Transcript Modern Atomic Theory

The Electromagnetic Spectrum
Light is composed of electric and magnetic fields and thus its alternate name
"electromagnetic spectrum". Light can be absorbed and emitted by atoms and
molecules. The precise details of which give us the world we see around us.
Chemists are interested in the details of absorption and emission of light by matter
because these details can be viewed as fingerprints of atoms and molecules as
well as their chemical properties. To understand the interaction of light with matter
we need to first understand the basic character of light
Light is a wave
Traditional physics views light as a wave - with all the properties usually
associated with waves. For example light can undergo constructive and
destructive interference - just like ripples on a lake.
Light is characterized by its wavelength and frequency
Since light has the characteristics of a wave then we can associate a wavelength
(l) and frequency (n) to it: The wavelength is the physical distence between two
successive crests of the wave and the frequency is the number of times the wave
oscillates per second (Hz).
The frequency and wavelength of light are related to one another by the speed of light c
According to Einstein's theory of special relativity nothing travels faster than light. The
speed of light (c) in a vacuum (e.g., outer space) is 2.998x10+8m/s. The speed of light is
related to the wavelength and frequency by the equation
λv=c
Since the speed of light does not change, if we know the wavelength then through this
equation we also can determine the frequency and visa versa.
Light has energy
The energy of light is proportional to its frequency and inversely proportional to its
wavelength. The proportionality constant is known as Planck's constant h.
Energy = hv = h c/λ
h=6.627x10-34 Joule second
The Spectrum
Light comes in a huge variety of wavelegths. The visible part of this spectrum
(the part that can be seen with the human eye) is only a very small part of
this spectrum. This spectrum, along with the sources of the radiation, are
given below.
The Discovery of the Quantum
By the late 1800's much of science had been well understood.
Naturally, scientists of the time generally believed that most major
problems in physics had been solved and that all that was left was
"clean-up" research. Nothing could have been further from the truth.
There were three little known experiments at the time that defied
explanation by traditional science. These experiments were:
• Black-body radiation
• Photoelectric Effect
• Emission Spectrum of Hydrogen
The eventual explanation of these experiments led to a revoltion in
science and how science viewed atoms and their interaction with
light.
Black-body Radiation
If a hollow black-body is heated to a temperature T it will emit light. The
wavelength dependence of the energy of this light can be recorded. The
resulting curve is the black-body radiation curve.
Science could not explain the wavelength dependence of the curve until Max Planck
focused on the problem around 1900. Max Planck was an expert in the science of
thermodynamics and he used the tools of thermodynamics to try and explain BB
radiation. However, after several failures he almost gave up. He made one last
attempt. He decided to throw away the ideas of classical science and make a bold
assumption: He assumed that the atoms in the black-body could not absorb just any
energy but could only absorb or emit energy in packets he called "quanta". With this
assumption he quickly derived a formula that exactly reproduced the black-body
radiation spectrum. Since Planck was the first scientist to suggest "quanta" he is
today considered the father of quantum theory.
Photo Electric Effect
The world of science did not pay too much attention to Planck's work because
his assumption of quanta was ridiculous to their minds. In 1905 Einstein
investigated the phenomenon known as the photoelectric effect. The
photoelectric effect is simply the ability of some metals such as potassium to
eject electrons when irradiated by light:
Traditional physics predicted that the energy of the ejected electron would
depend upon the intensity of light and independent of the wavelength. However,
experimentally the opposite was observed
Einstein knew of the work of Planck and decided that it might have application to the
photoelectric effect. Einstein suggested that light, although traditionally viewed as a
wave could instead be viewed as packets of light he called "photons". These light
packets each had energy which was given by
E(photon) = h n
With this view Einstein was able to completely explain the photoelectric effect. Einstein
clearly understood that his photons were similar to Plancks' quanta.
Emission Spectrum
By the turn of the century it was well known that an emission
spectrum existed for the various elements. The experiment is easy:
An element, such as hydrogen, is excited by an electrical potential
until it gives off light. The emitted light is then passed through a
prism - which separates it into its constituent wavelengths. The
wavelengths are then recorded on light sensitive film.
Each element gives a unique spectrum. The position of the lines
relative to one another changes from element to element and, as it
turns out, from molecule to molecule. In essence, the emission
spectrum is a fingerprint of the element/molecule that generates it.
The Bohr Atom
In 1913 Niels Bohr came to work in the laboratory of
Ernest Rutherford. Rutherford, who had a few years
earlier, discovered the planetary model of the atom
asked Bohr to work on it because there were some
problems with the model: According to the physics of
the time, Rutherford's planetary atom should have an
extremely short lifetime. Bohr thought about the
problem and knew of the emission spectrum of
hydrogen. He quickly realized that the two problems
were connected and after some thought came up with
the Bohr model of the atom. Bohr's model of the atom
revolutionized atomic physics.
The Bohr model consists of four principles:
1)Electrons assume only certain orbits around the nucleus. These
orbits are stable and called "stationary" orbits.
2)Each orbit has an energy associated with it. For example the orbit
closest to the nucleus has an energy E1, the next closest E2 and so
on.
3)Light is emitted when an electron jumps from a higher orbit to a lower
orbit and absorbed when it jumps from a lower to higher orbit.
4)The energy and frequency of light emitted or absorbed is given by the
difference between the two orbit energies, e.g.,E(light) = Ef - Ei
n = E(light)/h
h= Planck's constant = 6.627x10-34 Js
Where "f" and "i" represent final and initial orbits.
With these conditions Bohr was able to explain the
stability of atoms as well as the emission spectrum of
hydrogen. According to Bohr's model only certain orbits
were allowed which means only certain energies are
possible. These energies naturally lead to the
explanation of the hydrogen atom spectrum:
Bohr's model was so successful that he immediately
received world-wide fame. Unfortunately, Bohr's model
worked only for hydrogen. Thus the final atomic model
was yet to be developed.
The Aufbau Principle
The equations of modern atomic theory are difficult to solve. Fortunately,
many of the results can be obatined by following some simple rules. These
rules are known as the Aufbau principle. However, we first need to discuss
quantum numbers, shells, subshells and orbitals.
The principal quantum number n - the shell
Quantum numbers abound in quantum theory. These quantum numbers
serve the purpose of keeping track of the various quantum possibilities that
emerge. Perhaps the most important quantum number is the "principal"
quantum number n. The principal quantum number n can take on the values
1, 2, 3, 4, 5, 6, ... . Associated with each n is a principle energy level known
as a shell. Thus, shell 1 has n=1, shell 2 has n=2 etc. and so on associated
with it.
Each shell has subshells associated with it
Depending upon its quantum number, each shell can have one or more
subshells associated with it. For the n=1 shell there is only one subshell the s subshell. For the n=2 shell there are two subshells - the s and p
subshells and so on. The number of subshells within a shell is equal to n.
The shells, subshells and orbitals can be summarized with the diagram below for a
typical atom. (A mnemonic device exists to recall this order.)
Each subshell has one or more orbitals within it
The Aufbau Principle
The physical and chemical properties of elements is determined by
the atomic structure. The atomic structure is, in turn, determined by
the electrons and which shells, subshells and orbitals they reside in.
The rules af placing electrons within shells is known as the Aufbau
principle. These rules are:
1.Electrons are placed in the lowest energetically available subshell.
2.An orbital can hold at most 2 electrons.
3.If two or more energetically equivalent orbitals are available (e.g., p,
d etc.) then electrons should be spread out before they are paired
up (Hund's rule).
Alkali Metals And Reactivity
The reactivity of the alkali metals can be understood by condsidering
their electronic configurations. First, let's examine the reactivity of
lithium, sodium and potassium with water
1.lithium and water movie
2.sodium with water movie
3.potassium with water movie
The explanation is given in the slide sequence below
Atomic Radii
The radii of atoms decrease and increase in a periodically. Below
is a diagram showing the relative size of atoms. the atoms sizes
are in picometers (pm = 10-12 m).
Two factors must be taken into consideration in
explaining this periodic trend
(1) Increasing nuclear charge
(2) Increasing shell
Along a period (left to right) the the atomic number
increases while the valence electrons remain in the
same shell. Thus due to the increasing nuclear charge
(pulling electrons closer to the nucleus) the radii of the
atoms decrease left to right.Top to bottom along a
group the atomic number continues to increase.
However the shell increases from shell 1 to shell 2 etc..
The atomic orbitals for each successive shell get larger
and larger - more than compensating for the increased
nuclear charge. The result is atomic radii increase top
to bottom along a group.
Ionization Energy
Consider the following experiment: Starting with hydrogen and
proceeding through the periodic table, measure how much energy
ot takes to pull an electron away from each atom. The resulting
atom will be a cation and the energy it takes to pull the electron
away is called the ionization energy. M ----> M+ + e-I.E.
If we plot these ionization energies versus atomic number the
resulting graph below emerges.
Clearly, the most striking feature of this graph is that
there is an inherent periodicity. How can this periodicity
be explained? If we examine the electronic
configurations of these elements we find that all
elements with the lowest ionization energies -the alkali
metals - have similar electronic configurations - [NG]ns2.
Similarly, all the elements with the largest ionization
energies - the noble gases- have filled s and p electronic
configurations - [NG](nd10)ns2np6. The elements
inbetween these two extremes also have similar
electronic configurations.Therefore, the periodicity of the
data in the graph is a direct result of the underlying
periodicity in the electronic configuration of the elements.
Electron Affinity
Electron affinity is, essentially the opposite of the
ionization energy: Instead of removing an electron from
the element we add an electron to the element to create
an anion.
M + e- ----> M- E.A.
Generally, the energy that results from this process (the
electron affinity) is negative or close to zero. The more
negative this energy the more this process is favored. In
the figure below we see the trends in the electron affinity
for many of the elements.
Note that the noble gases, alkali metals and alkali earth metals have E.A. close to zero indicating that these groups of elements do not particularly like to become anions.
However, the nonmetals and especially the halogens are highly negative and thus
readily become anions. A periodic trend is evident, as was the case for the ionization
energy. This periodic trend can be understood as a reflection of the underlying
periodicity in the electronic configuration of the elements.
Additional Problems
1.The US navy has a system for communication with submarines. The system
uses radio waves with a frequency of 76 Hz. What is the wvaelength of this
frequency in meters? Miles?
2.Green light has a wavelength of approximately 100 nm. What is the
frequency of this light?
3.What is the energy of one photon of the green light in problem 2 above.
4.The most prominent line in the spectrum of mercury is found at 254 nm.
Other lines are found at 365 nm, 404 nm, 435 nm and 1014 nm. Which of
these lines represents the most energetic light?
5.What is the frequency of the most prominent line in problem 4 ?
6.What is the energy of a mole of photons of the most prominent line in
problem 4?
7.What is the color or colors of these lines?
8.Place the following types of radiation in
order of of increasing energy per photon
(a)yellow light from a sodium lamp
b) radiation froma microwave oven
c) gamma rays from a nuclear reaction
d) red light froma neon lamp
e) ultraviolet rays from a sun lamp