This is an introductory course for students with limited background in chemistry; basic concepts such as atomic and molecular structure, solutions, phases of matter, and quantitative problem solving will be emphasized with the goal of preparing students for further study in chemistry.
Light Wave Particle Duality
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From the course by Duke University
Introduction to Chemistry: Structures and Solutions
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From the lesson
light
We will cover introduction to light, Bohr model of the hydrogen atom, atomic orbitals, electron configurations, valence versus core electrons. Don’t forget to use this week’s discussion forum for any questions and discussions.
Meet the Instructors
Prof. Dorian A. CanelasAssistant Professor of the Practice
Chemistry
In the last lecture I discussed how light behaves as a wave and we looked
at a photograph of one of the pieces of experimental evidence that supports this.
The red laser light was defracted through a
grading into areas of constructive and destructive interference.
In this lecture I'm going to discuss how scientist were able
to reconcile the wave behavior of light with other experimental results
that couldn't be explained by the notion of light as wave alone.
[BLANK_AUDIO]
Before we launch into the new material, let's review
what we've already learned about describing light as a wave.
We can observe the different wavelengths of color contained in sunlight, routinely.
To illustrate, a rainbow is an example of a continuous spectrum, where
the colors are separated, but all blend together, without any breaks between them.
Here a continuous spectrum is observed.
Because the sunlight is being separated by the water droplets in the atmosphere.
And that sunlight is white light, containing
all of the different frequencies of visible light.
Visible light only exists in a narrow wavelength range.
So it represents only a small portion of the light in the electromagnetic spectrum.
We know that the wavelengths of visible light
go from about 700 nanometres to about 400 nanometres.
And there are corresponding frequencies to that
visible light and remember we did some calculations
and those frequencies were on the order of ten to the 14 cycles per second.
Remember as the frequency is the number of times that for
example the peak of a wave would pass by any stationary
object I use the example of our eye, in some time frame.
Here's we're using the time frame of one second.
But there are of course, larger wavelengths of light.
There are light waves that are radio waves, that we
can use in communication transmission, and those have very large wavelengths.
You can see much
larger than the wave lengths and here these wave
lengths are given in meters of the visible light.
We used microwaves which are also longer wave
lengths in visible light to cook our food.
Infrared light gets used frequently in not only heating
things but also in determining the structure of molecules.
We can also use ultra-violet light to determine the structure of molecules.
As the wavelength of the light becomes shorter,
the frequency of the light is becoming larger.
From 10 to the 14th cycle per second for the visible light.
To 10 to the 16th for ultra-violet, 10 to
the 18th for x-rays, which remember at this point
has so high of a frequency that it can
cause the atoms in our bodies to eject electrons.
And even higher energy
for Gama rays.
So classical physics said that light is a wave and there
is many experiments which supported this idea of light as a wave.
>> And in fact, at the end of the
1800's scientists agree that light indeed behaves as a wave.
However, there were a couple of phenomena that could not be explained.
I hope you've had a chance to watch
the demonstrations of Blackbody radiation and the Photoelectric effect.
These types of phenomena had been observed.
But there
was no way to use light to reconcile the observations that had been made.
There are some other excellent videos explaining this physics phenomena online.
And these we'll reference in the demonstration videos.
So be sure to check those out.
At the end of the 19th Century.
So around 1900, Max Planck was commissioned by the German government
to try to find a light-bulb that would emit more light.
So here is Max Planck in the 1800's long before he won the Nobel Prize in 1918.
Around 1900 he was studying black body radiation.
Because that's what causes a light-bulb filament to glow.
His goal was to produce the more efficient light-bulb.
But he had to consider the discrepancy between what he was observing, that the
object emits more and more red visible light as they get hotter and hotter.
And the classical physics prediction that comes from light being a wave.
And that gives us an ultra-violet catastrophe
as the object gets hotter and hotter.
So light exhibits quantization.
[BLANK_AUDIO]
Planck then had to throw out the entire theory that light was only a wave.
And he decided that the energy of light is not continuous.
And it comes in discrete amounts that he named quanta.
He came up with this breakthrough equation in his theory, and that is E= nhv.
In this case n is simply a positive integer.
It can be 1, 2, 3, 4, or 5. But n
is restricted only to integer values. There are only certain
values that are allowed. We don't have any fractional values
allowed in this theory. H is now called Planck's constant and
it has a value of 6.626 X 10-34 J*s. And again,
new is the frequency.
The frequency is in units of reciprocal seconds.
So, the energy then, if the frequency is
1/s and Planck's constant is in Joules per second.
So seconds are going to cancel and that gives
us our energy in Joules, for the light.
Remember N is just an integer.
[BLANK_AUDIO]
So light, according to Planck, exhibits quantization.
Discrete amounts of energy are allowed in this equation but those discrete
amounts can only be those that arrive by having energy values of n.
Other amounts of energy are not allowed
and this concept of quanitization that some things
are allowed and other things are not allowed
is one of things that gives students problems.
So let's do an analogy for the idea
of quantization with something that your more familiar with.
A good analogy for this quantization, that I think help students
understand the concept that some values are not allowed, is two
different ways that we could travel from the ground to hovering
on top of a platform that is 60 cm in the air.
Now some of you are young and very healthy and
spry and you might just be able to jump up
onto a platform that is 60 cm in the air
but I'm not that athletic so I would need to devise
a way to get up onto that platform.
The two ways to do that are the continuous method, which is a ramp.
If I was walking up a ramp to my platform that's 60 cm off the air,
I could stop at 20 cm and rest if I needed to, because I'm getting feeble.
Or I could stop at 40 cm.
Or in fact, if I wanted to, I could hover 50 cm above the ground on my
ramp, couldn't I? So the ramp is continuous.
All values of distance between me and what was the
original ground, if we call the ground right here, are allowed.
Everything is allowed in a continuous system.
But there's also a method I can use to get up
to the platform that is discrete or quantized and that is steps.
If I built some steps
that had a 20 cm rise I would be able to hover off
the ground 20 cm from the ground or 40 cm from the ground.
But I would not be allowed to remain 50 cm
off the ground for very long, because of gravity, would I?
In other words, the steps are quantized and there are certain
distances from the ground which are not allowed by the steps.
In this case, 50 cm.
In a continuous system, all values are allowed.
So what Plack said in his theory is that light is not continuous.
There are certain things that are not allowed in light.
Only discrete values are allowed. Now,
some of you are saying. But aren't waves continuous?
And in fact, in 1900 when Planck first set forth this theory
it was hard to recognize that waves had a way to be quanitized.
In fact Einstein came along in 1905 and said, wait
a minute light isn't entirely a wave. It is a stream of finite
chunks of light.
Packets of particles that behave like a light.
Now these packets of particles are called photons.
So light has a wave like nature and we can observe that wave like nature
in many experiments. But light also has particle nature.
Einstein was able to take Plunk's equation and split it into equations
for individual photons of light.
The energy of a photon that is large would be for light that has a high frequency
and if the energy of the photon is small then that light has a small frequency.
Einstein was able to say that Planck's equation was for a beam of light.
And that, that integers show which energies are allowed
for different types of photons.
But in the individual photon has an energy of E equals H new.
So he was still using Planck's constant.
So, this gave us the birth of quantum theory.
The idea that light is quantized and that
light is a particle that has wave-like behavior.
So, there's two important equations that we'll be using in chemistry.
The first one comes from the classical experiments to show light is a wave.
C equals lambda nu. This still applies.
We're not throwing this equation out of the window.
But Planck and Einstein refined the theory by
basically inventing quantum mechanics, by saying that light is
also composed of these particles called photons, and those
photons have an energy that relates to H new.
So with these two equations we have the wave particle duality of light.
And you see that both equations contain the frequency new.
So we can write a form of the equation for the energy that
contains both the speed of light and the wavelength of light, can't we?
So up here I could say well nu equals C divided by lambda
so I can plug in C divided by lambda for nu over here.
And I say that the energy equals H C divided by lambda.
That means if I know either
the wave length of light or the frequency of light...
I can calculate the energy of that light.
Because remember h is a constant, it's Planck's constant.
It's always the same value.
And c is a constant, it's the speed of light, it's always the same value.
You might as well memorize that the speed of light is
3 X 10 to the 8th meters per second in a vacuum.
So we have now something called Quantum Theory.
In introductory physics class, you learned about classical mechanics, things like
projectile motion that I really enjoyed studying when I was in school.
They're very useful for looking at large objects.
So, why do we need quantum mechanics?
Well, classical physics doesn't hold up and
is unable to describe two key situations.
One is if objects are going very fast.
And the other one is for objects that are very small.
Objects that are going very fast are described by the
Theory of Relativity, also written about by Einstein in 1905.
And objects that are going very small are best described by Quantum Mechanics.
Which, was initially put forth by Einstein and Planck.
Although, they didn't call it Quantum Mechanics at the time.
And was later to find, refined by other people
like de Broglie, Schrödinger and a whole group of people.
So since atoms are very small, we
need quantum mechanics to describe how they behave.
So quantum mechanics is used to describe the behavior of
objects that are roughly 10 billion times smaller than we are.
It's a mathematical theory that has a lot of calculus and partial derivatives.
You may or may not be comfortable with that.
But if you're not comfortable with that, that's okay.
This is an introductory class and we need to be using algebra.
And what we're going to take from the
quantum mechanics theory are these key concepts.
The first one we've talk about.
Quantization, the idea that for some systems there are certain
things that are Allowed and certain things that are not allowed.
This second key concept that we've already talked
about for quantum mechanics is wave particle duality.
The next key concepts of probability and uncertainty
will be the subjects of some future lectures.
Thank you for watching this video lecture on the wave particle dual nature of light.
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