Transcript VI: Electronic Structure in Atoms

TOPIC VIII: Electronic Structure in Atoms
LECTURE SLIDES
•
•
•
•
Electromagnetic Radiation: E, , 
Early Models
Quantum Numbers
Shells, Subshells, Orbitals
Kotz & Treichel, Chapter 7
WHERE THE ELECTRONS ARE.....
We are going to examine in historical succession
the ideas and experiments that led to the modern
atomic theory and sophisticated placement of the
electrons about the nucleus.
The current theory, based on quantum mechanics,
places the electrons around the nucleus of the atom
in “ORBITALS,” regions corresponding to allowed
energy states in which an electron has about 90%
probability of being found.
Let’s see how we got there!
Historical Events, Nature of
Electromagnetic Radiation
1. 1864 James Maxwell: Wave motion of electromagnetic
radiation
2. 1885 Rydberg, Balmer: Wavelength of atomic spectra
3. 1900 Max Planck: Quantum theory of radiation, packets
of specific energy
4. ~1905 Einstein: Particle- like properties of radiation,
“photons”
James Maxwell described all forms of radiation in
terms of oscillating (wave like) electric and magnetic
fields in space. The fields are propagated at right angles
to each other.
All “forms of radiation” include visible light but also,
x-rays, radioactivity, microwaves, radio waves: all
are described today as electromagnetic radiation.
The waves have characteristic frequency and wavelength,
and travel at a constant velocity in a vacuum,
3.0 X 10 8 m/s.
Wave description:
wavelength
crest
crest
trough
node
trough
node
cycle
Frequency: # cycles / sec
Important Relationship, all electromagnetic radiation:
c = 
speed light, vacuum = wavelength X frequency
3.00 X 108 ms-1 = , m X
Same as m/s
, s-1 (hertz)
hertz, Hz, s-1
# cycles per second
Rearranging:
 = c/
 = c/
A red light source exhibits a wavelength of 700 nm,
and a blue light source has a wavelength of 400 nm.
What is the characteristic frequency of each of these
light sources?
Red light:
700 nm = ? m = ? s-1
700 nm
1m
= 700 X 10-9 m = 7.00 X 10-7 m
109 nm
 = c /  = 3.00 X 108 ms-1
7.00 X 10-7 m
= 4.29 X 1014 s-1
= 4.29 X 1014 cycles per sec = 4.29 X 1014 Hz or s-1
Blue Light:
400 nm = ? m = ? s-1
400 nm
1m
= 400 X 10-9 m = 4.00 X 10-7 m
109 nm
 = c /  = 3.00 X 108 ms-1
4.00 X 10-7 m
= 7.50 X 10 14 s-1
= 7.50 X 1014 cycles per sec = 7.50 X 1014 Hz
longer
lowe
r
700 nm,
4.29 X 1014 Hz
BLUE light: 400 nm,
7.50 X 1014 Hz
RED light:
shorter
higher
Point to remember: the shorter the wavelength, the
higher the frequency: the longer the wavelength,
the lower the frequency.
GROUP WORK 8.1
Microwave ovens sold in US give off microwave
radiation with a frequency of 2.45 GHz. What is the
wavelength of this radiation, in m and in nm?
 = c/
2.45 GHz = ? m = ? nm
109 Hz (s-1) = 1 GHz
c = 3.00 X 108 ms-1
1. Convert GHz to Hz; call Hz “s-1”
2. Calculate wavelength, , in m
3. Convert m to nm (109 nm = 1 m)
Max Planck made a major step forward with his
theory that energy is not continuous but rather is
generated in small, measurable packets he called
quantum (which refers back to the Latin, meaning
bundle).
He related the energy of the quantum to its frequency
or wavelength as below:
For one quantum of radiation:
Energy = h x radiation = h x c
 radiation
h is Planck’s constant, 6.63 X 10-34 joule sec
Energy Units
The “ calorie”: “The quantity of energy required to raise
1.00 g of water 1oC”. Very small amount of energy, so
Kcal are generally used:
1000 calories(cal) = 1 kilocalorie, kcal
SI unit of energy is the “joule”, defined in terms of
kinetic energy rather than heat energy. One joule is the
amount of kinetic energy involved when a 2.0 kg object
is moving with a velocity of 1.0 m/s. Again, a very small
amount of energy, so kilojoules are generally used:
1000 joules (J) = 1 kilojoule kJ (kJ)
Relationship:
1 calorie = 4.184 joules
Sample Calculations:
E=h= hc

Blue light,  = 4.00 X 10-7 m
E = 6.63 X 10-34 joule s x 3.00 X 108 ms-1
4.00 X 10-7 m
E = 4.97 X 10-19 joule
Microwave oven,  = 2.45 X 109 Hz or s-1
E = 6.63 X 10-34 joule s x 2.45 X 109 s-1
E = 1.62 X 10-24 joule
The relationships expressed by this equation
include the following:
Energy of a quantum is directly proportional to the
frequency of radiation: high frequency radiation is
the highest energy radiation (x rays, gamma rays)
Energy of radiation is inversely proportional to its
wavelength: long waves are lowest in energy, short
waves are highest. Radio waves, microwaves, radar
represent low energy forms of radiation.
View CD ROM sliding spectra here
Group Work 8.2a: Rank radiation types by
increasing energy (#5 = highest)
wavelength
microwave
2.36 cm
cosmic ()
radiation
Infrared
radiation
X ray
radiation
FM radio
2.36 pm
2.36 m
2.36 nm
2.36 m
Energy rank
Group Work 8.2b: Rank radiation types by
increasing energy (#5 = highest)
frequency
FM radio
89.7 MHz
Microwave
2.45 GHz
Submarine 76 Hz
Radio waves
14 -1
Violet Light 7.3 X 10 s
Orange Light 4.8 X 1014 s-1
Energy rank
Einstein took the next step in line by using Planck’s
quantum theory to explain the photoelectric effect
in which high frequency radiation can cause electrons
to be removed from atoms.
Einstein decided that light has not only wave- like
properties typical of radiation but also particle- like
properties. He renamed Planck’s energy quantum as
a “photon”, a massless particle with the quantized
energy/frequency relationships described by Planck.
“Quantized” refers to properties which have specific
allowed values only.
Wavelength, frequency, energy relationships:
c, speed of light = Wavelength,  X frequency, 
 = c

 = c

c = 3.00 X 108 ms-1, speed of light in vacuum
energy of photon = h, Planck’s constant x 
E=
h=
hc

h = 6.63 X 10-34 joule s
It was discovered in this time frame that each element
which was subjected to high voltage energy source
in the gas state would emit light.
When this light is passed through a prism, instead of
obtaining a continuous spectrum as one obtains for
white light, one observes only a few distinct lines of very
specific wavelength.
Each element emits when “excited” its own distinct “line
emission spectrum” with identifying wavelengths.
This important discovery lead directly to our modern
understanding of electronic structure in the atom!
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Historical
Events, the Nature of Electron
1. 1804 Dalton: Indivisible atom
2. 1897 Thomson: Discovery of electrons
3. 1904 Thomson: Plum Pudding atom
4. 1909 Rutherford: The Nuclear atom
5. 1913 Bohr: Planetary atom model, e’s in orbits
JJ Thompson’s Picture of the atom:
The Plum Pudding Atom:
Positive matter with electrons embedded like
raisins in a pudding
Rutherford’s Picture of the Atom:
:motA raelcuN drofrehtuR ehT
suelcun ynit ni egrahc evitisop dna ssaM
desrepsid snortcele ;smota fo retnec ni
suelcun edistuo
Bohr combined the ideas we have met to present
his “planetary” model of the atom, with the electrons
circling the nucleus like planets around the sun:
Bohr used all the ideas to date:
• electron in the atom outside the tiny positive nucleus
• excited elements emit specific wavelengths of energy
only
• radiation comes in packets of specific energy and
wavelength
Bohr’s atom placed the electrons in energy quantized orbits
about the nucleus and calculated exactly the energy of the
electron for hydrogen in each orbit.
n, integer values for shells around nucleus, = 1-6-->infinity
1
2
3
4
5
6
each orbit is quantized: has an energy of a specific frequency only
n=1, lowest energy orbit n=6, highest energy orbit pictured
4
4
3
e
3
e
e 2
e
2
e
e
1
e
left: e excited, photon of
correct, matching energy
1
e
right: e returning to origin,
emitting light: line spectra
allowed transitions shown by arrows: e may be "excited" to higher orbit
only if energized by photon of energy of matching frequency; it falls back
to lower shell emitting the energy it has gained in form of light.
The wavelength of the light emitted represents the energy difference
between the orbits
Bohr also predicted that each shell or orbit about the
nucleus would have its occupancy limited to 2n2
electrons, where n = the orbit number.
Many of Bohr’s ideas, in modified form, remain in the
present day quantum mechanics description of atomic
structure.
Bohr was able to calculate exactly the energy values for
the hydrogen spectrum using his model; however the
calculations only worked for one electron systems and
did not explain the electronic behavior of larger atoms.
GROUP WORK 8.3
Predict maximum occupancy (2n2 )of each shell:
n=1 = _____ e’s
n=5 = _____ e’s
n=2 = _____ e’s
n=6 = _____ e’s
n=3 = _____ e’s
n=7= _____ e’s
n=4 = _____ e’s
Summation:
Planck
Energy is “quantized”, comes in packets called quantum
with energy hv
Einstein
Energy can interact with matter, photoelectric effect,
quantum renamed “photon”
Bohr
Photons of energy can interact with electrons in orbits of
lowest possible energy around the nucleus and “excite”
e’s to higher energy orbits. The e’s give off this energy
as light, spectral lines as they return to “ground” state.
Electron as matter/energy particle
1. 1925 DeBroglie: Matter Waves
2. 1926 Heisenberg’s Uncertainty Principle
3. 1926 Schroedinger’s Wave Equation and Wave
Mechanics
4. Modern Theory: Use of wave equation to describe
electron energy/probable location in terms of
three quantum numbers.
DeBroglie next suggested that all matter moved in
wavelike fashion, just like radiation. Large
macroscopic matter (moving golf balls, raindrops,
etc) have characteristic wavelengths associated
with their motion but the wavelengths are too tiny
to be detectable or significant.
Electrons, on the other hand have very significant
wavelengths in comparison to their size.
Einstein gave radiation matter- like, particle
properties; DeBroglie gave matter wave- like
properties.
Heisenberg’s Uncertainty Principle:
If an electron has some properties that are wave like
and others that are like particles, we cannot
simultaneously describe the exact location of the
electron and its exact energy. The accurate
determination of one changes the value of the other.
The Bohr atom tried to describe exact energy and
position for the e’s around the nucleus and worked
only for H.
Born’s interpretation of Heisenberg’s Uncertainty
Principle:
If we want to make an accurate statement about the
energy of an electron in the atom, we must accept
some uncertainty in its exact position. We can only
calculate probable locations where an electrons is to
be found.
Schroedinger’s wave equation describes the electron as
as a moving matter wave, and results in a picture in
which we place electrons in probable locations about
the nucleus based on their energy.
Schroedinger’s Wave Equation
The mathematics employed by Schroedinger to describe
the energy and probable location of the electron about
the nucleus is complex and only recently been solved
for larger atoms than hydrogen.
However, it yields a description of the atom which
accounts for the differences between the elements.
IT WORKS!
Schroedinger’s wave equation describes the
electrons in a given atom in terms of probable
regions of differing energies in which an electron
is most likely to be found.
We call the regions “orbitals” rather than
“orbits”, and each is centered about the nucleus.
The description of each orbital is given in the
form of three “quantum numbers”, which give
an address - like assignment to each orbital. The
quantum numbers are in the form of a series of
solutions to the wave equation.
Summation:
Heisenberg:
Uncertainty Principle: cannot determine simultaneously
the exact location and energy of an electron in atom
Schroedinger:
Wave equation to calculate probable location of e’s
around nucleus using dual matter/wave properties of e’s.
Three quantum numbers from equation locate e’s of
various energies in probable main shells, subshells,
orbitals.
Group Work 8.4: Match
Scientist with Contribution
a) Bohr
Energy of Quantum
b) Dalton
Indivisible Atom
c) Einstein
Nuclear Atom
d) Heisenberg
Plum Pudding Atom
e) Planck
Quantum to Photon
f) Rutherford
Solar System Atom
g) Schroedinger
Uncertainty Principle
h) Thompson
Wave Equation
The
Quantum
Numbers
QUANTUM
NUMBERS
“Locators, which describe each e- about the nucleus
in terms of relative energy and probable location.”
The first quantum number, n, locates each electron
in a specific main shell about the nucleus.
The second quantum number, l , locates the electron in a
subshell within the main shell.
The third quantum number, ml , locates the electron in
a specific orbital within the subshell.
Locator #1, “n”, the first quantum number
“n”, the Principal quantum number:
• Has all integer values 1 to infinity: 1,2,3,4,...
• Locates the electron in an orbital in a main shell
about the nucleus, like Bohr’s orbits
• describes maximum occupancy of shell, 2n2.
The higher the n number:
• the larger the shell
• the farther from the nucleus
• the higher the energy of the orbital in the shell.
"n" MAIN SHELLS ABOUT THE NUCLEUS
7
6
5
4
3
2
1
Locator #2, “l”, the second quantum number
•locates electrons in a subshell region within the
main shell
• limits number of subshells per shell to a value equal
to n:
n =1, 1 subshell
n = 2, 2 subshells
n= 3, 3 subshells .....
•only four types of subshells are found to be
occupied in unexcited, “ground state” of atom.
These subshell types are known by letter:
“s”
“p”
“d ”
“f”
Diagram of available shells and
subshells
On the next slide is a schematic representation
of the shells and subshells available for electron
placement within the atom.
Note that the 5th, 6th and 7th types are given
the alphabetical letters following “f”.
None of these types are occupied in the ground
state of the largest known atoms.
n=7
7s
(7p 7d
7f
7g 7h 7i)
n=6
6s
6p
6d
(6f 6g 6h)
n=5
5s
5p
5d
5f
n=4
4s
4p
4d
4f
n=3
3s
3p
3d
n=2
2s
2p
n=1
1s
Highest,
biggest
(5g)
Lowest energy, smallest shell
Locator #3, “ml”, the third quantum number
“ml”, the third quantum number, specifies
in which orbital within a subshell an electron
may be found.
It turns out that each subshell type contains a unique
number of orbitals, all of the same shape and energy.
Main shell
n#
subshells
l#
orbitals
ml #
The Third Q#, ml continued
“ml” values will describe the number of orbitals within a
subshell, and give each orbital its own unique “address”:
s subshell
p subshell
d subshell
1 orbital
3 orbitals
5 orbitals
f subshell
7 orbitals
“l”
f
d
p
s
“ml”
f
f
f
f
d
d
d
d
p
p
p
s
f
f
f
d
All electrons can be located in an orbital within a
subshell within a main shell. To find that electron one
need a locating value for each:
the “n” number describes a shell
(1,2,3...)
the “l” number describes a subshell region
(s,p,d,f...)
the “ml” number describes an orbital within the
region
(Each of these quantum numbers has a series of
numerical values. We will only use the n numerical
values, 1-7.)
Group Work 8.5
Shell n#
#1
#2
#3
#4
Name
Allowed
Subshells
Total
Orbitals
Available
The 4th Quantum Number, ms
It was subsequently discovered that each orbital
we have described is home to not just one but two
electrons, with opposite spins!
We are now treating an electron as a spinning charged
matter particle, rotating clockwise or counterclockwise
on its axis: (next slide)
To describe this situation, a fourth quantum number
is required, the magnetic quantum number, “ms”.
As a consequence, we now know:
s subshell, one orbital, 2 e’s
p subshell, three orbitals, 6 e’s,
d subshell, five orbitals, 10 e’s,
f subshell, seven orbitals, 14e’s,
This 4th Q# completes the set of “descriptors” or
“locators” needed to assign each electron a unique
position in the arrangement around the nucleus.
Pauli’s Exclusion Principle sums it up: no two e’s in the
same atom, can have the same four Q#’s. .
“l”
f
d
p
s
“ml”
“ms”
n=4
n=3
n=2
n=1
2e’s
6 e’s
10 e’s
14 e’s
s
p
d
f
Group Work 8.6: Number of Electrons per Shell
Shells
#1
Name,
Allowed
Subshells
1s
Total Number,
Allowed
Orbitals
1
#2
2s, 2p
1 + 3 =4
#3
3s, 3p, 3d
1+3+5=9
#4
4s, 4p, 4d, 4f
1 + 3 + 5 + 7 =16
Total
Number,
Electrons
Now that we have found places to put our electrons,
in orbitals within subshells within shells, let’s take a
look at the shapes of the various types of orbitals.
The “orbital shapes” are simply enclosed areas of
probability for an electron after a three dimensional
plot is made of all solutions for that electron from the
wave equation.
Each orbital within a subshell is centered about the
nucleus and extends out to the boundaries of its
main shell. Its exact orientation within the subshell
depends on the value of its ml number.
all s orbitals
all p orbitals
d orbitals
Checkout CD-ROM!
Energy Description of e’s
The first two quantum numbers, n and l, give
information about the relative energy of electrons
in their location:
As the “n” number increases, the energy of the e
in that shell increases: 1<2<3<4<5<6<7
As the “l” number increases, the energy of the e
in a subshell within the shell increases: s<p<d<f
The “ml” number describes the number of orbitals
within a subshell of the same energy.
Accordingly, the relative energy of an electron in
any given orbital within a subshell is given by the
sum of its “n” and “l” numbers.
We have described the following subshells for the
electrons:
1s; 2s, 2p; 3s, 3p, 3d; 4s, 4p, 4d, 4f; 5s, 5p, 5d, 5f;
6s, 6p, 6 d; 7s
Let’s next discuss their relative energy...
2e’s
6 e’s
10 e’s
14 e’s
s
p
d
f
n=4
4
4+1 =5
4+2=6
3
3+1 =4
3+2=5
2
2+1 =3
n=3
n=2
n=1
1
4+3=7
Relative energy of subshells
s
p
d
f
n=7
7
n=6
6
7
8
n=5
5
6
7
8
n=4
4
5
6
7
n=3
3
4
5
n=2
2
3
n=1
1
Order of Filling, Lowest energy to Highest
s
p
d
f
n=7
7
n=6
6
7
8
n=5
5
6
7
8
n=4
4
5
6
7
n=3
3
4
5
n=2
2
3
n=1
1
START HERE
Periodic Table as Guide
The periodic table lists all elements sequentially in order
of atomic number: this means that each element in turn
has one more electron than its predecessor.
We’ll call this electron, the last one to be placed around
the nucleus, the “distinguishing electron”...
We can subdivide the PT into four blocks, showing which
elements have their “distinguishing” or “final” electron
in an “s” or a “p” or a “d” or a “f” type subshell.
Subshells, relative energy (n + l)
s-block
p-block
1
2
1s,1
d-block
2p,3
2s,2
f-block
3p, 4
3
3s,3
4
4s,4
3d, 5
5
5s,5
4d,6
6
6s,6
4f,7
5d, 7
7
7s,7
5f,8
6d,8
PERIODS
4p,5
5p,6
6p,7
Subshells by order of filling,
Lowest energy to highest
1s
1s
2s 2s
2p 2p 2p 2p 2p 2p
3s 3s
3p 3p 3p 3p 3p 3p
4s 4s 3d
3d 3d 3d 3d 3d 3d 3d 3d 3d 4p 4p 4p 4p
4p 4p
5s 5s 4d
4d 4d 4d 4d 4d 4d 4d 4d 4d 5p 5p 5p 5p 5p 5p
6s 6s 5d 4f
5d 5d 5d 5d 5d 5d 5d 5d 5d 6p 6p 6p 6p 6p 6p
7s 7s 6d 5f
6d 6d 6d 6d 6d 6d
Where the Final Electron Goes:
s,f,d,p Blocks of Elements
2 e’s
14 e’s
10 e’s
s
6 e’s
p
d
f
Our next task is to fill electrons around the nucleus into
the orbitals we have described. The electrons will fill
from lowest energy subshell to highest.
The sum of n + l gives us a ranking order of filling
subshells which does not simply progress from
completion of one shell to beginning of another.
However, We will use the periodic table to guide us
quickly through this complex sequence order.
Group Work 8.7: Order of Subshell Filling By PT
Name subshell
1st Period
2nd Period
3rd Period
4th Period
5th Period
6th Period
7th Period
s
f
d
p