1
The most stable arrangement of the nucleus and the electrons in an atom is
one for which the total energy of the atom (kinetic energy and potential energy) is at a
minimum. When an atom is exposed to heat, light, or when it collides with another particle
, it
may absorb additional energy.
Electromagnetic radiation
:
is
most simply defined as light
–
and as you know, not all light is
visible to the human eye.
2
Relative size of the wavelengths for the EM spectrum
As the EM radiation
travels through space, it creates both oscillating electric and magnetic fields
along the way. The two fields are perpendicular to one another.
Radiation is more than just the invisible stuff that nuclear bombs leave behind. Ultraviolet,
microwave, i
nfrared, FM radio signals, visible light;
these
are all considered radiation. The EM
spectrum
(above)
refers to all of the different types of radiation that exist.
EM radiation is
naturally transmitted by stars (including our sun), travels at the speed o
f light, and can vary in
wavelengths from 0.000000000001 meter (Gamma rays) to 10,000 m (television & radio)! In
theory, the possible wavelengths extend in size to infinitely large and small.
3
Wave Properties of EM radiation:
Imagine a buoy floating on w
ater. As a boat passes by, the waves
produced
will cause the buoy
to bob up and down. This
wave
is a periodic disturbance or oscillation that passes through
space. A wave consists of repeating units called cycles. The vertical motion of the buoy is
caused by the passage of successive crests and troughs as the waves move through the water.
The wave properties of electromagnetic radiation are described by two independent variables.
Frequency
: (
) the number of cycles that pass a given point each s
econd. This is the vertical
motion. The buoy will bob up and down
times per second.
Wavelength
: (
) the distance between two successive points on the wave. Simply speaking,
peak to peak or trough to trough is typically defined as the wavelengt
h.
4
Types of radiation are arranged in order by their wavelengths. The wavelength of a wave is the
distance between 2 consecutive points of a wave. Typically we say peak to peak or trough to
trough as these points are
very
easy to pick out on the wave.
But one could look at the middle
of the peak to the middle of the next peak and call that the wavelength. Radiation in the EM
spectrum is made up of waves that contain an Electric field and a Magnetic field (see figure
above). The frequency of a wave ma
y be defined by how often the wave passes a fixed point in
space in 1 second. For example, 1 peak/second = 1 Hz; 10 peaks/second = 10 Hz.
Units for frequency are sec

1
(or
sec
1
) often called Hertz (Hz)
. Remember we are talking about
cy
cles, so the units could also be labeled as
sec
cycles
Units for wavelength are
meters or
cycle
meters
The speed of the w
ave is the distance traveled per some period of time. Thus,
sec
meters
We can get those units
by multiplying frequency x wavelength
Speed of a wave:
x
(units are
sec
meters
)
In a vacuum, the speed of any type of EM radiation is the same and is defined as
2.9979 x 10
8
meters
/
sec
. This is defined as the speed of light
–
and is
defined as c
–
which is a
constant.
c =
x
2.9979 x 10
8
meters
/
sec
=
x
There is an
inverse
relationship between frequency and wavelength. If we rearrange the
equation for the speed of light for
and then again for
, the relationship becomes mo
re
apparent.
=
c
/
=
c
/
If you are having trouble seeing the relationship, we can divide up the equation even further:
= c
x
1
/
= c
x
1
/
5
As you can see above, if the wavelength is long (red and orange lines for example) the
frequency
(how many wavelengths pass a point in a certain period of time) is low. Large
wavelengths thus mean low frequency. If the wavelength is short (blue and purple lines) then
the number wavelengths that pass a particular point in a certain period of time is
high. For
example, if the above picture is a snapshot of 1 second, the red line has 1.5 wavelengths (or
thereabouts) passing a point in a second. The purple line has 14 wavelengths passing in 1
second.
Large wavelength = small frequency
Small waveleng
th = High frequency
We can use this relationship as an answer check when we do light calculations!
Given: What is the frequency of a radar wave with a
= 1.0 cm?
6
Another term to be aware of is
amplitude
, which simply refers to the height
of the wave. Waves
with higher amplitude have higher intensities, and waves with lower amplitudes have weaker
intensities
–
but they represent the same species (e.g. the same color of light) as their
wavelength and frequency are the same.
It is import
ant to know the visible spectrum: ROYGBIV (red, orange, yellow, green,
blue,
indigo, violet), and their
relative wavelengths and
frequencies
. Red has the longest wavelength
and thus the lower frequency while violet has the shortest wavelength and thus the
highest
frequency. If asked, be sure to know the order of the colors and the relative frequencies!!
Light of a given wavelength travels at different speeds depending on the medium in which it is
located: e.g. air, a vacuum, water, etc . .. When light
passes from one media to another, the
speed of the wave changes. The speed of light through media such as water or glass is
somewhat less than 2.9979 x 10
8
m
/
sec
. The change in speed is also accompanied by a change in
direction
–
thus it gets bent at so
me angle which depends on the media from which it came and
the media which it now entered. This is a phenomenon known as
refraction
. It does not
happen to particles (e.g. think of a stone thrown into water, it follows a curved path, not a new
bent line p
ath even though its speed did change).
Refraction happens when a wave passes from one material to another
of different densities
. As
the wave crosses the boundary, it bends. This kind of bending is called refraction. Waves travel
at different speeds in
different materials. The change in speed is what causes the wave to bend.
Waves do not refract if they cross the barrier at a perpendicular angle. Examine a pencil in a
glass straight up and down
–
it appears no different
–
but slanted we see the refract
ion). But if
7
they cross the barrier at any other angle, they will bend as they go through it. One edge of the
wave will slow down or speed up before the other edge does. That is why it appears broken.
We see refraction if we look at something through a
glass or water. Eye glasses and contacts
have lenses which refract light to correct vision problems.
Insight: How many have noticed that when you put an ice cube in water it develops swirls
around it? If you stare at the ice cube in the water you will
see these swirls. We know
–
from
looking in the CRC Handbook of Chemistry and Physics that water has different densities at
different temperatures. Although the change might be small, it is sufficient enough to change
the path of the light that travels
through our ice water. When you are driving down the
highway in the summer and you stare at the road ahead and see the “oasis” in front of you on
the asphalt, the same thing is happening. It is still air
–
but it is air at a different temperature
which h
as a different density. As the light travels through the air it gets refracted
–
“bent” and
we see it in front of us as a mirage of liquid on the road!
When a wave is forced to go through a smaller opening, it actually bends around the opening in
a proce
ss known as
diffraction
. This forms a semicircular wave on the other side of the opening.
Particles behave very differently. When forced through an smaller opening, some of the
particles will hit the
barricade
and the others will pass through as if unde
flected
–
just like cars
merging on an interstate.
If waves travel through adjacent slits, the resulting circular waves interact with one another.
Think about when two boats pass one another going in opposite directions. Both boats
travel
ing
through the water are making waves, as those waves come in contact with one another
they can combine to form a larger wave (called constructive interference) or they can smash into
8
each other
–
and neutralize each other (if they were the same “size” wa
ve) called destructive
interference.
At this point you may think that it
i
s pretty obvious that light behaves like a wave. But where
i
s
the proof that light is really composed of particles called photons? The proof comes from an
experiment that is calle
d the photoelectric effect.
Max Planck: proposed that energy emitted is not done so in a continuous manner but is given
off in small packets which he called quanta. He determined that an atom can emit only certain
amounts of energy and therefore they mu
st contain certain quantities of energy and that those
are fixed. Thus, the energy of an atom is
quantized
. The change in the atom’s energy results
from the gain or loss of one or more packets of energy.
Planck
derived an equation to explain
this quan
tized form of energy (as opposed to the idea that energy emitted was continuous)
E
atom
= h
where h = Planck’s constant = 6.626 x 10

34
J
s
= frequency (as above)
Despite the fact that Planck thought that energy was quantized, physicists continued to t
hink of
energy as
traveling
in waves. Energy as waves, however, could not explain the photoelectric
effect.
9
The electron is emitted from the metal with a specific kinetic energy (i.e. a specific speed).
The energy associated with a wave
is related to its amplitude or intensity. For example, at the
ocean the bigger the wave, the higher the energy associated with the wave. It
i
s not the small
waves that knock you over it's the big waves! Wave theory associates the energy of the light
with
its amplitude, not its
color
. So everyone who thought light is just a wave was really
confused when the intensity (amplitude) of the light was increased (brighter light) and the
kinetic energy of the emitted electron did not change. What happens is that a
s you make the
light brighter more electrons are emitted but all have the same kinetic energy. The wave theory
thus predicts that an electron would break free when it absorbs enough energy from light of any
color.
It was already known that light of suffi
cient energy emitted electrons from a metal surface.
Well, they thought the kinetic energy of the emitted electron must depend on something. So
they varied the frequency of the light and this changed the kinetic energy of the emitted
electron. Varying th
e frequency of the light changes its color!
This is the idea behind the
threshold frequency
. Light shining on the metal object must be of
a
sufficient frequency in order to eject and electron from the metal. Different metals have
different minimum frequ
encies. According to the photon theory
presented by Einstein
, a beam
of light consists of an enormous amount of photons.
Einstein viewed light as being particulate
in nature.
Light intensity (amplitude) is related to the number of photons striking the s
urface
per unit of time. Therefore, a photon of a certain minimum energy must be absorbed for the
electron to be ejected.
The
absence of a time lag
, a current is detected the minute the light hits the metal plate,
regardless of how intense the light is
. This violates the wave theory in that dimmer light would
10
have to shine on the plate longer in order to eject the electron. Basically it was determined that
the metal and thus the electrons cannot “save up”
or” bank
” their energy until they store
enough
for the electron to be emitted. The electron will break free the moment a photon of
enough energy hits the metal. The current was weaker in dim light than in brighter light
(amplitude again) because there are fewer photons per unit of time, but those ph
otons had the
correct energy in order to emit the electron.
This result is not consistent with the picture of light as a wave. An explanation that is consistent
with this picture is that light comes in discrete packages, called photons, and each photon mu
st
have enough energy to eject a single electron. Otherwise, nothing happens. So, the energy of a
single photon is:
E
atom
= E
photon
= h
When this was first understood, it was a very startling result. It was Albert Einstein who first
explained the photoe
lectric effect and he received the Nobel Prize in Physics for this work.
So, in summary

light is a particle, but has some wave

like behavior.
Given: Calculate the energies of a photon from the UV region (
= 1 x 10

8
m), visible (
= 5 x 10

7
m), and i
nfrared (
= 1 x 10

4
m)
E = h
A spectrum obtained from a glowing source is called an emission spectrum. When white light
is passed through a prism we see a myriad of colors
–
specifically what we term to be a rainbow.
This
dispersion
of white light
demonstrates that
white light contains all the wavelengths of
color and is thus considered to be continuous. Each color blends into the next with no
discontinuity.
When elements are vaporized and then thermally excited, they emit light, however, this l
ight
was not in the form of a continuous spectrum as was observed with white light. Instead, a
discrete line spectrum was seen when the light was passed through a narrow slit. A series of
fine lines of different colors separated by large black spaces was
observed. The wavelengths of
those lines are characteristic of the element producing them
–
thus, elements can be identified
based on the spectral line data that they produce.
Typically, we can examine the visible line spectra produced by an element in
lab
–
using
electricity, tubes filled with elements in the gaseous state and a spectroscope or diffraction
grating which separates the light emitted by the gas into its components.
11
Spectroscopists studied the emission spectrum of hydrogen and identified
lines in different
regions of
the EM spectrum. All hydrogen emits these same lines reproducibly. Using a
particular equ
ation, the location or waveleng
t
h
of emission lines cou
ld be predicted.
1
= R
2
2
2
1
1
1
n
n
where R =
1.096776 x 10
7
m

1
n
2
> n
1
The observation of the line spectra did not correlate with classical theory for the electron
spinning around the nucleus. It was believed that the electron spinning around the nucleus
should emit radiation and slowly spiral inw
ards until it collided with the nucleus. As the
electron spirals inwards, it
would
do so smoothly and thus should emit a
continuous
array of
frequencies
–
but that is not so
–
line spectra from elements are not continuous.
Niels Bohr was working in Ru
therford’s lab and
suggested
a model for the H atom that
predicted the existence of line spectra. Bohr used Planck and Einstein’s ideas about
quantization of energy and proposed three postulates:
1.)
The H atom has only certain allowable energy levels. Thes
e were termed stationary
states and can be thought of as a fixed circular orbital that the electron travels in around
the nucleus.
2.)
The atom does NOT radiate energy when an electron is in one of its stationary states.
Thus, this violated the ideas of class
ical physics as Bohr postulated that the atom does
NOT change its energy
while the electron moves in orbit.
3.)
The atom can change to another stationary state by the electron moving to another orbit,
only by absorbing or emitting a photon whose energy equals
the difference between the
two stationary states. Thus:
E
photon
= E
state A
–
E
state B
= h
where the energy of state A is greater than the energy of state B
The spectral line results when a photon of a specific energy (and thus specific frequency and
wav
elength
) is emitted as the electron moves from a higher energy state to a lower energy state.
Bohr’s model explained that the reason that a line spectrum is not continuous because the atom
has only certain discrete levels which the electron can travel bet
ween.
Think of the discrete levels like steps on a ladder, or
lily pads
on a pond. A frog (the electron)
can only jump on the
lily pads
–
just like a person climbing a ladder can only climb up the
ladder by standing ON the steps. It is very tough to cli
mb a ladder when you are not standing
on the steps! In fact, I would be that you can’t climb a ladder that way!
12
In Bohr’s atoms, the principal quantum number, n, is associated with the orbital location (the
radius of the orbit from the nucleus)
. The lo
wer the n value, the closer the electron is to the
nucleus. When the electron for H is in the first energy level it is said to be in the
ground state
.
When
energy
is imparted to the atom, the electron will take that energy and “jump” to a new
level, perh
aps on n=2 or 3. This is the
excited or high energy state
.
Maintaining the high
energy state requires too much energy (think of water at the top of the waterfall
–
how difficult
it would be for that water to stay at the top). Eventually, the electron f
alls back down to its
ground state
–
and releases the energy it had absorbed as a photon. Remember that there are
6.022 x 10
23
atoms of H in 1 mole of H
–
which means that the 1 single electron can have
different percentages of electrons in different exci
ted states dropping to different levels. The
electron can drop from 5 to 2, 4 to 2, 3 to 2 etc . . . When electrons drop from an excited state to
the third level
(
Paschen series
)
, infrared energy is emitted. When electrons drop from an
excited state to t
he second level, visible energy is emitted
(
Balmer series
)
. When electrons drop
from an excited state to the first energy level
(
Lyman series
)
, ultraviolet energy is emitted.
Unfortunately, Bohr’s theory only worked for Hydrogen, or Hydrogen like eleme
nts (e.g. other
1 electron species, such as ions formed from He, Li, Be, B, C, N, and O). The reason for this is
simply, multi

electron systems have
1.)
electron electron repulsion
2.)
electron nucleus attraction
3.)
because electrons aren’t really in “fixed” or
bitals
Bohr’s work did generate an equation which can be used to determine energy levels that the
electrons are “jumping” between and also the energy associated with the movement of
electrons between energy states:
E
n
=

2.179
x 10

18
J
n
2
whe
re n = level the electron occupies
It can be further expanded to examine the changes between two energy states such that:
E
photon
=

2.179 x 10

18
J
2
2
1
1
L
H
n
n
where n
H
= higher energy level
N
L
= lower energy level
This energy can then be
used to calculate
or
Why the negative value for E (equation above). It is due to an arbitrary assignment of the zero
point energy. The zero point energy is defined as when the electron is completely removed
from the nucleus. Thus, all values for E
are negative. It is an arbitrary assignment
–
try not to
think about it too hard
–
it does boggle the mind a bit! Just remember that our frequencies
and
13
wavelengths are
not
negative. Refer back to the diagram of EM radiation
–
none of the numbers
are ne
gative!!
Light seems to be able to behave as if it is a wave, and also a particle
–
known as the wave

particle duality. The wave nature is evident when light is shined through a prism, the particle
nature is evident when examining the photoelectric ef
fect. So, if energy is particle like, then
maybe matter is wave

like s
a
id Louis de Broglie.
The waves associated with moving particles are called matter waves. It was proven by J.J.
Thomson’s son when he detected electron (particles and thus matter)
waves by passing streams
of electrons through thin metal foils and onto photographic plates. What he observed
were
interference patterns similar to those observed when light waves passed through a double slit.
Thomson’s work could only mean that electro
ns behave like waves . Similar patterns were soon
obtained by beaming neutrons and protons through various crystals. Further work confirmed
de Broglie’s equation:
=
mv
h
where once again we see
wavelength
, velocity
, and Planck’s co
nstant
m stands for the mass of the object
One can see that if the mass of the object is very large, the resulting wavelength will be very
small. In fact, calculating the wavelength for a car moving at 100 mph results in a wavelength
that is far shorter
than anything on our EM radiation figure. It is
virtually
undetectable.
However, for smaller particles, the wavelengths can be observed. An electron moving at a
speed of 100 mph has a wavelength of about 10

5
m
–
almost 100,000 times the size of its a
tomic
radius!
Both matter and energy exhibit wave

like and particle

like properties. This is known as the
wave

particle duality.
If an electron is a moving particle, the we should be able to determine a few things about it
–
namely its speed, and i
ts location in the atom. Heisenberg came along in 1927 and said we
could not determine both simultaneously. That by determining the electron’s momentum we
14
would change its location in the orbital, and by determining its exa
c
t location, we would alter its
momentum.
If we measure the position of an electron we must bombard it with photons
–
this interferes
with th
e electrons original momentum as well as its location
–
r
emember that when we
bombard an
electron in the H atom with photons we actually excite t
he atom and move the
electron from some ground state energy level to an excited state energy level.
Ultimately this means that we cannot assign fixed paths that the electrons travel in, such as the
orbits proposed by Bohr. We thus, can only determine t
he probability of finding an electron
within some region of the space contained in the atom.
Thus, Bohr’s atomic model with fixed orbital was abandoned for a model that was less precise
and based on probabilities
–
known as the quantum

mechanical mode
l of the atom.
Quantum Mechanics examines the wavelike properties of matter on an atomic scale. Erwin
Schrödinger
came up with his own theory about the structure of the atom and he called it the
quantum

mechanical model of the atom. Based on the work
of Heisenberg, he abandoned the
idea of set energy levels described by Bohr and instead focused on the wave motion of the
electron and the probability of the electron being located in some general space.
Remember that space is 3

dimensional! We all have
volume!
Electrons, therefore, move in 3

dimensional space as they travel along their path around the nucleus.
Schrödinger
came up
with an equation to describe the motion of the electrons. Regardless of what the scary equation
looks like
:
(don’t panic, we won’t talk about it or do anything with it!!) the “answer” to the solved
equation results in a given wave function called an
atomic orbital
.
This orbital has nothing to
do with Bohr’s description of electron orbit (like planets around the sun).
Heisenberg showed us that we cannot possibly know the location of the electron and its
momentum.
Schrödinger
showed us that we can get some “idea”
or the probability of the
location of the electron
–
e.g. where it is most likely to be found or most likely to spend most of
its time. Using
Schrödinger’s
equation, we can identify the probabl
e
location of the electron
15
using an electron density diagram.
These density diagrams a
re
then transposed into pretty
pictures in textbooks and are given a less scary name and called electron cloud diagrams. Just
know that some artist did not make up those pictures, they are based on
Schrödinger’s
complex
equation
(want more on the equation?? Take Physical Chemistry
or upper level physics classes
offered at any of your local or distant universities!!).
Schrödinger’s
equation also verifies that
the electron does not reside in the nucleus but outside (confirms pre
vious theories!!) and shows
that as the distance away from the nucleus increases, the
likelihood
of finding the electron there
decreases. Unfortunately, we do not know the location to an accuracy of 100%. These electron
cloud diagrams are given for the 9
0% probability of finding an electron in that location! Where
it goes the other 10% of the time???!! Maybe nowhere
–
but all they can say for these
probabilities is that the electron spends 90% of its time there . . .
We have already talked about the
periodic table have the answers right on it
–
well, here is
another example of the periodic table giving you the answer. It is important to realize that the
electron probability diagrams have given way to 4 main types of orbital/electron cloud
diagrams.
They are known as the s orbital, the p orbital, the d orbital and the f orbital.
Remember we are talking about space
–
and space is 3 dimensional. So these orbitals much
account for space in the x, y, and z directions. Each orbital can only hold two e
lectrons
–
we
will get into that more when we do electron configurations
–
right now
–
take my word for it!
The
s
orbital
s
: spherical in shape
–
like a basketball
Notic
e that there is a chance (10%) that the electron will be outside
this sphere
–
but for the most part, the electron density is centered.
16
___________________________________
__________________________________________________
The
p
orbitals: elliptical in shape
–
like a dum
b
bell
17
The electron density of the p orbita
l is shown above. Notice the p orbital is split into an x
component, a y component and a z component. Putting the 3 p orbitals together results again in
a spherical motif of electron density and contribute to the spherical shape of the atom:
___________________________________________________________________________________
The d orbitals: elliptical in shape
–
like a double

dum
b
bell
Again:
these shapes indicate the electron clouds indicating the probable location for finding an
electron in the d sublevel. E
xamining the total composite of each of the d orbitals shows a
spherical overall shape:
18
_________
_______________________________________________________________________
The f orbitals: elliptical in shape
–
like a triple

dum
b
bell
19
S orbital: s subshel
l: spherical in shape with the nucleus in the center. As the principal shell
level increases, the size of the s orbital increases. Thus a 2s subshell is bigger than a 1s, and a 5s
is bigger than a 4, 3, 2, or 1s subshell.
All elements have the s subshe
ll.
P orbital: p subshell:
dumbbell
shapes with the two regions, or lobes, indicating the high
probability of finding the electron on either side of the nucleus. Neither lobe is favored. The
nucleus lies at a nodal plane (meaning that the probability
of finding the electron at that location
is between slim and none
–
and slim is out of town
Unlike the s orbital, the p orbital is
directional
–
meaning that there is one p orbital in the x direction, one in the y, and another in
the z. Each orbital c
an “hold” two electrons. One p orbital consists of BOTH lobes. Again,
as
the principal shell number increases, the size of the p orbital increases, such that a 5p is bigger
than a 4, 3, and 2p orbital.
The joining of the p orbitals in a group
–
showin
g all at the same
time gives one the overall impression of a spherical shape
–
lending credence to our belief that
atoms are spherical in nature. The minimum principal quantum number needed to see the p
subshell is n=2.
D orbital: d subshell: double
dum
bbell
shapes with four regions, or lobes, indicating the high
probability of finding the electron on sides of the nucleus in this double figure 8 pattern (except
for the d
z
2
orbital). Again there is a node at the nucleus. Again, as the principal shell nu
mber
increases, the size of the d orbital increases, such that a 6d is bigger than a 5, 4, and 3d orbital.
The joining of the
d
orbitals in a group
–
showing all at the same time gives one the overall
impression of a spherical shape
–
lending credence to
our belief that atoms are spherical in
nature. The minimum principal quantum number needed to “see” the d subshell is n=3.
Back to the periodic table giving us the answers! The table IS organized to tell us the subshells
for particular elements. These
regions on the periodic table are known as s, p, d, and f “blocks”.
The “block” is a pretty obvious term since they form squares or rectangles on the periodic
tables.
The rows on the sides of the periodic table tell us the principal level that we are in for a
particular element. This number in turn, becomes our principal quantum number. Row 1 has a
principal quantum number of n=1. Row 2 has an n=2, row
3 has an n=3, row 4 has an n=4, row
20
5 has an n=5, row 6 has an n=6. You get the idea!! The “exception” to the rule (because
remember, there always seems to be in chemistry!!) is the d block. They do not follow the row
number as being the principal quan
tum number, instead, that d block is a principal quantum
number
behind
. Thus, when you are in Row 4, the d block principal quantum number = 3.
When you are in row 5, the d block
n=
4. When you are in row 6,
n
=5.
Notice the atomic numbers of the f bloc
k elements. They slide into the periodic table in row 6.
Their principal quantum numbers are
2 behind
their row number. This means that when in row
6, the f block n=4, and when in row 7, the f block n=5.
1.
The principal quantum number = n
n is a positive integer and its value is indicated by the row number (with some
exceptions shown above!). It indicates the relative size of the atoms and wha
t energy
level the electron is located in. When n=1, the electron is in the first energy level, when
n=5, the electron is in the fifth energy level.
21
2.
The angular momentum quantum number =
l
l
tells us the shape of the
orbital or
subshell where the elect
ron is located. The s orbital
has been assigned the
l
value =0, p=1, d=2, f=3 and so on
subshell
l
value
s
0
p
1
d
2
f
3
g
4
The largest
l
value is ALWAYS n

1!!! Thus, for a principal quantum number (n) = 0, the
only
l
value possible
0, which co
rresponds to the s subshell
.
When n=2, we can have
l
values equal to 1 and 0. This corresponds to the s and p subshells.
Notice that the
number of possible
l
values always equals the principal quantum number value (e.g.
when n=2 we have 2
l
values
). No
tice the correlation between the principal quantum
number and the appearance of orbitals
Given: For an n=3 we can have
l
values of ?????
Which orbitals do these numbers correspond to?
Does this make sense off the periodic table and our “blocks”?
Giv
en: For an n=4, we can have
l
values of ?????
Which orbitals do these numbers correspond to?
Does this make sense off the periodic table and our “blocks”?
3.
The magnetic quantum number m
l
:
m
l
tells us the orientation of the orbital in space. Remember
that we can have p
x
, p
y
, and
p
z
orbitals? Each one of the orbitals is assigned a number to identify it from its identical
twins. The number assignment is arbitrary, but each orbital gets its own ID number. If
there are 3 p orbital types, then there must
be 3 numbers to identify them with. The
l
value for the p subshell is 1. So we take the + value, the
–
value and every integer
in

between
to assign the m
l
values. Thus, p
x
=

1, p
y
= 0, and p
z
= 1. AGAIN, the number
assignments are arbitrary! Notice t
hat the m
l
value =

l . . . +1 increasing by integers.
Given:
l
=2 : what subshell is this? What are the possible m
l
values?
If
l
=2 then we
have values of

2 . . . +2 by integers, that means we have

2,

1, 0, 1, and 2
as possible m
l
values. By golly
–
how many d orbitals do we have?? Why there are 5!!
Each number above corresponds to one of those orbitals!!
Quantum numbers can be used to determine what level the electron is in, what orbital the
electron is in, and even which specific orbital the ele
ctron is in!
22
Blackbody radiation:
A black body is a theoretical object that absorbs 100% of the radiation that hits it. Therefore it
reflects no radiation and appears perfectly black.
In practice no material has been found to absorb all incoming ra
diation, but carbon in its
graphite form absorbs all but about 3%. It is also a perfect emitter of radiation. At a particular
temperature the black body would emit the maximum amount of energy possible for that
temperature. This value is known as the black
body radiation. It would emit at every
wavelength of light as it must be able to absorb every wavelength to be sure of absorbing all
incoming radiation. The maximum wavelength emitted by a black body radiator is infinite. It
also emits a definite amount o
f energy at each wavelength for a particular temperature, so
standard black body radiation curves can be drawn for each temperature, showing the energy
radiated at each wavelength. All objects emit radiation above absolute zero.
Some Examples:
Objects
at around room temperature emit mainly infra

red radiation (l» 10mm) which is
invisible. The sun emits most of its radiation at visible wavelengths, particularly yellow (l »
0.5mm). A simple example of a black body radiator is the furnace. If there is a sm
all hole in the
door of the furnace heat energy can enter from the outside. Inside the furnace this is absorbed
by the inside walls. The walls are very hot and are also emitting thermal radiation. This may be
absorbed by another part of the furnace wall or
it may escape through the whole in the door.
This radiation that escapes may contain any wavelength. The furnace is in equilibrium as when
it absorbs some radiation it emits some to make up for this and eventually a small amount of
this emitted radiation
may escape to compensate for the radiation that entered through the hole.
Stars are also approximate black body radiators. Most of the light directed at a star is absorbed.
It is therefore capable of absorbing all wavelengths of electromagnetic radiation,
so is also
capable of emitting all wavelengths of electromagnetic radiation. Most approximate blackbodies
are solids but stars are an exception because the gas particles in them are so dense they are
capable of absorbing the majority of the radiant energy.
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