Hello everyone welcome back, I am Charles Clark we'll continue now by completing
our discussion with Bohr model and looking at some of its applications.
Let me remind you again that there is some original literature available on the
subject we'll discuss today in case you have, want to have a deeper
understanding. And the two relevant things are the,
accounts for the discovery of deuterium that are found in the usual location.
So, to recall where we left off Bohr by quantizing the angular momentum of a
circular orbit in the hydrogen atom found a series of discreet energy levels with
energies given by this formula. Most conveniently in my opinion,
expressed in terms of the redbird constant.
And so now what does this imply for the interaction of atoms with light?
Well the the photon is absorbed or emitted in a transitions between n1 and
n2 so if this is, if this is energy in this direction then transition from n1 to
n2 corresponds to abortion of the photon, a transition from n2 to n1 corresponds to
emission. In any event the frequency of, of the
photon is just, we take a convenient passive definition.
the energy difference is h nu, which is hc over lambda, and now you see why
there's this expression HC in the the, the ex, expression for the energy.
Because we can now go in and substitute the energies for the wavelength and we
get this convenient expression. So the inverse of the wavelength is just
the Rydberg constant times the the difference in in the inverse squares of
the principle quantum members. I think I made that notation clear.
N is called the principle quantum number. Principal with an a I guess, quantum
number. That's a notation that still used in in
modern wave mechanics. And this is an, this is an expression
that's good for that's valid for when the nuclear masses is infidently large
compared to the electronic mass. if one wants more detailed description,
more accurate description then one must use the reduced mass.
And then the result for a finite mass is just again the infinite Ryd, has the
infinite Rydberg constants modified by the ratio of mu over m.
So in the turns in which we describe things, it turns out at the, There's a
Balmer series which corresponds to the value of n1 equal to 2.
there's something else we'll come across in a minute, the Lyman series, which has
n1 equal to 1. But in this case the the low, the Balmer
series that we see in the visible is associated with transitions that all
terminate or originate on n1 equal to 2. So here are the first, we can see the
first 4 members of that series, n equal 3, so the Balmer alpha, 4 Balmer beta and
so on, 5 and 6. Now there are an infinite number of other
terms, other lines in this series. We believe but you don't see them here,
because they're not perceptible to the eye.
They lie, the, the, they lie in the ultraviolet region of the spectrum.
When Bohr published his paper, it produced something quite remarkable.
It was the first sort of rational and quantitative theory that actually
predicted accurately the existence of known spectral lines.
So in particular all known members of the Balmer series for which n1 is equal to 2
and lie in visible. And the Paschen series which are lie in
the infrared were described to within the experimental uncertainties.
Furthermore, there was something called the Pickering series which was a series
of lines in helium plus. That's a hydrogen-like system like the
one that we've been talking about during these past few lectures.
so this I think, particularly significant in that the Bohr theory applies not just
to hydrogen, but to another chemical element, admittedly still a one electron
one. But then, what really set the pace was
the discovery in the following year by Theodore Lyman of Harvard University of a
new lines that on the far ultraviolet spectrum of the hydrogen atom, there to,
around 100, the longest wavelength one is around 121 nanometers.
these are the, these are the, the series associated with the ground state of
hydrogen. So again those are found to be exactly
where Bohr's theory replace them, then there was a spell of two years.
At Johns-Hopkins university in which Fredrick Brackett found the, the series
with n1 equal to 4. Which is the next one after Paschen.
And then his PHD thesis supervisor August Pfund reported a series with the
principal quantum number five. So you can impress your physicist friends
if you memorize the sequence Lyman Balmer, Paschen, Brackett, Pfund.
Most of them won't get it and somewhat later the next series for n 1 equals to 6
is observed. This is the last series exactly named for
anyone because by this time 1953, there was no doubt that under the right
conditions you would be able to get more highly excited states of hydrogen that
had been seen here to form. We'll see a moment of that, an example of
that in the next slide. But this was a what do you call it,
technical triumph, because these the transitions between these states lie off
in the far infrared region of the spectrum.
And so getting some standard wavelengths in, in a region like that is a very
useful thing, indeed. Now here we have what I think is just an
amazing example of the existence of these very highly excited quantized states of
atoms. This is a paper by a team from, Ukraine
and India published in the monthly notices of the royal astronomical society
in 2007. And this spectrum that are, that are
dealt with you see here that are they are, these are absorption lines in the
radio band, in a radio frequency, of around 26 megahertz.
And these absorption lines are associated with transitions of the type delta n
equal plus 1 in principle quantum number. So there's something like transitions n
equal 1,009, going to n equal 1,010. these, so where, where do, where do atoms
in the interstellar medium get these extraordinary, large principle quantum
numbers? Do recall that the, the radius of an
atomic state in the Bohr model increases as the square of the principle quantum
number. So these atoms are a million times larger
than the ordinary atoms, which were familiar.
You could, you could, you could, see them with your eye, if they were solid, which
of course they're not. And the way that they're produced is that
there are electrons in the interstellar medium that are cap slow electrons are
captured into these very highly excited states.
And then those states this is sufficient number of them you can see this regular
series of absorption lines. So now we see that the again there given
by the board transition frequencies so we see this Bohr like behavior starting in
the far ultraviolet with the, the Lyman alpha transition going up into the radio
wave region. So there's eight decades of frequency
over which this theory renders very useful predictions.
Now we're going to look at one of the most important applications ever made of
Bohr's theory. In fact it was a, perhaps the only case
in which a new isotope of an element was discovered by the use of atomic
spectroscopy. Now back in the early part of the 20th
century it was discovered that a number of the chemical elements had constituents
that seemed to be chemically similar but had different masses.
So one of the first was neon which was found by J.J.
Thompson to have 2 isotopes, one of a mass number 20 and the other was mass of
22. Now these mass numbers are, their mass is
in the units of the protons mass. And so we know today where that the
origin of, of these different masses but at the time, it was a mystery.
And most of these discoveries were made by the use of mass spectrometry where
you'd put a, a charged particle through a combination of electric magnetic fields
and then you'd get a a trajectory that dependent upon the charge to mass ratio
so you could separate out the the different isotopes.
Today we understand the origin of the isotopes and the, well, the easy to
explain way there's the proton, which is the carry of charge in the atom, and then
we know of the, the neutron which is a neutral particle that's almost exactly
the same mass as the proton. In some senses it's considered to be a, a
partner of the proton in a two level quantum system.
Maybe we'll talk about that a bit in the lectures on symmetries.
But the story that we're going to discuss now starts in 1931, a time in which the
neutron had not yet been discovered. And most people in those days thought
that isotopes were due to having different numbers of protons of the same
element and then a and then something called nuclear electrons.
So the idea which is first stated by Rutherford.
Was that for some reason what we, what we think of now as helium 4, for example, 4
helium which is equal to, we would say 2 protons and 2 neutrons.
Rutherford would say 4 protons plus 2 nuclear electrons.
But once again, the underlying, there wasn't a good understanding of what the
so-called nuclear electrons were or why they would be bound inside the nucleus
versus the, the electrons in the Bohr, the Bohr model.
now here is a picture of a little road map that was constructed by a man name
Harold Urey, Harold Clayton Urey then a Junior Professor at Columbia University,
in New York. And it shows a map, this is a chart in
terms of this proton and nuclear electron schematic that shows the, the solid
circles here. some which are labeled, are known
isotopes. And you see there is this tendency
downward. and then there are some empty circles
that suggest places where there might be isotopes that have not yet been observed.
And the, the target, principal target of Urey's investigation was hydrogen 2 the,
the, the hydrogen isotope of mass 2 as it was called today we call that Deuterium
or the nucleus we call the Deuteron. there were clues from Chemical from
atomic weights analysis that a heavy isotope of hydrogen might exist.
But it couldn't be seen in mass spectrometry because when, when hydrogen
gas is ionized, there's always a large quantity of the molecular ion h2 plus.
And that has the essential the same chart to mass ratio as an isotope of mass 2
graph. Here we have the idea that it might be
possible to see the heavy isotopes of hydrogen in the optical spectrum of
hydrogen that we've been looking at for a little while during these lectures.
And here is how he presents the idea in his Nobel lecture.
He was awarded the Nobel prize in 1934, for this discovery of heavy hydrogen,
which was published on January 1st 1932 in the physical review.
Here he says Bohr's theory, given some 20 years ago, permits the calculation of the
Balmer spectrum of the heavier, heavier isotopes of hydrogen from this spectrum
of hydrogen by the well known theoretical formula for the Rydberg constant.
So I'd just like to note that Urey was the first American, or one of the two
first Americans to co-author a book on wave mechanics.
And he knew very well that Bohr's theory was obsolete in the light of
Schrodinger's equation. Nevertheless, he choose to present his
motivation and justification for the way the experiment was done in terms of the
Bohr model. That shows the, the influence and respect
that it, had. Now, we're going to have a little
in-video quiz here, which I'm, I'm not asking you to repeat Urey's calculations.
But I've set up, discussion of where the isotope shift, what effects give rise to
the isotope shift, and you are invited to answer some well, sort of qualitative
questions. So I hope that most of you were able to
develop the feeling that it's the heavier isotope.
to which the electron is more tightly bound and therefore the wavelength of the
transition is lower for the heavier isotope.
you know by a small amount and its the, the deviation the wavelength is just
linear int he ratio of the lectern mass to the mass of the isotope.
How was Urey idea implemented? His concept was to get the, a
concentrated form of the heavy hydrogen, heavy isotope hydrogen, if any existed.
By taking just regular molecular hydrogen, liquefying it at low
temperatures and then evaporating the, the liquid off by by heating.
presumably in this process the heavier isotope will be less likely to evaporate.
Volatile. And so the liquid that's left in the in,
in the residue might be concentrated in any heavier isotope.
So he sought out colleague a man whom he'd known as a young professor at Johns
Hopkins University, Ferdinand Brickwedde. Brickwedde was the head of the low
temperature physics laboratory at the National Bureau of Standards.
And earlier in the year 1931 he was, he led a team that was the first American
effort to produce liquid helium. So he was he had a very well equipped
laboratory. Able to to, to take large quantities of
liquid hydrogen. So he evidently started with about five
to six liter of liquid nit- hydrogen. And boiled away all but 2 cubic
centimeters of it. So very heavily evaporated.
And it was sent up to Columbia University where it was looked at in Urey's
spectrometer. Here is the original data from, a second
paper by Ur-, by Urey, and, Brickwedde and Murphy.
Published in Physical Review in 1932. And this shows, this shows the photo
emission spectrum. which is, I mean, it's, it's, the
notation here is h1 beta. This is the Balmer beta line, this is,
this, this line here. And this central peak.
You see, what's going on here, is these are, this is photographic film.
It's strongly saturated by the strong central line.
And then according to the predictions we see the fee, the predicted value,
predicted wavelength of an isotope of mass two is shown here h2 beta.
And what you are seeing here are three different samples of distillate with
increasing constant, increasing concentration of any heavy isotope that
might be in there based on the degree of distillation.
And so this shows conclusively that there's a line that grows with the
expected increase in concentration of the mass two isotope.
Now, as you can see there are many other features in this spectrum.
Some are called ghosts. Maybe you've heard of ghosts.
people in those days believe in ghosts, we still do in spectroscopy.
And and then there are other, other things going on.
These are dealt with in the paper they're artifacts of of spectrosity.
so note that there's, there's no apparent no apparent feature associated with a
mass three isotope even though there is. We know there is a, mass 3 isotope called
Tritium which is radioactive. It has a half life of about 12 years, if
I recall correctly. It's not present in any great abundance
in the earth's atmosphere. But nevertheless, there are a sufficient
number of artifacts In this spectrum that it was really essential for the use of
this distillate to show that they increase with concentration.
But it also suggests that maybe deuterium isn't such a big deal after all.
I mean it's, it's seems to be you know very I think the natural abundance of
deuterium is about a part in 10 to the 4th.
So you might ask well why bother? Why should such a little bump be such a
big deal?. Well it turned out to be a huge deal, and
you can read more about this in the literature in the supplemental materials
section. it became a, it became a big deal, not
because of the, that little bump that was seen in the spectrum.
But because that once people knew that the heavy isotope of hydrogen existed,
there were very clever ideas that were developed to figure out how, how to
acquire it more easily than by boiling off all this liquid hydrogen.
And the the breakthrough was made and this was something done jointly by Urey
and Edward Wight Washburn, who was the chief chemist of the National Bureau of
Standards at the time, Together they developed a means for
producing deuterium efficiently by electrolysis.
So you know, this striking thing that on Thanksgiving Day which is when the
experiments were done in New York City, Thanksgiving Day of 1931, making Urey
late for his Thanksgiving dinner. You know, up to that moment no one had
any evidence for this, this mass two isotope at all.
But just a few months later there was a method that was developed by Washburn and
Urey to produce it efficiently by electroloysis.
And this was rapidly taken up on an industrial basis by Norsk Hydro, the main
electricity generating company in, in Norway.
And by 1935 so really just three years later they were shipping 99% pure heavy
water at a price of 50 cents, 50 American cents per gram.
And there was a wide demand for this for a, a large number of uses in chemistry
and biology. Well furthermore, it turns out that the
only suitable moderators for a nuclear chain reaction are deuterium and ultra
pure graphite. And there was a Nazi nuclear power
project that was started during the second World War.
And they made the decision to go with with Deuterium.
So the Nazis had invaded Norway in 1940, they took over this, the heavy water
plant to use the the Deuterium to develop nuclear power perhaps even a nuclear
weapon. And well, I don't have time for this, but
there's a very striking set of events involving great individual heroism and
sacrifice that are told in a book and the movie The Heroes of Telemark.
They're dealt with to some extent in the, the the supplementary material with
[INAUDIBLE]. Okay, well that's it for the Bohr model.
I hope you found it entertaining and interesting and learned something.
And in the next lecture we'll start on the use of wave mechanics to discuss
simple material systems.