Download Atomic Structure-ppt

Chemistry, The Central Science, 11th edition
Theodore L. Brown; H. Eugene LeMay, Jr.;
and Bruce E. Bursten
Chapter 7 (Zumdahl)
Electronic Structure
of Atoms
John D. Bookstaver
St. Charles Community College
Cottleville, MO
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Waves
• To understand the electronic structure of
atoms, one must understand the nature of
electromagnetic (EM) radiation.
• The distance between corresponding points
on adjacent waves is the wavelength ().
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Waves
• The number of waves
passing a given point per
unit of time is the
frequency ().
• For waves traveling at
the same velocity, the
longer the wavelength,
the smaller the
frequency.
• Frequency is measured
in the following units: Electronic
Structure
-1
s , = waves/s = Hz (hertz)of Atoms
© 2009, Prentice-Hall, Inc.
Electromagnetic Radiation
• All electromagnetic
radiation travels at the
same velocity: the
speed of light (c),
3.00  108 m/s.
• Therefore,
c = 
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Sample Exercise 7.1 (p 292)
• (Copy from text into notes.)
• Follow as I review the book solution to
this problem.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Practice Problems: Text, p 337,#39-40
• #39: The laser in an audio compact disc player
uses light with a wavelength of 7.80 x 102 nm.
Calculate the frequency of this light.
• Solution: label your given(s) & your unknown.
  = given = unknown
• Identify the connection between given(s) and
unknown. (c= )
• Recognize that you know the value of c for all EM
radiation ( c =3.00 x 108 m/s)
• Substitute in all given/known values & solve for the
unknown. (NOTE: Convert nm to m first!)
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Nature of Energy
• The wave nature of light
does not explain how
an object can glow
when its temperature
increases.
• Max Planck explained it
by assuming that
energy comes in
packets called quanta.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Nature of Energy
• Einstein used this
assumption to explain the
photoelectric effect.
• He concluded that energy is
proportional to frequency:
E = h
where h is Planck’s
constant, 6.626  10−34 J-s.
• He also concluded that
wave energy has mass!
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Nature of Energy
• Therefore, if one knows the
wavelength of light, one
can calculate the energy in
one photon, or packet, of
that light (also known as a
“quantum” of energy):
c = 
E = h
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Sample Exercise 7.2
p 293-294
• Copy this problem and solution.
• Follow along as we walk thru the
solution together.
• The blue color in fireworks is often achieved by
heating copper(I) chloride (CuCl) to about 1200 C.
Then the compound emits blue light having a
wavelength of 450 nm. What is the increment of
energy (the quantum) that is emitted by CuCl?
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
• Solution: label your given(s) & your unknown.
  = given E= unknown
• Identify the connection between given(s) and
unknown.
– There is not a direct connection. No equation we have includes both E and .
– However, we know that E = h.
– We also know the value of h (=6.626 x 10−34 J-s).
– If we know the value of , we can calculate E. Can we find ? (is there a
connection between  and?
– YES! c= .
• Substitute given values into this second equation and
solve for . (Don’t forget to convert from nm to m first!)
• When  is obtained, substitute it and the value of h into the firstElectronic
Structure
equation and solve for E.
of Atoms
© 2009, Prentice-Hall, Inc.
Practice Problems
p 337, #41-44
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Nature of Energy
Another mystery in
the early 20th
century involved the
emission spectra
observed from
energy emitted by
atoms and
molecules.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Nature of Energy
• For atoms and
molecules one does
not observe a
continuous spectrum,
as one gets from a
white light source.
• Only a line spectrum of
discrete wavelengths
is observed.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Nature of Energy
•
Niels Bohr adopted Planck’s
assumption and explained
these phenomena in this
way:
1. Electrons in an atom can only
occupy certain orbits
(corresponding to certain
energies).
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Nature of Energy
•
Niels Bohr adopted Planck’s
assumption and explained
these phenomena in this
way:
2. Electrons in permitted orbits
have specific, “allowed”
energies; these energies will
not be radiated from the atom.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Nature of Energy
•
Niels Bohr adopted Planck’s
assumption and explained
these phenomena in this
way:
3. Energy is only absorbed or
emitted in such a way as to
move an electron from one
“allowed” energy state to
another; the energy is defined
by
Electronic
Structure
E = nh
of Atoms
Where n=main energy level2009, Prentice-Hall, Inc.
©
Solving for e- energy if  & are
unknown
• The energy of an electron in a hydrogen
atom is
• E= (-2.178 x 10-18 J) Z2
n2
[ ]
Where Z= nuclear charge (atomic #) and
n = main energy level and
RH = the Rydberg constant, 2.18  10−18 J
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Nature of Energy
The energy absorbed or emitted
from the process of electron
promotion or demotion can be
calculated by the equation:
E = −RH (
12
12
- 2
nf2
ni
)
ni and nf are the initial and final
energy levels of the electron.
Electronic
And Z = 1 (atomic # of hydrogen!)
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Sample Exercise
• P 338 #51a.
• Calculate the energy emitted when the
following transition occurs in a hydrogen
atom: n=3  n= 2
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Solution
• Our givens are
– nfinal (level 2)
– ninitial (level 3)
• Our unknown is the energy released
(E)
• Identify the connection between
given(s) & unknown:E= -RH(1/nf2-1/ni2)
• Substitute given values & solve for
unknown!
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Calculating  of light from energy
released
• Continue w/#51 from p 338
• Calculate the wavelength of light emitted when the following
transition occurs in the hydrogen atom. What type of EM
radiation is emitted?
• Givens: E (from prior slide)
• Unknown: 
• Connection: E = h to solve for 
• then use c=  to solve for 
Substitute & Solve:
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
ALTERNATIVE APPROACH
• Derive formula that includes all the variables you are
using: , , & E
• Use both eqns E = h
&
c= 
1. Set both eqns equal to 
– E=
&
c= 
h

2. Set both eqns equal to one another
– E =
c
h

3. Isolate , since this is your unknown.
  = hc
E
4. Substitute values (c, h, E) to solve for .
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Practice Problems:
p 338, #51, 52, 53, 54, 55, 56
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Wave Nature of Matter
• Louis de Broglie posited that if light can
have material properties, matter should
exhibit wave properties.
• He demonstrated that the relationship
between mass and wavelength was
h
 = mv
This formula is
on the AP
exam formula
sheet
Please note: the base units for Joules are
kg●m2/s2 . This will be important for
calculations
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Wave-Particle Duality
• Site with Cool Visuals & Explanation of
Wave Interference, Including electron
waves
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Sample Exercise (from Brown/Lemay) p 223
• What is the wavelength of an electron moving with a
speed of 5.97 x 106 m/s? The mass of the electron is
9.11 x 10-31 kg.
SOLUTION:
Givens:
melectron = 9.11 x 10-31 kg
velectron = 5.97 x 106 m/s
Unknown = 
CONNECTION between givens & unknown:
 =h
mv
Substitute given & constant values, solve for .
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Sample Exercise, cont.
Substitute given & constant
values, solve for .
 =
h
mv
 = 6.626 x
10-34 kg●m2/s
Where did the
exponent go?
J= kg●m2/s2
(9.11 x 10-31 kg)(5.97 x 106 m/s)
 = 1.22 x 10-10
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Practice Problems
6.41) Determine the wavelength of the
following objects
a) An 85-kg person skiing at 50 km/hr
b) A 10.0 g bullet fired at 250 m/s.
c) A lithium atom moing at 2.5 x 105 m
d) An ozone molecule in the upper
atmosphere moving at 550 m/s.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Practice Problems:
• 6.42) Among the elementary subatomic
particles of physics is the muon, which
decays within a few nanoseconds after
formation. The muon has a mass
206.8 times that of an electron.
Calculate the deBroglie wavelength
associated with a muon traveling at
8.85 x 105 cm/s.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Uncertainty Principle
• Heisenberg showed that the more precisely
the momentum of a particle is known, the less
precisely is its position known:
(x) (mv) 
h
4
• In many cases, our uncertainty of the
whereabouts of an electron is greater than the
size of the atom itself!
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Sample Exercise
P 338, # 59
• Using Heisenberg uncertainty principle,
calculate ∆x for each of the following:
a) electron with a v = 0.100 m/s
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Practice Problems
• Complete p 338 #59 & 60
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Quantum Mechanics
• Erwin Schrödinger
developed a
mathematical treatment
into which both the
wave and particle nature
of matter could be
incorporated.
• It is known as quantum
mechanics.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Quantum Mechanics
• The wave equation is
designated with a lower
case Greek psi ().
• The square of the wave
equation, 2, gives a
probability density map of
where an electron has a
certain statistical likelihood
of being at any given instant
in time.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Quantum Numbers
• Solving the wave equation gives a set of
wave functions, or orbitals, and their
corresponding energies.
• Each orbital describes a spatial
distribution of electron density.
• An orbital is described by a set of three
quantum numbers.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Principal Quantum Number (n)
• The principal quantum number, n,
describes the energy level on which the
orbital resides.
• The values of n are integers ≥ 1.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Angular Momentum Quantum
Number (l)
• This quantum number defines the
shape of the orbital.
• Allowed values of l are integers ranging
from 0 to n − 1.
• We use letter designations to
communicate the different values of l
and, therefore, the shapes and types of
Electronic
orbitals.
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Angular Momentum Quantum
Number (l)
Value of l
0
1
2
3
Type of orbital
s
p
d
f
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Magnetic Quantum Number (ml)
• The magnetic quantum number
describes the three-dimensional
orientation of the orbital.
• Allowed values of ml are integers
ranging from -l to l:
−l ≤ ml ≤ l.
• Therefore, on any given energy level,
there can be up to 1 s orbital, 3 p
orbitals, 5 d orbitals, 7 f orbitals, etc.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Magnetic Quantum Number (ml)
• Orbitals with the same value of n form a shell.
• Different orbital types within a shell are
subshells.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
s Orbitals
• The value of l for s
orbitals is 0.
• They are spherical in
shape.
• The radius of the
sphere increases with
the value of n.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
s Orbitals
Observing a graph of
probabilities of finding
an electron versus
distance from the
nucleus, we see that s
orbitals possess n−1
nodes, or regions
where there is 0
probability of finding an
electron.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
p Orbitals
• The value of l for p orbitals is 1.
• They have two lobes with a node between
them.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
d Orbitals
• The value of l for a
d orbital is 2.
• Four of the five d
orbitals have 4
lobes; the other
resembles a p
orbital with a
doughnut around
the center.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Energies of Orbitals
• For a one-electron
hydrogen atom,
orbitals on the same
energy level have
the same energy.
• That is, they are
degenerate.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Energies of Orbitals
• As the number of
electrons increases,
though, so does the
repulsion between
them.
• Therefore, in manyelectron atoms,
orbitals on the same
energy level are no
longer degenerate. Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Spin Quantum Number, ms
• In the 1920s, it was
discovered that two
electrons in the same
orbital do not have
exactly the same energy.
• The “spin” of an electron
describes its magnetic
field, which affects its
energy.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Spin Quantum Number, ms
• This led to a fourth
quantum number, the
spin quantum number,
ms.
• The spin quantum
number has only 2
allowed values: +1/2
and −1/2.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Pauli Exclusion Principle
• No two electrons in the
same atom can have
exactly the same energy.
• Therefore, no two
electrons in the same
atom can have identical
sets of quantum
numbers.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Sample Exercise: 7.6 p 308
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Electron Configurations
• This shows the
distribution of all
electrons in an atom.
• Each component
consists of
– A number denoting the
energy level,
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Electron Configurations
• This shows the
distribution of all
electrons in an atom
• Each component
consists of
– A number denoting the
energy level,
– A letter denoting the type
of orbital,
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Electron Configurations
• This shows the
distribution of all
electrons in an atom.
• Each component
consists of
– A number denoting the
energy level,
– A letter denoting the type
of orbital,
– A superscript denoting
the number of electrons
in those orbitals.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Orbital Diagrams
• Each box in the
diagram represents
one orbital.
• Half-arrows represent
the electrons.
• The direction of the
arrow represents the
relative spin of the
electron.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Hund’s Rule
“For degenerate
orbitals, the lowest
energy is attained when
the number of electrons
with the same spin is
maximized.”
Another translation: “Don’t
pair electrons in
degenerate orbitals until
there is 1 electron in
each orbital.”
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Periodic Table
• We fill orbitals in
increasing order of
energy.
• Different blocks on the
periodic table (shaded
in different colors in
this chart) correspond
to different types of
orbitals.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Some Anomalies
Some
irregularities
occur when there
are enough
electrons to halffill s and d
orbitals on a
given row.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Some Anomalies
For instance, the
electron
configuration for
copper is
[Ar] 4s1 3d5
rather than the
expected
[Ar] 4s2 3d4.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Some Anomalies
• This occurs
because the 4s
and 3d orbitals
are very close in
energy.
• These anomalies
occur in f-block
atoms, as well.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.