Transcript Chapter 6 - Clayton State University

CHAPTER 6
Electronic Structure
and the Periodic Table
Electromagnetic Radiation
Wave nature of light
wavelength - l
distance from the top (crest) of one wave to the top of
the next wave
units of distance - m,cm, Å
1 Å = 1 x 10-10 m = 1 x 10-8 cm
frequency - u
number of crests or troughs that pass a given point per
second
units of 1/time - s-1
Electromagnetic Radiation
Speed of the wave, v
Frequency multiplied by wavelength
V=lu
For light, speed = c
relationship for electromagnetic radiation c=lu
c = velocity of light 3.00 x 108 m/s
Electromagnetic Radiation
Electromagnetic Radiation
What is the frequency of green light of
wavelength 5200 Å?
Electromagnetic Radiation
What is the frequency of green light of
wavelength 5200 Å?
c  l  
c
l
 1 x 10 -10 m 
-7

(5200 Å) 

5.200

10
m


1Å


3.00  108 m/s
 
5.200  10 -7 m
  5.77  1014 s -1
Electromagnetic Radiation
Max Planck - 1900
energy is quantized
light has particle character
Planck’s equation
E  h  or E 
hc
l
h  Planck’ s constant  6.626 x 10-34 J  s
Electromagnetic Radiation
What is energy of a photon of green light
with wavelength 5200 Å?
Electromagnetic Radiation
What is energy of a photon of green light
with wavelength 5200 Å?
  5.77 x 1014 s -1 from before
E  h
E  (6.626  10-34 J  s)(5.77  1014 s -1 )  3.83  10-19 J per photon
Electromagnetic Radiation
What is energy of a photon of green light
with wavelength 5200 Å?
  5.77 x 1014 s -1 from Before
E  h
E  (6.626  10-34 J  s)(5.77  1014 s -1 )  3.83  10-19 J per photon
for 1 mol of photons we have
(6.022  10 23 photons)(3 .83  10-19 J per photon)  231 kJ/mol
Atomic Spectra & Bohr Theory
emission spectrum
electric current passing through a gas in a
vacuum tube (at very low pressure) causes the
gas to emit light
emission or bright line spectrum
Line Spectra
Radiation composed of only one
wavelength is monochromatic
Radiation that spans an array of different
wavelengths is continuous
White light is continuous
Atomic Spectra & Bohr Theory
absorption spectrum
shining a beam of white light through a sample
of gas gives an absorption spectrum
shows the wavelengths of light that have been
absorbed
Atomic Spectra & Bohr Theory
spectra are fingerprints of elements
use spectra to identify elements
can even identify elements in stars
Atomic Spectra & Bohr Theory
“how atoms talk to us”
we have to interpret their language
Bohr, Schrodinger, and Heisenberg were
some of the first scientists to translate the
language of atoms
Atomic Spectra & Bohr Theory
An orange line of wavelength 5890 Å is
observed in the emission spectrum of
sodium. What is the energy of one photon
of this orange light?
Atomic Spectra & Bohr Theory
An orange line of wavelength 5890 Å is
observed in the emission spectrum of
sodium. What is the energy of one photon
of this orange light?
 1  10-8 cm 
  5.890  105 cm
l  5890 Å 
Å


hc
E  h 
l

6.626  10

J  s 3.00  108 cm/s 
5.890  105 cm
 3.375  1021 J
34
Atomic Spectra & Bohr Theory
Rydberg equation
empirical equation that relates the wavelengths
of the lines in the hydrogen spectrum (Equ. 6.4 text)
 1
1 
 R  2  2 
l
 n1 n 2 
R  1.097  107 m-1
called the Rydberg constant
n1  n 2
1
n’ s refer to the numbers of the
lines in the emission spectrum
Atomic Spectra & Bohr Theory
Neils Bohr - 1913 - incorporated Planck’s
quantum theory into the H spectrum
explanation
Postulates of Bohr’s theory
Atomic Spectra & Bohr Theory
Atom has a number of definite and discrete
energy levels (orbits) in which an electron
may exist without emitting or absorbing
electromagnetic radiation.
increasing radius of orbit increases the
energy
K<L<M<N<O......
Atomic Spectra & Bohr Theory
An electron may move from one discrete
energy level (orbit) to another and in
doing so monochromatic radiation is
emitted or absorbed in accordance with
the following equation.
E
2
-E
1
 E  h 
E
2
 E
hc
l
1
E absorbed as electron jumps to higher orbit
E emitted as electron falls to lower orbit
Atomic Spectra & Bohr Theory
An electron moves in a circular orbit about the nucleus
and its motion is governed by the ordinary laws of
mechanics and electrostatics, with the restriction that
the angular momentum of the electron is quantized
(can only have certain discrete values).
angular momentum = mvr = nh/2p
h = Planck’s constant n = 1,2,3,4,...(energy levels)
v = velocity of electron m = mass of electron
r = radius of orbit
Atomic Spectra & Bohr Theory
Bohr theory correctly explains H emission
spectrum
fails for all other elements
just not an adequate theory
The Origin of Spectral Lines
light of a characteristic wavelength (&
frequency) is emitted when electron falls
from higher E (orbit) to lower E (orbit)
Origin of the emission spectrum
light of a characteristic wavelength (&
frequency) is absorbed when electron jumps
from lower E (orbit) to higher E (orbit)
origin of absorption spectrum
The Wave Nature of the Electron
Louis de Broglie -1925
electrons have wave-like properties
their wavelengths are described by the de
Broglie relationship
h
l
mv
h  Planck’ s constant
m  mass of particle
v  velocity of particle
The Wave Nature of the Electron
verified by Davisson & Germer two years
later
electrons (in fact - all particles) have both a
particle and a wave like character
wave-particle duality is a fundamental
property of submicroscopic particles
Quantum Mechanical Picture
Werner Heisenberg - 1927
Uncertainty Principle
It is impossible to determine simultaneously
both the position & momentum of an
electron.
Quantum Mechanical Picture
devices for detecting motion of electron disturbs
its position
like measuring position of a car with a wrecking
ball
must speak of electrons in terms of
probability functions
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).
Quantum Numbers
Atoms or molecules emit or absorb radiation
(light) as they change their energies. The
frequency of the light emitted or absorbed is
related to the energy change by a simple
equation.
hc
E  h 
l
Quantum Numbers
• The allowed energy states of atoms and
molecules can be described by sets of
numbers called quantum numbers.
Quantum Numbers
Quantum numbers are solutions of the
Schrodinger, Heisenberg & Dirac equations
electron wave functions
Four quantum numbers are necessary to
describe energy states of electrons in atoms
Quantum Numbers
Principal quantum number - n
n = 1, 2, 3, 4, ...... “shells”
n = K, L, M, N, ......
electron’s energy depends principally on n
Quantum Numbers
Subsidiary Quantum number - l
l = 0, 1, 2, 3, 4, 5, .......(n-1)
l = s, p, d, f, g, h, .......(n-1)
tells us the shape of orbitals
volume that the electrons occupy 90-95% of
the time
Quantum Numbers
Magnetic quantum number - ml
ml = - l, (- l + 1), (- l +2),.....0,.......,(l -2), (l -1), l
l = 0, ml = 0
only 1 value
s orbital
l = 1, ml = -1,0,+1
3 values
p orbitals
Quantum Numbers
l = 2, ml = -2,-1,0,+1,+2
5 values
d orbitals
l = 3, ml = -3,-2,-1,0,+1,+2, +3
7 values
f orbitals
theoretically, we can continue this series on to
g,h,i, orbitals
Quantum Numbers
Spin Quantum Number - ms
ms = +1/2 or -1/2
ms = ± 1/2
tells us the spin and orientation of the magnetic
field of the electrons
Wolfgang Pauli - 1925
Exclusion Principle
No two electrons in an atom can have the same set of 4
quantum numbers.
Atomic Orbitals
regions of space where the probability of finding
an electron about an atom is highest
described by either
n (1,2,3,4,5,...) or
letters (K,L,M,N,O,...)
s orbitals
spherically symmetric
one s orbital per n level
l=0
1 value of ml
Atomic Orbitals
s orbitals
Atomic Orbitals
p orbitals
start with n = 2
3 mutually perpendicular peanut shaped volumes
directed along the axes of a Cartesian coordinate system
3 per n level,
px, py, pz
l=1
ml = -1,0,+1 3 values of ml
Atomic Orbitals
p orbitals
Atomic Orbitals
d orbitals
start with n = 3
4 clover leaf shaped and 1 peanut shaped
with a doughnut around it
on Cartesian axes and rotated 45o
Atomic Orbitals
d orbitals
start with n = 3
4 clover leaf shaped and 1 peanut shaped with a
doughnut around it
on Cartesian axes and rotated 45o
5 per n level
l=2
ml = -2,-1,0,+1,+2
d xy , d yz , d xz , d x2 -y2 , d z2
5 values of ml
Atomic Orbitals
d orbitals
Atomic Orbitals
f orbitals
start with n = 4
most complex shaped orbitals
7 per n level, complicated names
l=3
ml = -3,-2,-1,0,+1,+2, +3
7 values of ml
important effects in lanthanides & actinides
Atomic Orbitals
f orbitals
Atomic Orbitals
spin effects
every orbital can hold up to two electrons
one spin up one spin down 
spin describes the direction of their
magnetic field
unpaired electrons have their spins aligned
or 
Atomic Orbitals
paired electrons have spins unaligned 
2 electrons in same orbital must be paired
consequence of Pauli Exclusion Principle
Atomic Orbitals
number of orbitals per n level is given by n2
maximum number of electrons per n level is
2n2
Atomic Orbitals
Energy Level
n
1
2
3
4
# of Orbitals
n2
1
4
9
16
Max. # of e2n2
2
8
18
32
Electronic Configurations
Aufbau Principle - The electron that
distinguishes an element from the
previous element enters the lowest
energy atomic orbital available.
Electronic Configurations
Electronic Configurations
Aufbau Principle
Electronic Configurations
use mnemonic
Electronic Configurations
use periodic chart - best method
Electronic Configurations
Write the electronic configuration for
EVERY ATOM on the PERIODIC
TABLE!!
Effective Nuclear Charge
Orbitals of the same energy are said to be
degenerate.
Effective nuclear charge is the charge experienced
by an electron on a many-electron atom.
The effective nuclear charge is not the same as the
charge on the nucleus because of the effect of the
inner electrons.
Effective Nuclear Charge
Electrons are attracted to the nucleus, but repelled by the
electrons that screen it from the nucleus.
The nuclear charge experienced by an electron depends on
its distance from the nucleus and the number of core
electrons.
As the average number of screening electrons (S)
increases, the effective nuclear charge (Zeff) decreases.
As the distance from the nucleus increases, S increases and
Zeff decreases.
Energies of Orbitals
The result of the Effective nuclear charge on the
electronic configuration is a shift of the orbital
ordering for large (n = 4 or more) electronic
systems.
Energies of Orbitals
Sizes of Atoms
Electron Shells in Atoms
Consider a simple diatomic
molecule.
The distance between the two
nuclei is called the bond distance.
If the two atoms which make up
the molecule are the same, then
half the bond distance is called
the covalent radius of the atom.
Atomic Radii
•As a consequence of the ordering in the periodic
table, properties of elements vary periodically.
•Atomic size varies consistently through the periodic
table.
•As we move down a group, the atoms become larger.
•As we move across a period, atoms become smaller.
There are two factors at work:
•principal quantum number, n, and
•the effective nuclear charge, Zeff.
Atomic Radii
decreasing across a period is due to:
shielding or screening effect
inner electrons [He] or [Ne], etc.
block the nuclear charge for 2 or 10 or __
electrons
consequently the outer electrons feel a
stronger effective nuclear charge
Li [He] shields effective charge is +1
Be [He] shields effective charge is +2
Atomic Radii
Atomic Radii
All radii are in angstroms.
Ionic Radii
Cations (+ ions) are always smaller than
their neutral atoms
Li
1.52
Li+
0.6
Na
1.86
Na+
0.95
Be
1.11
Be2+
0.31
Mg
1.6
Mg2+
0.65
Al
1.43
Al3+
0.5
Ionic Radii
Anions (- ions) are always larger than their
neutral atoms
N
0.7
N
3-
1.71
O
0.66
2O
1.4
F
0.64
F
-
1.36
Ionization Energy
minimum amount of energy required to
remove the most loosely held electron from an
isolated gaseous atom
measure of an element’s ability to form positive
ions
first ionization energy
Atom(g) + energy  ion+(g) + eMg(g) + 738kJ/mol  Mg+ + e-
Ionization Energy
second ionization energy
energy required to remove a 2nd electron
ion+ + energy  ion2+ + eMg+ + 1451 kJ/mol Mg2+ + e-
•
can have 3rd, 4th, etc. ionization energies
Ionization Energy
generally increases as you go across a
period
important exceptions at Be & Mg, N & P
generally decreases as you go down a group
Ionization Energy (kJ/mol) vs Atomic Number
2500
He
2
Ne
10
2000
F
9
1500
N
7
H
1
1000
Be
4
C
6
B
5
Li
3
500
O
8
Na
11
P S
15 16
Si
Mg
12 Al 14
13
Cl
17
Ar
18
K
19
Ca
20
0
0
5
10
15
20
Ionization Energy
First 4 ionization Energies (kJ/mol) - Period 3
1stIE
2ndIE
3rdIE
4thIE
IA
Na
496
4562
6912
9540
IIA
Mg
738
1451
7733
10,550
IIIA
Al
578
1817
2745
11,580
IVA
Si
786
1577
3232
4356
Ionization Energy
these energies are exactly why these ions
form
Na becomes Na+
Mg becomes Mg2+
Al becomes Al3+
Si does not form simple ions
Ionization Energy
Electronegativity
The attraction of an atom to electrons
This is not a measurable property BUT it is
very useful in helping to predict bonding
(attraction of electrons)
Electronegativity
Synthesis Question
What is the atomic number of the element that
should theoretically be the noble gas below
Rn?
The 6 d’s are completed with element 112 and
the 7d’s are completed with element 118. Thus
the next noble gas (or perhaps it will be a
noble liquid) should be element 118.
Group Question
In a universe different from ours, the laws of
quantum mechanics are the same as ours with
one small change. Electrons in this universe
have three spin states, -1, 0, and +1, rather
than the two, +1/2 and -1/2, that we have.
What two elements in this universe would be
the first and second noble gases? (Assume
that the elements in this different universe
have the same symbols as in ours.)