This course will cover the topics of a full year, two semester General Chemistry course. We will use a free on-line textbook, Concept Development Studies in Chemistry, available via Rice’s Connexions project. The fundamental concepts in the course will be introduced via the Concept Development Approach developed at Rice University. In this approach, we will develop the concepts you need to know from experimental observations and scientific reasoning rather than simply telling you the concepts and then asking you to simply memorize or apply them. So why use this approach? One reason is that most of us are inductive learners, meaning that we like to make specific observations and then generalize from there. Many of the most significant concepts in Chemistry are counter-intuitive. When we see where those concepts come from, we can more readily accept them, explain them, and apply them. A second reason is that scientific reasoning in general and Chemistry reasoning in particular are inductive processes. This Concept Development approach illustrates those reasoning processes. A third reason is that this is simply more interesting! The structure and reactions of matter are fascinating puzzles to be solved by observation and reasoning. It is more fun intellectually when we can solve those puzzles together, rather than simply have the answers to the riddles revealed at the outset. Recommended Background: The class can be taken by someone with no prior experience in chemistry. However, some prior familiarity with the basics of chemistry is desirable as we will cover some elements only briefly. For example, a prior high school chemistry class would be helpful. Suggested Readings: Readings will be assigned from the on-line textbook “Concept Development Studies in Chemistry”, available via Rice’s Connexions project. In addition, we will suggest readings from any of the standard textbooks in General Chemistry. A particularly good free on-line resource is Dickerson, Gray, and Haight, "Chemical Principles, 3rd Edition". Links to these two texts will be available in the Introduction module.
CDS 5 Quantum Energy Levels in Atoms II
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From the course by Rice University
General Chemistry: Concept Development and Application
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From the lesson
Electron Energies and Orbitals
The electron shell model does not account for all of the observable properties of atoms, including the energies and motions of electrons. In this module, we observe that these energies are quantized. We also observe behaviors which reveal the surprising fact that electron motion is described by waves or “orbitals” which provide the probability for the movement of the electrons about the nucleus. This module takes us into the strange world of quantum mechanics.
Meet the Instructors
John Steven HutchinsonDean of Undergraduates and Professor of Chemistry
Now that we understand something about the energy of radiation, we can use that
to analyze the energies of electrons and atoms.
Remember in the previous lecture I mentioned something about spectroscopy,
which is the study of matter by its interaction with radiation.
In particular, we can shine light on matter, atoms or molecules, and see what
frequencies of light are absorbed by them, by the atom or molecule.
Or, we can energize atoms and molecules, and see what frequencies of light that
they emit. We're going to focus on this particular
lecture on one substance, most notably, hydrogen, the simplest of all of the
elements. We're going to analyze something called
the Hydrogen Atom Spectrum. Here is the concept.
We're going to take a sample of hydrogen. We're going to put it in the electric
arc, that's going to energize the hydrogen in there.
And as a consequence of that, the hydrogen's actually going to emit a
number of frequencies of radiation. To see each of those frequencies, we're
going to pass them through a simple prism, that will separate the frequencies
of light spatially so that we can see them either with our own eyes or with
instruments. Here, we've illustrated what is called
the visible spectrum of Hydrogen. It's four different frequencies of light
which are emitted, or four different wavelengths of light which are emitted.
But these aren't the only ones, these are just the ones that our eyes will respond
to. In fact there are a huge number, of
frequencies of light which are omitted when hydrogen is excited in this way.
And, many of these have to be detected by instruments.
Here is a complete set well, a nearly complete set of the set of frequencies
which, and wavelengths. Which are omitted by excited hydrogen
atoms. And you can see, here, the relationship
that we, talked about before. Which is the inverse relationship between
the wavelength and the frequency. The shorter the wavelength, the higher
the frequency and vice versa. In this case, we've also identified the
region of the spectrum particularly there are those for frequencies that we saw in
the previous slide for the visible spectrum of hydrogen.
We look at the pattern of the data here, let's say we just sort of look down these
frequencies and say, anything there that looks like a pattern that we can observe.
and the answer turns out to be, not particularly, there just seem to be a set
of number there. We've put them in sequence.
But they don't necessarily seem to correspond to anything.
But it turns out there actually is a remarkably beautiful relationship amongst
these numbers. Won't go into the history of how that
relationship was developed, but it goes under the name of the Rydberg equation.
It turns out the Rydberg equation can predict every one of the frequencies
which is in this chart. And it is this simple formula that we've
illustrated back over here. And what is the idea here?
The idea is a pretty simple one. Pick a particular integer n.
And predict, say, one or two. We're taking another integer m.
Make it two or three. Don't make it the same number, and
calculate a frequency of radiation based upon that value of n and m.
And it turns out for every choice of n and m you want to make, there is a
frequency over here that will show up in the table.
Alternative for every frequency that's in that table there exists a choice of N and
M, which can predict it from the Rydberg equation.
Not it's not obvious why the Rydberg equation looks the way it does.
Why should there be a relationship between the frequencies and two different
integers, and what do those integers mean?
None of that is told to us immediately by this experimental data.
Because the experimental data is simply collected and then analyzed to determine
to have this particular form. Let's see how we can now interpret the
fact there are only a select set of frequencies which were emitted by the
hydrogen atom. We're going to walk through a line of
reasoning here, that tells us that individual atoms are, of hydrogen, are
only emitting very specific frequencies of radiation.
That's the experimental observation. Now we're going to combine that
information with what we learned in the previous Concept of Elements study.
Which is that the frequency of radiation is related to the energy of the photons
which are being emitted since only certain frequencies are emitted.
Then only certain photons with certain energies are emitted.
And as a consequence, what we can say is that the atom itself is only capable of
losing rather specific energies. That is, if I'm emitting, if I'm an atom,
and I emit a photon. I lose the energy associated with that
photon. If only certain energies of photons are
permitted then I can only lose certain energies.
But I can only lose certain energies, it must be true, that I can only have
certain kinds of energy transitions that can take place.
In particular, we think back over here, let's imagine first.
I've got an atom and it is emitting radiation, and that radiation corresponds
to an energy loss of H nu. And that must correspond to the energy
loss of the individual electrons in the atoms and as a consequence, if I try to
plot What the energies must for the electrons.
They can't just be anywhere. Because if they could be anywhere I could
lose any amount of energy. Since I can only lose specific amounts of
energy, then there must only be specific energy levels that can exist for the
electrons. Such that I could lose that amount of
energy, or I could lose that amount of energy.
But I couldn't lose just some sort of random amount of energy out here
corresponding to, say that energy loss. Because that wouldn't correspond to the
transition between any two energy levels here.
I might have that one. But I could not have just any random
number energy loss. Therefore since only certain energy
transitions are possible, I can conclude that only certain energies are possible
within the atom. There are only certain energies that the
electron can have in the Hydrogen atom. As a consequence, looking at the spectrum
of hydrogen atom, we can clearly conclude, that the hydrogen atom
electrons must be in one, of a number of quantized energy levels.
Let's see if we can figure out what those energy levels are, from the Rydberg
equation. Let's back our way up, here's the Rydberg
equation again. Remember, this is the frequency of light
which is being emitted over here in the diagram.
What that corresponds to, a certain photon frequency, h nu, that's being
emitted. But that photon energy must correspond to
a certain amount of energy lost by the electron.
So in the next line in the equation here, what we have specified Is that the energy
of the photon is now the negatives of the energy change of the electrons.
So I've inserted a minus sign in there. So the amount of the energy that the
electron can lose is minus h times the frequency of the photon emitted and the
photon emitted must fit the rydberg equation.
Well if that's the case then we can also just algabraically rewrite the change in
the energy of the electrons. All we've really done here is to divide
the previous equation into two pieces corresponding to the n squared and the m
squared, so here's the n squared piece. And here's the n squared piece.
But if I now analyze those, what I clearly see, is that this looks like the
difference, which between two different terms, that look very similar.
Both of those terms have a minus hR, divided by an integer squared And I
subtract by a minus HR divided by a different integer square.
So the energy difference is the difference between two very similar terms
that is strongly suggestive that the energy the electron is simply given by a
very simple formula. Minus H a proportionality constant called
Plank's Constant times R. Proportionality constant called Rydberg's
constant, divided by n squared, where n is just some integer.
One, this actually tells us what the energies are, associated with an electron
in an hydrogen atom. And this formula exactly predicts the
spectrum from the Rydberg equation because we derived it from the Rydberg
equation. But it also tells us something funny
here, it says that the energy of a hydrogen electron depends upon an
integer, n, and that integer is a quantum number.
A quantum number n that has just shown up rather naturally, by examining the
experimental data. So we have our first observation, then,
of quantized energy levels corresponding to individual quantum numbers.
Now that's all true for Hydrogen, what about for other atoms?
Turns out each atom has it's own characteristic spectrum, you can look
these up on the internet, on any place that you want to.
I actually recommend a particular site from the University of Oregon.
Which I have pulled up here for you. That actually allows you to see the
frequencies of light which are emitted, by whatever element you might be
interested in. Lets click on hydrogen here.
Here are those four frequencies of light that we've seen before.
Lets click on Helium. There are quite a few frequencies of
light here. Notice again that these are only the
visible spectrum that we are looking at. There are a number of frequencies which
are outside the visible range for each of these elements.
Pick on your favorite element. How about phosphorus?
We can click on this. There are a significant number of
different frequencies in the visible range.
The important point of this conversation is that each Atom from each element has
it's own characteristic set of frequencies.
And since it has it's own characteristic set of frequencies, they don't apply the
Rydberg equation doesn't apply. So this formula that we created does not
apply to other atoms only to the Hydrogen atom.
However, we can conclude that since each atom has its own characteristic set of
frequencies, then each atom must have its own characteristic set of energy levels.
And those energy levels can actually be determined experimentally and measured
simply by measuring the spectrum that is omitted, the spectrum of frequencies that
is omitted. By each individual atom.
Now it's a different question to ask why can you only have certain energy levels.
Or for that matter, why are those energy levels characterized by a quantum number.
We're going to pick that up by digging into quantum mechanics in the next
lecture.
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