by solving the mathematical
wave-function!!
Erwin Schrödinger won the Nobel prize in 1933
together with Paul Dirac for his work in solving
the wave-function.
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• Orbitals are characterized by a set of three
  quantum numbers
• n principle quantum number. All orbitals with
  the same principle quantum number are in the same
  shell. Allowed values the set of positive
  integers.
• l secondary quantum number which divides the
  orbitals in a shell into smaller groups called
  subshells. Allowed values from 0 to (n 1).
• ml magnetic quantum number which divides the
  subshells into individual orbitals. Allowed
  values integers from l to l.

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The quantum numbers

• The principle quantum number, n

Energy levels in an atom are arranged according
to principle shells or principle levels
determined by the principle quantum number.
The larger the value of n, the bigger the energy
of the orbital. The value of n will also
determine the size of the orbital. As in the Bohr
theory, n can take values of 1, 2, 3, ., ?.
n 1 2 3 4.. K L M N.
Symbolic representation
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• The azimuthal quantum number, l.

The quantum mechanical wave function predicts
that every principle energy level may contain one
or more sub levels.
Every sub-level is represented by a secondary
quantum number, l.
l determines the shape of the orbital and also
its energy.
For a given principle quantum number n, l can
take values of 0, 1, 2, 3, 4, , n-1.
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n l
1 0 2 0, 1 3 0, 1, 2 4 0, 1, 2, 3 .
. . . n 0, 1, 2, 3,., n-1
Observe that the number of sub-levels is the same
as the value of n!!
The values l are also represented by alphabets as
you may already have learned, as follows
l value 0 1 2 3 4 5 6 s
p d f g h i
representation
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• The magnetic quantum number, ml

Every sub-level will have one or more orbital.
Each orbital in a sub-level is distinguished from
each other by its ml value. The value of ml will
determine the orientation in space of the
orbitals relative to other orbitals.
ml can take values of
ml -l,0,., l
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Relationships between n, l, and ml.

• n l sub-level ml no.
  of orbitals
• 0 1s 0
  1
• 0 2s 0
  1
• 1 2p -1 0 1
  3
• 0 3s 0
  1
• 1 3p -1 0 1
  3
• 2 3d -2 -1 0 1 2
  5
• 0 4s 0
  1
• 1 4p -1 0 1
  3
• 2 4d -2 1 0 1 2
  5
• 3 4f -3 2 1 0 1 2 3 7

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• The approximate energies of the subshells in an
  atom with more than one electron

The quantum numbers associated with the first two
shells are shown.
Electrons also behave like tiny magnets!!
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Remember that wave mechanics produces only 3
quantum numbers

• Electrons within atoms interact with a magnetic
  field in one of two ways
• Electron spin is important in determining
  electronic structure

Electrons can spin in either direction in the
presence of an external magnetic field. This
gives rise to the spin quantum number, ms with
allowed values of 1/2 (spin up) or 1/2 (spin
down).
This is the 4th quantum number!!
What characteristic is the electron displaying
wave or particle?
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• According to the Pauli exclusion principle no two
  electrons in the same atom can have identical
  values for all four quantum numbers
• Thus two electron can occupy the same orbital
  only if they have opposite spin and are said to
  be paired
• A substance with more spin in one direction is
  said to contain unpaired electrons

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Tugasan 4(a)
Pages from 347
No. 3 and 8.4 8.39 8.5 8.46 8.20 8.86 8.35 8.
90 8.38
ATTENTION!! Pass this up to your tutors by the
19 th August 2005.
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Order of Subshell Energies

• Follow the arrows from the top 1s, 2s, 2p, 3s,
  3p, 4s, 3d, 4p, etc.
• Subshells that are far from the nucleus may
  exhibit exceptions to the filling order.

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The Aufbau Principle

• The Aufbau principle describes a hypothetical
  building-up of an atom from the one that
  precedes it in atomic number.
• (Z 1) H 1s1
• (Z 2) He 1s2
• (Z 3) Li 1s2 2s1

To get He, add one electron to H.
To get Li, add one electron to He.

• Noble-gas-core abbreviation we can replace the
  portion that corresponds to the electron
  configuration of a noble gas with a bracketed
  chemical symbol. Its easier to write
• (Z 3) Li He2s1
• (Z 22) Ti Ar4s2 3d2

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We can also represent this in terms of electron
spin

• - represent spin up 1/2
• - represent spin down -1/2.

The electron distribution in the orbital can be
represented by these arrows. For hydrogen, the
electronic configuration can be represented by
?
H
1s
This is called the orbital diagram
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Orbital 1s can hold 2 electrons. But from Paulis
exclusion Principle, both the electrons must have
opposite spins and bein the same orbital.
Two arrows are drawn in opposite
directions to indicate opposite spins on the line
that represents an orbital.
??
He
1s
Paired spin
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Li and Be follow He with 3 and 4 electrons and
their orbital diagrams are as follows
1s2 2s1
?? ? ?? ??
Li Be
1s2 2s2
1s 2s
The noble gas configuration can also be used as
follows
He 2s1
He ? He ??
Li Be
He 2s2
2s
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He 2s1
He ?
Li
core electron
Electron involved in chemical reaction
helium core
This method shows the electrons in the outermost
orbital.
At helium, the 2s orbital have been fully
occupied. In boron its 5th electron will be
placed in the 2p orbital. B He
?? ?
2s 2p
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ml -1 or 0 or 1 ms -1/2 with any combination
of ml or 1/2 with any combination of ml
We can draw 3 possible orbital diagrams for B.
B He ?? ?
B He ?? ?
B He ?? ?
2s 2p
All three diagrams are the same in terms of
energy and they cannot be distinguished from
each other.
For carbon C 1s2 2s2 2p2
Three orbital diagrams can be drawn.
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Paired electrons
C He ?? ??
C He ?? ? ?
C He ?? ? ?
unpaired electrons
2s 2p
Which is the ground state configuration for
carbon?
Hunds rule
electrons entering sub-orbitals that have the
same energy will distribute themselves in all the
available orbitals with the all their spins in
the same direction parallel spin. These are
called degenerate orbitals.
degenerate orbitals having the same energy
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The ground state configuration for carbon will be
C He ?? ? ?
This will be followed by nitrogen.
2s 2p
N 1s2 2s2 2p3
N He ?? ? ? ?
Followed by O, F dan Ne
2s 2p
8O He ?? ?? ? ?
2s 2p
9F He ?? ?? ?? ?
2s 2p
10NeHe ?? ?? ?? ??
2s 2p
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C He ?? ? ?
2s 2p
N He ?? ? ? ?
2s 2p
Parallel spin
The half-filled orbital will result in
enhancement of stability.
10NeHe ?? ?? ?? ??
2s 2p
Fully-filled orbitals also results in extra
stability.
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After Ne, the lowest energy orbital is the 3s and
will be filled for Na to Mg (Z 11 dan 12).
After this the 3p orbitals will begin to fill
beginning with Al until Ar (Z 13 to 18).
13Al Ne 3s2 3p1 . . 15P Ne 3s2
3p3 . . 18Ar Ne 3s2 3p6
Contradiction in the filling rule will be seen
after this as the 4s orbital is lower in energy
than the 3d orbital!!!
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Orbital 4s will be filled by K and Ca (Z 19 dan
20).
Only after this the 3d orbital will start to
fill. The filling of the 3d orbitals will
generate the first fow transition elements as
seen in the periodic table!!
Element after Ca is Sc
21Sc Ar 4s2 3d1
Normally all the orbitals with the same prinsiple
uantum number will be collected together when
writing the electronic configuration. So that the
electronic configuration for scandium will be
21Sc Ar 3d1 4s2
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The orbital diagram for Sc is shown as
21Sc Ar ? ??
3d 4s
.
23V Ar ? ? ? ??
3d 4s
On reaching Cr (Z 24) a strange phenomena takes
place
This will be the expected electronic
configuration for Cr.
24Cr Ar ? ? ? ? ??
3d 4s
The 3d orbital has 4 electrons and the 4s orbital
has 2 electrons. Reorganization of the electrons
takes place to make the respective orbitals more
stable, and the electronic configuration will
become
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24Cr Ar ? ? ? ? ? ?
3d 4s
The 3d orbital is now half-filled and is
associated with greatly enhanced stability!!
Greatly enhanced stability of the half-filled
d-orbitals!!
The reason for this stability is very complex an
will not be discussed here.
However, this phenomena is a very important one
and you have to remember to make the changes when
discussing electronic configuration involving the
transition elements!!!
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A simila phenomena occurs when the Cu atom (Z
29) reached
29Cu Ar 3d9 4s2
Greatly enhanced stability of the fully-filled
d-orbital
29Cu Ar ?? ?? ?? ?? ? ??
3d 4s
Will undergo re-organization to
29Cu Ar ?? ?? ?? ?? ?? ?
3d 4s
The fully-filled 3d orbital will bring greater
stability to the atom and hence the electronic
configuration will be written as
29Cu Ar 3d10 4s1
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Magnetic Properties

• Substances with unpaired electrons are slightly
  attracted to a magnet and are called
  paramagnetic.
• Substances in which all electrons are paired are
  called diamagnetic.
• The distribution of electrons among the orbitals
  of an atom is called the electronic structure or
  electronic configuration.

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Magnetic Properties (contd)

• The magnetic properties of a substance can be
  determined by weighing the substance in the
  absence and in the presence of a magnetic field.

Of course you will need a very sensitive balance!!
The mass appears to have increased, so this
substance must be ____________ and must have
(paired, unpaired) electrons.
paramagnetic
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• To indicate the ground state electron
  configuration we can
• List the sub-shells that contain electrons and
  indicate their electron population with a
  superscript.
• Represent each orbital with a circle and use
  arrows to indicate the spin of each electron.
• Electron configurations must be consistent with
  the Pauli principle, aufbau principle, and Hunds
  rule
• Example N 1s22s22p3, Na 1s22s22p63s1

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• Electron configurations explain the structure of
  the periodic table

The periodic table is divided into regions of 2,
6, 10, and 14 columns which is the maximum number
of electrons in s, p, d, and f sublevels. Subshel
ls that fill across the periods.
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Main Group andTransition Elements

• The main group elements are those in which the
  orbital being filled in the aufbau process is an
  s or a p orbital of the outermost shell.

In transition elements, the subshell being filled
in the aufbau process is in an inner principal
shell.
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Using the Periodic Table to Write Electron
Configurations
The electron configuration of Si ends with 3s2 3p2
The electron configuration of Rh ends with 5s2 4d7
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Exceptions to the Aufbau Principle
Half-filled d subshell plus half-filled s
subshell has slightly lower in energy than s2 d4.
Filled d subshell plus half-filled s subshell has
slightly lower in energy than s2 d9.
More exceptions occur farther down the periodic
table. They arent always predictable, because
energy levels get closer together.
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Valence Electrons and Core Electrons

• The valence shell is the outermost occupied
  principal shell. The valence shell contains the
  valence electrons.
• For main group elements, the number of valence
  shell electrons is the same as the periodic table
  group number (2A elements two valence electrons,
  etc.)
• The period number is the same as the principal
  quantum number n of the electrons in the valence
  shell.
• Electrons in inner shells are called core
  electrons.

Example As Ar 4s2 3d104p3
84
Electron Configurations of Ions

• To obtain the electron configuration of an anion
  by the aufbau process, we simply add the
  additional electrons to the valence shell of the
  neutral nonmetal atom.
• The number added usually completes the shell.
• A nonmetal monatomic ion usually attains the
  electron configuration of a noble gas atom.
• O2 1s2 2s2 2p6 Ne
• Br Kr

85
Electron Configurations of Ions (contd)

• A metal atom loses electrons to form a cation.
• Electrons are removed from the configuration of
  the atom.
• The first electrons lost are those of the highest
  principal quantum number.
• If there are two subshells with the same highest
  principal quantum number, electrons are lost from
  the subshell with the higher l.

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Electron Configurations of Ions (contd)
Atom Ion (or) F 1s2 2s22p5 F 1s2 2s22p6
Ne S Ne 3s2 3p4 S2 Ne 3s2 3p6 Ar
Sr Kr 5s2 Sr2 Kr 5s2 Kr
Ti Ar 4s2 3d2 Ti4 Ar 4s2 3d2 Ar
Fe Ar 4s2 3d6 Fe2 Ar 4s2 3d6 Ar 3d6
What would be the configuration of Fe3? Of
Sn2?
Valence electrons are lost first.
87

• For the representative elements (A Groups) the
  electrons with the highest n value or valence
  shell are normally the only electrons important
  for chemical properties
• For these elements the valence electrons consist
  of just the s and p sub-shells encountered
  crossing the period that contains the element in
  question
• Example the valence configuration of bromine is
• Br 4s24p5

88

• There are few important exceptions to the
  expected electronic figurations of commonly
  encountered elements
• Following the rules for Cr, Cu, Ag, and Au using
  noble gas notation

89
The shapes of orbitals

• The position of an electrons must be described
  with probabilities
• Heisenbergs uncertainty principle says that it
  is impossible to measure with complete precision
  the velocity and position of a particle
  simultaneously

90

• These limitations are not important for large
  objects but are very important for small
  particles like electrons
• Quantum mechanics requires that we talk about the
  probability of finding an electron in a
  particular region of space
• This probability is often represented as an
  electron cloud about the nucleus
• The probability varies with distance from the
  nucleus

91

• This type of plot shows that electron density
  varies from place to place
• Electron density variations define the shape,
  size, and orientation of orbitals

(a) A dot-density diagram for an electron in a 1s
orbital. (b) Graph of probability versus distance.
92
Orbitals get larger as the principle quantum
number n increases. Nodes, or regions of zero
electron density, appear beginning with the 2s
orbital.

• p orbitals are quite different from s orbitals
• They posses a nodial plane which includes the
  nucleus and separates the lobes of high
  probability

93
Dot-density diagrams of the cross section of the
probability distribution of a single (a) 2p and
(b) 3p orbital showing the nodal plane.

• Recall that there are three different orbitals in
  each p subshell

The directions of maximum electron density lie
along lines that are mutually perpendicular. It
is convenient to label the orbitals as px, py,
and pz
94

• The shape and orientation of d orbitals are more
  complicated than for p orbitals
• Shape and directional properties of the five d
  orbitals in a d su-bshell. These orbitals are
  dxy, dxz, dyz, dx2-y2 and dz2 orbitals
• The f orbitals are even more complex than the d
  orbitals

95
The effective nuclear charge

• The amount of positive charge felt by outer
  electrons in atoms other than hydrogen is called
  the effective nuclear charge
• It is lower than the atomic number because of
  shielding

If the 2- charges of the 1s2 core of lithium were
100 effective at shielding the 2s electron from
the nucleus, the valence electron would see a
charge of 1.
96

• The effective nuclear charge felt by outer
  electrons is determined primarily by the
  difference between the charge on the nucleus and
  the charge on the core- read pg. 337 onwards
  carefully!
• Effective nuclear charge controls a number of
  properties
• Atomic size increases top to bottom in a group
  because of increasing n and gets smaller left to
  right in a group because the effective nuclear
  charge increases

97

• Variation in atomic and ionic radii. Values in
  picometers (10-12 m)

98
Periodic Properties Atomic Radius

• Half the distance between the nuclei of two atoms
  is the atomic radius.
• Covalent radius half the distance between the
  nuclei of two identical atoms joined in a
  molecule.
• Metallic radius half the distance between the
  nuclei of adjacent atoms in a solid metal.

99
Lanthanide contraction
When a row of transition metals is traversed from
right to left, a reduction in atomic size occurs.
This is because the inner orbitals are being
filled. These partially filled inner orbitals are
not able to give the full shielding effect to the
outer valence electrons. These outer electrons
are thus progressively drawn more closer to the
nucleus making the atom smaller.
- The filling of the d orbitals!!
The same phenomena takes place for the inner
transition metals i.e. the lanthanides and the
actinides where the 4f and the 5f orbitals are
being filled.
100
Lets look at the example

• Y Zr
• La Hf

The lanthanide elements occurs between the two
elements shown.
In period 5, there are no transition elements
like the lanthanides.
39Y 40Zr a difference of one
proton
Only a small change in size occurs.
57La 72Hf a difference of 15
protons
A drastic change in size occurs between La and Hf
as compared to the sizes of Y and Zr!!!
101
As a result!
39Y 40Zr 162 145
57La 72Hf 169 144
This contraction results in the size of Zr and Hf
having almost the same size although Hf is below
Zr in the group IVB.
This drastic reduction in size is called the
lanthanide contraction.
102
Ionic Radii
The ionic radius of each ion is the portion of
the distance between the nuclei occupied by that
ion.
103
Ionic Radii

• Cations are smaller than the atoms from which
  they are formed the value of n usually
  decreases. Also, there is less electronelectron
  repulsion.

104
Ionic Radii

• Anions are larger than the atoms from which they
  are formed.
• Effective nuclear charge is unchanged, but
  additional electron(s) increase electronelectron
  repulsion.
• Isoelectronic species have the same electron
  configuration size decreases with effective
  nuclear charge.

105
SomeAtomicandIonicRadii
106

• The size trends in ions can be summarized
• Positive ions are always smaller than the atoms
  they are formed
• Negative ions always larger than the atoms from
  which they are formed

Adding electrons leads to an increase in size of
a particle, as illustrated for fluorine. Removing
electrons decreases the size of the particle, as
shown for lithium and iron.
107

• Ionization energy (IE) is the energy required to
  remove an electron from an isolated, gaseous atom
• Successive ionizations are possible until no
  electrons remain
• The trends in IE are the opposite of the trends
  in atomic size

108
Variations in first ionization-energies. Elements
with the largest ionization energies are in the
upper right of the periodic table. Those with the
smallest ionization energy are at the lower left.
109
Variations in successive ionization energies.
Note that it is extremely difficult to break into
the noble gas core (2nd through 8th ionizations
for Li through F, respectfully.
110
Selected Ionization Energies
Compare I1 to I2 for a 2A element, then for the
corresponding 1A element.
Why is I2 for each 1A element so much greater
than I1?
Why dont we see the same trend for each 2A
element? I2 gt I1 but only about twice as great

111
Ionization Energy

• Ionization energy (I) is the energy required to
  remove an electron from a ground-state gaseous
  atom.
• I is usually expressed in kJ per mole of atoms.
• M(g) ? M(g) e ?H I1
• M(g) ? M2(g) e ?H I2
• M2(g) ? M3(g) e ?H I3

112
Ionization Energy Trends

• I1 lt I2 lt I3
• Removing an electron from a positive ion is more
  difficult than removing it from a neutral atom.
• A large jump in I occurs after valence electrons
  are completely removed (why?).
• I1 decreases from top to bottom on the periodic
  table.
• n increases valence electron is farther from
  nucleus.
• I1 generally increases from left to right, with
  exceptions.
• Greater effective nuclear charge from left to
  right holds electrons more tightly.

113
Selected Ionization Energies
General trend in I1 An increase from left to
right, but
The electron being removed is now a p electron
(higher energy, easier to remove than an s).
I1 drops, moving from 2A to 3A.
I1 drops again between 5A and 6A.
Repulsion of the paired electron in 6A makes that
electron easier to remove.
114
First Ionization Energies
Change in trend occurs at 2A-3A and at 5A-6A for
each period
115
Why are these anomalies present in the First
Ionization Energies?
The ionization produces a more stable electronic
configuration less energy is required driving
force!!
Let us look at an example.
IE Be gt IE B
1s2 2s2 1s2 2s2 2p1
900
800
Be B
1s2 2s1 1s2 2s2
The stable electronic configuration is destroyed
energy required is high!!
116
Another example..
IE N gt IE O
1s2 2s2 2p3
1s2 2s2 2p4 (1402)
(1314)
N O
1s2 2s2 2p2 1s2
2s2 2p3
The stable half-filled electronic configuration
is destroyed energy required is high!!
The ionization produces a more stable half-filled
electronic configuration less energy is
required driving force!!
117
IE Mg gt IE Al
Ne3s2 Ne3s2 3p1
Mg Al Ne3s1
Ne3s2
The ionization produces a more stable
fully-filled electronic configuration less
energy is required driving force!!
The stable fully-filled electronic configuration
is destroyed energy required is high!!
118
First Ionization Energies
Change in trend occurs at 2A-3A and at 5A-6A for
each period
119
Electron Affinity

• The electron affinity (EA) is the potential
  energy change associated with the addition of an
  electron to a gaseous atom or ion in its ground
  state
• The addition of one electron to a neutral atom is
  exothermic for nearly all atoms
• The addition of more electrons requires energy ?
  to over come the electrostatic repulsion from the
  electrons already present.

120
Electron Affinity
Electron affinity can also be explained in terms
of stable electronic configuration
Cl(g) e- Cl-(g) (process exothermic)
Ne3s2 3p5 Ne3s2 3p6 ? Ar
O(g) e- O-(g) He2s2 2p4 He2s2
2p5 O-(g) e- O2-(g) He2s2 2p5
He2s2 2p6
Exothermic Process
Endothermic Process (?)
Electron affinity is difficult to determine.
121
Selected Electron Affinities
The halogens have a greater affinity for
electrons than do the alkali metals, as expected.
122
Variation of Electron Affinities
123

• Consider the addition of electrons to oxygen
• The results for first electron affinities can be
  generalized

124

• In general
• EA increases from left to right in a period
• EA increases bottom to top in a group

125
Metals

• Metals have a small number of electrons in their
  valence shells and tend to form positive ions.
• For example, an aluminum atom loses its three
  valence electrons in forming Al3.
• All s-block elements (except H and He), all d-
  and f-block elements, and some p-block elements
  are metals.

126
Metallic Character

• Metallic character is related to atomic radius
  and ionization energy.

• Metallic character generally increases from right
  to left across a period, and increases from top
  to bottom in a group.

127
Nonmetals

• Atoms of a nonmetal generally have larger numbers
  of electrons in their valence shell than do
  metals.
• Many nonmetals tend to form negative ions.
• All nonmetals (except H and He) are p-block
  elements.

Nonmetallic character generally increases
right-to-left and increases bottom-to-top on the
periodic table (the opposite of metallic
character).
128
Metalloids

• A heavy stepped diagonal line separates metals
  from nonmetals some elements along this line are
  called metalloids.
• Metalloids have properties of both metals and
  nonmetals.

129
A Summary of Trends
130
The Noble Gases

• The noble gases are on the far right of the
  periodic table between the highly active
  nonmetals of Group 7A and the very reactive
  alkali metals.
• The noble gases rarely enter into chemical
  reactions because of their stable electron
  configurations.
• However, a few compounds of noble gases (except
  for He and Ne) have been made.

131
Flame Colors
Atoms emit energy when electrons drop from higher
to lower energy states (Ch.7).
K
Na
Li
Elements with low first ionization energies can
be excited in a Bunsen burner flame, and often
emit in the visible region of the spectrum.
Ba
Sr
Ca
Elements with high values of IE1 usually require
higher temperatures for emission, and the emitted
light is in the UV region of the spectrum.
132
Oxidizing and Reducing Agents Revisited

• The halogens (Group 7A) are good oxidizing
  agents.
• Halogens have a high affinity for electrons, and
  their oxidizing power generally varies with
  electron affinity.

When Cl2 is bubbled into a solution containing
colorless iodide ions
Displaced I2 is brown in aqueous solution
the chlorine oxidizes I to I2, because EA1 for
Cl2 is greater than EA1 for I2.
but dissolves in CCl4 to give a beautiful
purple solution.
133
Oxidizing and Reducing Agents Revisited

• The s-block elements are very strong reducing
  agents.
• All the IA metals and the heavier IIA metals will
  displace H2 from water, in part because of their
  low values of IE1.
• A low IE1 means that the metal easily gives up
  its electron(s) to hydrogen in water, forming
  hydrogen gas.

while magnesium is largely non-reactive toward
cold water.
Potassium metal reacts violently with water. The
liberated H2 ignites.
Calcium metal reacts readily with water
134
Acidic, Basic, and Amphoteric Oxides

• An acidic oxide produces an acid when the oxide
  reacts with water.
• Acidic oxides are molecular substances and are
  generally the oxides of nonmetals.
• Basic oxides produce bases by reacting with
  water.
• Often, basic oxides are metal oxides.
• An amphoteric oxide can react with either an acid
  or a base.

135
Properties of the Oxides of the Main-group
Elements
The metalloids and some of the heavier metals
form amphoteric oxides.
136
Assignment 4(b)
Thats all for this chapter
Do the following exercise at the end of your
text book.
Dont go away there is a surprise!!!
8.139 8.145 8.140 8.146 8.141 8.147 8.142 8.14
9 8.144 8.150
To be handed in on or before 5/9/2005