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.