Chapter 5 - Blinn College

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Blinn College, Bryan Campus

Dr. Beverly A. Clement

Copyright, 2002

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Dr. Beverly A. Clement

Copyright, 2007

CHAPTER 5

Periodicity an Atomic
Structure

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The Periodic Table

Developed in 1869 by Dmitri Mendeleev.

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Electromagnetic Radiation

wavelength

l

(Greek lower case lambda)


distance from the top (crest) of one wave to the
top of the next wave

units of distance
-

m, cm,

Å

1

Å =
1




10

m = 1




8
cm

frequency



(Greek lower case nu)





this is sometimes represented as


(italicized v)


number of crests (wavelengths) that pass a given
point per second

units of frequency = 1/time or s

1
or Hertz (Hz)

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Electromagnetic Radiation

Relationship for electromagnetic
radiation


c

=
l



c = velocity of light

3.00



8

m/s or 3



10

cm/s

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Electromagnetic Radiation


Example 1: What is the frequency of green light of
wavelength 5200

Å
? (c = 3.00



8

m/s)

First convert

Å

to
m

m
10
200
.
5
Å
m

0
1
1

Å
5200
7
10






l

l
c



c



m
10


5.200

10


3.00


7
s
m
8





1
14
s

10


5.77






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Atomic Spectra and Bohr Theory


Rydberg’s equation is an empirical equation that
relates the wavelengths of the lines in the
hydrogen spectrum.


m

n

constant)

s
(Rydberg'

m

10


1.097


R

1
7



H

of

spectrum

emission

the

in

lines

the

of

number

the

to

refer

n

and

m





















2
2
2
2
n
1
m
1
c
R

or

n
1
m
1
R


1

l
You will encounter the universal gas constant
R

later.
Don’t confuse it with Rydberg’s constant R.

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Electromagnetic Radiation

Why worry about wavelength and
frequency?


These can be used to calculate energy.

Again, why?


Energy does lots of things both good and bad.


How much light at what frequency is needed to cause
cancer?


How many cells are required to work a calculator in dim
light?


How sensitive is a motion detector or electric eye timer?


How much light is required to darken light sensitive
glasses?

Etc.

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Electromagnetic Radiation


Max Planck calculated the energy that is
quantized in a photon.

The energy of light can be expressed as

l

c



or


h
E
h
E


s
J

10


6.626


constant

s
Planck’


34





h
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Electromagnetic Radiation


Example 2: What is energy of a photon of green light
with wavelength 5200 Å? (c = 3.00



8

m/s;
h =
6.626



10

34
J∙s
)

l

c



or


h
E
h
E


5200 Å = 5.200




7

m

m
10
200
.
5
)
10

s)(3.00
J
10
626
.
6
(
7
s
m
8
34







E
J/photon
10
83
.
3
19



E
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Electromagnetic Radiation


Example 3: What is energy of 1 mole of photons
of green light with wavelength 5200 Å?

From the previous example


J/photon
10
83
.
3
19



E
l)
photons/mo
10
6.02
(

J/photon)
10
83
.
3
(
23
19




E
kJ/mol

231

or

J/mol

10
31
.
2
5


E
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The Wave Nature of the Electron


Louis de Broglie postulated that electrons have
wave
-
like properties


The wavelengths of electrons are described by
the
de Broglie relationship.

v
h
m



l
constant

s
Planck’



h
kg)

(in

particle

of

mass


m

particle

of
velocity


v

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Photoelectric Effect


Albert Einstein explained that light had both particle
and energy characteristics.


The particle/energy unit of light was called a photon.



FYI.
Einstein won the 1921 Nobel Prize in Physics
for this discovery.

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Atomic Spectra and Bohr Theory


It had been known that an electric current passing
through a gas in a vacuum tube (at very low
pressure) caused the gas to emit light.


This light could be broken into its components and
was found to be a series of
bright
lines.

This is a
bright line

or
emission

spectrum

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Atomic Spectra and Bohr Theory


It was also known that if you passed a beam of
white light through a sample of gas, the spectrum
would show a series of dark lines where the specific
wavelengths of light had been absorbed.

This is
dark line

or
absorption

spectra.

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Atomic Spectra and Bohr Theory


These spectra are as characteristic as fingerprints
and can be used to identify elements.


This is commonly used to identify the elements in
individual stars and the atmospheres of their
planets.

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Atomic Spectra and Bohr Theory


The spectra of atoms provides quite a bit of
information about their internal structure.


Bohr, Schrodinger, and Heisenberg were some of
the first to translate the language of atoms.

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The Origin of Spectral Lines


Light of a characteristic wavelength (and
frequency) is absorbed when an electron
jumps from lower
E

(orbit) to higher
E

(orbit).



This jump in energy is the original
quantum
leap
.




This is the origin of absorption spectrum.




The energy is specifically characteristic of
the energy quantum levels available to the
electrons in an elements electron shell.

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The Wave Nature of the Electron


Electrons, all particles for that matter, have both
a particle and a wave like character.



Wave
-
particle duality is a fundamental property of
submicroscopic particles.



Newtonian physics (gravity, friction, etc.) deals
with regular objects.



Subatomic particles follow their own laws of
physics called
quantum mechanics
.

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Quantum Mechanical Picture

Heisenberg Uncertainty Principle


It is impossible to determine simultaneously both
the position and momentum of an electron.



Any device for detecting the motion of an electron
disturbs its position and/or momentum.


Therefore the positions and momentum of
electrons must be described in terms of probability
functions (

Ⱐ瑨攠䝲敥欠
psi
)
.


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Quantum Numbers

Basic Postulates of Quantum Theory


Atoms and molecules can exist only in certain
energy states. In each energy state, the atom or
molecule has a definite energy. When an atom
or molecule changes its energy state, it must
emit or absorb just enough energy to bring it to
the new energy state (the quantum condition).



The allowed energy states of atoms and
molecules can be described by sets of numbers
called
quantum numbers
.

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Quantum Numbers


Quantum numbers

are solutions of the
Schr
ö
dinger, Heisenberg & Dirac
equations


Four quantum numbers are necessary to
describe the energy states of electrons in
atoms

n


the principle quantum number





subsidiary quantum number

m




magnetic quantum number

m
s


spin quantum number

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Quantum Numbers

Principal Quantum Number



n


This is the first quantum number and describes the
shell or layer that the electrons are found in.


These are numbered sequentially with the
innermost level beginning with the number
1
.

n = 1, 2, 3, 4, ......


There is an alternate numbering system using
letters, the first level begins with letter
K
.

n = K, L, M, N, ......


The electron’s energy depends principally on n.


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Quantum Numbers

Subsidiary Quantum number





The subsidiary quantum number,

Ⱐ摥d捲楢敳c瑨t

shape of the orbital
the electron occupies
.


These have the value of
n
-
1

and are assigned the
values of



= 0, 1, 2, 3, 4, 5, .......(
n
-
1
)


Like n, these values may also be described as
letters



=
s

(0),
p
(1),
d

(2), f (3),
g

(4),
h

(5),..


This is the shape (volume) that the electrons
occupy 90
-
95% of the time.

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Quantum Numbers

Magnetic quantum number


m



This quantum number indicates specifically which
orbital the electron resides in.


Unlike

,

m


楳湬n 摥d捲楢敤⁢c 湵浢n牳⁡湤慹
桡h攠愠癡汵攠潦‫e

, 0,




⡯爠
±



and 0).

For n = 1,


=

0
,
and m


= 0


this describes the
s

orbital


there is only 1
s

orbital per quantum level (shell)


and

the first shell only has one type of orbital

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Quantum Numbers

Magnetic quantum number


m


For n = 2,


㴠=⁡湤‱


景爠渠㴠=†


㴠=Ⱐ,


㴠=



this is an
s
orbital (remember 1
s

per level)




for n = 2


㴠=Ⱐ,


㴠⬱Ⱐ〬0

1



this is a
p

orbital, there are 3
p
orbitals

Row 2 (the L shell) is the first shell to have
p

orbitals.


The 3
p

orbitals are described according to the axis
they lie along.

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Quantum Numbers

Magnetic quantum number


m


For n = 3,


㴠=Ⱐㄬ⁡湤′


景爠渠㴠=


㴠=Ⱐ,


㴠=



this is an
s
orbital (remember 1
s

per level)




for n = 3


㴠=Ⱐ,


㴠⬱Ⱐ〬0

1


this is a
p

orbital, beginning with row 2 there are 3
p
orbitals per shell


for n = 3


㴠=Ⱐ,


㴠⬲Ⱐ⬱Ⱐ〬+

1,

2


this is a
d

orbital, beginning with row 3, the
possibility of
d
orbitals exists (even though
d

orbitals don’t show up until an element has already
begun to fill shell 4)

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Quantum Numbers

Magnetic quantum number


m


For n = 4,


㴠=Ⱐㄬ′ⱡ湤,3


景爠渠㴠=


㴠=Ⱐ,


㴠=

(1 orbital)



this is an
s
orbital (remember 1
s

per level)



for n = 4


㴠=Ⱐ,


㴠⬱Ⱐ〬0

1


this is a
p

orbital, 1 group of 3
p

orbitals per shell
beginning with Row 2


for n = 4


㴠=Ⱐ,


㴠⬲Ⱐ⬱Ⱐ〬+

1,

2


this is a
d

orbital, 1 group of 5
d

orbitals (possible) per
shell beginning with Row 3

for n = 4


㴠=Ⱐ,


㴠⬳Ⱐ⬲Ⱐ⬱Ⱐ〬0

1,

2,

3


these are
f

orbitals, 1 group of 7
f

orbitals (possible) per
shell beginning with Row 4

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Quantum Numbers

Spin Quantum Number
-

m
s



This is the final quantum number and represents the
spin of the electron.


The spin of an electron is arbitrarily assigned a
value of
±

½.


Each orbital may hold a maximum of 2 electrons,
one with a spin of +
½
, the other with a spin of

½


Pauli Exclusion Principle


No two electrons in an atom can have the same
set of 4 quantum numbers.

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Atomic Orbitals


Atomic orbitals are defined as regions of space
where the probability of finding an electron about an
atom is highest.


The orbital levels are described either as:



n = 1, 2, 3, 4, 5…



or by K, L, M, N, …..


FYI
. There is a specific type of nuclear decay in
which the nucleus captures an interior electron as
part of its radioactive decay. This decay is called K
-
capture after the orbital the electron came from.

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Atomic Orbitals


The innermost orbital of any level is the
s

orbital.


There is
one
s

orbital per level.





㴠=†慮搠m


㴠=

The
s
orbital is spherically symmetrical.

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Atomic Orbitals

Row 2 is the first to have
p

orbitals




㴠=†慮搠m


㴠ㄬ‰Ⱐ

1


These orbitals are described as dumbbell or peanut
shaped.

There are 3 mutually perpendicular
p
orbitals
directed along the axes of a Cartesian coordinate.

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Atomic Orbitals

Row 3 is the first to have
d

orbitals allowed




= 2 and m


㴠㈬ ㄬ1〬0

1,

2



There are 4 clover leaf shaped
d

orbitals
rotated 45
°

off the Cartesian axes

And 1
peanut

shaped orbital with a halo or
donut around it.

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Atomic Orbitals

Row 4 is the first to have
f

orbitals allowed



㴠=†慮搠m


㴠㌬′Ⱐㄬ,〬0

1,

2,

3

These are the most complex shaped orbitals.


Four are described as double cloverleaf or double
dumbbell shaped orbitals.

The remaining three
f

orbitals are dumbbell
shaped each with a pair of halos or donuts

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Atomic Orbitals


Each atom from H through the most recently
discovered is built up sequentially one electron at
a time.

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Atomic Orbitals


The last quantum number deals with the spin of
the electrons.


Electrons spin and since they carry a charge, this
spinning results in a magnetic field.


Experimentally it has been determined that
unpaired electrons have their spin aligned (their
magnetic fields add together).


Each orbital may contain a maximum of 2
electrons.


For electrons to pair, they must have opposite
spins.

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Atomic Orbitals


Compounds which contain unpaired
electrons are paramagnetic.

paramagnetic


attracted to a magnet


Compounds in which all electrons are
paired are diamagnetic.

diamagnetic


repelled by a magnet


There is one more type of magnetism
associated with compounds,
ferromagnetism.

ferromagnetic


compounds of Fe, Co, or Ni,
which may be permanently magnetized

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Atomic Orbitals


The maximum number of orbitals per n level is may
be calculated by n
2


The maximum number of electrons that may exist
per n level is 2n
2

Energy Level

# of Orbitals

Max. # of e




n



n
2



2n
2



1




1




2



2




4




8



3




9



18



4



16



32

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Quantum Mechanics


and Atomic Line Spectra









2
2
1
1
λ
1
n
m
R
1
2
nm
10
097
.
1

constant

Rydberg





R
shell

inner

to

is

transition

the

shell

m
shell

outer

from

is

transition

the

shell

n
Lyman series


ultraviolet

Balmer series


visible

Paschen series
-

infrared

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Electronic Configurations

Aufbau Principle


The electron that distinguishes an
element from the previous element
enters the lowest energy atomic orbital
available.


Hund’s Rule


Electrons will occupy all orbitals singly
before pairing can begin.


The spins of these electrons will be aligned.

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Electronic Configurations


According to the Aufbau Principle, electrons enter
the lowest energy atomic orbital available.


The first hitch in this orderly progression occurs at
the end of row 3 of the periodic table.

4
s

is lower in energy than 3
d

which is followed by 4
p


This is repeated again at the end of row 4

5
s

is lower in energy than 4
d

which is followed by 5
p


This is repeated again and develops a new twist at
the lanthanides.

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Electronic Configurations

The reason for this anomaly is
Hund’s Rule.


Electron Orbital Stability


Completely filled orbitals are very stable.


Completely empty orbitals are very stable.


Half
-
filled orbitals, while not as stable as filled or
empty orbitals, are much more stable than
partially filled orbitals.

Reactions occur to obtain orbital stability.

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Electronic Configurations


Consider the two possibilities available to an
electron entering after 3
p.


4


3












s
d

partially filled orbital
unstable


4


3













s
d

half filled orbital
stable

Now add the second electron to these two possibilities.


4


3













s
d


partially filled orbitals
unstable


4


3











s
d

filled orbital
very

stable

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Electronic Configurations


The easiest way to see this is to use the
periodic table.

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Electronic Configurations

An alternate method to view the periodic table is:

1

2

3

4

5

6

7

3
d

4
d

5
d

6
d

4
f

5
f

d
-
transition elements

f
-
transition elements

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Electronic Configurations


Just as each element differs from its
predecessor by the addition of one proton,
each element differs from the preceding
element by the addition of 1 electron to its
orbital configuration.


Atomic orbitals are built up by this step
-
wise addition of electrons.

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Electronic Configurations

1
st

Row Elements

ion
Configurat

Electronic

1

s
1
1
1




H
s

2
2
1



He
s

Remember, the atomic number is equal to the number
of electrons found in the neutral atom.

Each positive charge means 1 less electron than this
number.

Each negative charge means 1 more electron than the
number of protons present.

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Electronic Configurations

2
nd

Row
Elements

ion
Configurat

Electronic

2

2

1

p
s
s
1
2
3
2
1










Li
s

s


2
2
4
2
1










Be
s

s



1
2
2
5
2
2
1










B
p

s

s




2
2
2
6
2
2
1










C
p

s

s





3
2
2
7
2
2
1










N
p

s

s






4
2
2
8
2
2
1









O
p

s

s






5
2
2
9
2
2
1








F
p

s

s






6
2
2
10
2
2
1







Ne
p

s

s






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Electronic Configurations

3
rd

Row Elements

ion
Configurat

Electronic

3


3


p
s




1
11
3

Ne









Ne

Na
s





2
12
3

Ne








Ne

Mg
s





1
2
13
3
3

Ne








Ne

Al
p

s






2
2
14
3
3

Ne








Ne

Si
p

s







3
2
15
3
3

Ne








Ne

P
p

s








4
2
16
3
3

Ne







Ne

S
p

s








5
2
17
3
3

Ne






Ne

Cl
p

s








6
2
18
3
3

Ne





Ne

Ar
p

s




49

Blinn College, Bryan Campus

Dr. Beverly A. Clement

Copyright, 2002

49

Blinn College, Bryan Campus

Dr. Beverly A. Clement

Copyright, 2007

Electronic

Configurations

4
th

Row
Elements

ion
Configurat

Electronic

4

4


3
p
s
d
Two half filled orbitals are more stable than a filled and
partially filled orbital.

This is seen throughout the elements.





1
19
4

Ar



















Ar
K
s





2
20
4

Ar


















Ar

Ca
s





1
2
21
3
4

Ar


















Ar
Sc
d

s






2
2
22
3
4

Ar


















Ar

Ti
d

s







3
2
23
3
4

Ar


















Ar
V
d

s








5
1
24
3
4

Ar



















Ar

Cr
d

s






50

Blinn College, Bryan Campus

Dr. Beverly A. Clement

Copyright, 2002

50

Blinn College, Bryan Campus

Dr. Beverly A. Clement

Copyright, 2007

Electronic Configurations

4
th

Row Elements





5
2
25
3
4

Ar


















Ar

Mn
d

s










6
2
26
3
4

Ar

















Ar

Fe
d

s










7
2
27
3
4

Ar
















Ar

Co
d

s










8
2
28
3
4

Ar















Ar

Ni
d

s










10
1
29
3
4

Ar














Ar

Cu
d

s










10
2
30
3
4

Ar













Ar

Zn
d

s






ion
Configurat

Electronic

4

4


3
p
s
d
51

Blinn College, Bryan Campus

Dr. Beverly A. Clement

Copyright, 2002

51

Blinn College, Bryan Campus

Dr. Beverly A. Clement

Copyright, 2007

Electronic Configurations

4
th

Row Elements

ion
Configurat

Electronic

4

4


3
p
s
d




1
10
2
31
4
3
4

Ar













Ar

Ga
p

d

s











2
10
2
32
4
3
4

Ar













Ar

Ge
p

d

s












3
10
2
33
4
3
4

Ar













Ar

As
p

d

s













4
10
2
34
4
3
4

Ar












Ar

Se
p

d

s













5
10
2
35
4
3
4

Ar











Ar

Br
p

d

s













6
10
2
36
4
3
4

Ar










Ar

Kr
p

d

s









52

Blinn College, Bryan Campus

Dr. Beverly A. Clement

Copyright, 2002

52

Blinn College, Bryan Campus

Dr. Beverly A. Clement

Copyright, 2007

Electronic Configurations


What about the direction of the arrows
indicating the spin on the electron?


It doesn’t what direction of spin you choose to use
first for an atom as long as you are consistent.


If the first arrow is shown pointed down, each of the
electrons must enter empty orbitals with a downward
pointing electron.

(or vice versa)

53

Blinn College, Bryan Campus

Dr. Beverly A. Clement

Copyright, 2002

53

Blinn College, Bryan Campus

Dr. Beverly A. Clement

Copyright, 2007

Atomic Radii


(A Group Elements Only)


Atomic radii describes the size of atoms.


This increases as you go from the right to the left.
(opposite what you would think since more e


are
added.)


This increases from top to bottom.

(as expected


more shells are being added)

radii increases

54

Blinn College, Bryan Campus

Dr. Beverly A. Clement

Copyright, 2002

54

Blinn College, Bryan Campus

Dr. Beverly A. Clement

Copyright, 2007

Atomic Radii

All radii are in angstroms,
Å
.

55

Blinn College, Bryan Campus

Dr. Beverly A. Clement

Copyright, 2002

55

Blinn College, Bryan Campus

Dr. Beverly A. Clement

Copyright, 2007

Atomic Radii


The decreasing radii across a period is due to the
shielding or screening effect of the inner electrons
[He] or [Ne], etc.


Consequently the outer electrons feel a stronger
effective nuclear charge than expected.


Li [He] shields effective charge is +1


Be [He] shields effective charge is +2


F [He] shields effective charge is +7


Na [Ne] shields effective charge is +1

56

Blinn College, Bryan Campus

Dr. Beverly A. Clement

Copyright, 2002

56

Blinn College, Bryan Campus

Dr. Beverly A. Clement

Copyright, 2007

End of Chapter 5