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.