 So, in our last lecture, we saw that the theoretical predictions of Maxwell and the experimental validation by Hertz seem to give us an idea about the fundamental nature of light. Light seems to be consisting of electromagnetic waves or electromagnetic oscillations. However, this idea would probably only survive a couple of decades before it would be questioned again due to some experimental observations related to what is known as thermal radiation. Now, based on this, I am going to make three or four video lectures discussing what black body radiation is, the classical explanation towards black body radiation and the Planck's postulate giving us a resolution to the ultraviolet catastrophe and giving us an explanation of what black body radiation is. So, this is going to be the very first lecture of that. In today's video, I want to discuss what black body radiation is and what are the experimental observations associated with black body radiation. So, first of all, let us try to understand what is black body radiation. You see everything around us, all the objects are emitting thermal radiation by virtue of their temperature, by virtue of the heat contained in them. Now, if I say something like that, you are going to ask me, but sir, I don't really see objects glowing automatically, right? For example, if I have a chalk, a piece of chalk, like this is blue in color, this is orange in color, if I take another object like a ball, which is yellow in color, if I switch off all the lights, I cannot see them, they are not glowing in light, right? They are only reflecting the light that is falling on them. Well, you see, I used to watch, when I was a child, I used to watch in Discovery Channel these episodes of search and rescue missions, where the police or the detective would search for somebody in the dark or maybe in the forest, where they would have these infrared cameras and they would detect people moving through the woods or through the forest or in the dark by virtue of the infrared cameras, because infrared cameras are capable of detecting the light that is being emitted from our bodies at all times, but we cannot really see them. By virtue of the heat contained in our body, we release infrared radiation or radiation having wavelength just slightly larger than visible wavelength that we cannot really see with our eyes, but they can get detected by certain kinds of cameras and using those cameras, people can detect where people are, other people are by virtue of their heat released through their bodies. So you see, our bodies are emitting infrared radiation all the time, not just our bodies. Other objects are also emitting various kinds of electromagnetic radiation at room temperature that do not really fall in the visible spectrum. For example, if I take some kind of a piece of metal and heat it to sufficient temperature, it would start glowing with red colour. If I increase the temperature, it would become slightly orange in colour. If I increase the temperature further, it might become yellow and then slightly whitish or bluish. So you see that not only objects are emitting thermal radiation by virtue of the heat contained within it by virtue of its temperature, but when we increase the temperature, the wavelength that we see that is being emitted is usually also changing with respect to that particular temperature. The reason we don't really see this in our day to day lives is because most of these objects emit radiation at a particular spectrum or at a particular frequency that is not really in the visible spectrum that our eyes are capable of detecting. But nonetheless, they are emitting this radiation. And this radiation is called thermal radiation. And it is this radiation that we are interested in studying and it is this radiation that will reveal to us some of the fundamental concepts in physics that we had previously in classical physics that we would need to change as we go forward in our understanding of modern physics. So how do we study this radiation? How do we detect this radiation? Well you see, if you have any kind of an object or a metal surface, let's suppose, when I maintain this metal surface at a particular temperature, then usually the light that falls onto the metal surface or is incident on the metal surface, most of it gets absorbed by the body because of the pigments that it usually has. But some of these wavelengths will not be absorbed by the body and they may get reflected backwards. So the wavelengths that are reflected and are not absorbed by the object usually give us their distinct colors. So for example, if I have this chalk that is blue in color and white light is falling on this chalk, some of the wavelengths are going to be absorbed by the pigments in the chalk and the blue wavelength is not going to be absorbed, it is going to be reflected and as it falls into my eyes, I see that it has blueish color. Similarly, if I have an orange chalk, then it is absorbing all the wavelengths other than the orange colored wavelengths which is getting reflected back and falling into my eyes. And this is how various objects get their characteristic color. But apart from this reflected radiation, you see, I had on one hand incident radiation, some of it is absorbed by the object surface and reflected radiation based on the characteristics of the surface. Apart from all of that, I may also have thermal radiation, may or may not be in the visible spectrum, but the object also emits, all objects emit what is called thermal radiation. And it is this radiation that we are interested in studying. Another question is, how do I separate the reflected radiation from the thermal radiation? We do not really have a filter that if I put a detector here, it will be able to detect okay, this is the reflected wavelength and this is the thermal radiation, so I am going to separate it. We do not have any kind of a filter like that, therefore, we need to create a special kind of an object that will emit all the reflected radiation falling on the surface, so that the only emitted radiation coming out of the surface is the thermal radiation. So for example, if I can create a new surface, let's suppose, and this surface is also at a particular temperature T and all the incident radiation falling on this surface gets absorbed. If all the incident radiation falling on this object gets absorbed, then the surface would appear black, okay. So if the object is at room temperature and the thermal radiation does not really fall in the visible spectrum and it absorbs all the incident radiation falling on it, then the object would look black. So then we can call this a black body. So a black body is essentially some kind of an object that absorbs all the radiation falling on it. So it is a perfect absorber. But because it is a perfect absorber, it is also a perfect emitter in the sense that now all the radiation that comes out of the surface will be purely thermal radiation and this thermal radiation will be called black body radiation. So therefore, if we can create an object that absorbs all the radiation falling on it so that it becomes a perfect absorber, that is a black body, and then it emits radiation by virtue of its temperature, by virtue of its thermal energy contained within it, and that thermal radiation is the black body radiation that we are interested in studying. An example of this kind of an object would be like something that has been painted with a very dark black colored pigment like Vantablack or something like that. But even in those cases, vast majority of the radiation, even though they will be absorbed, a very small tiny portion of the radiation will get reflected backwards. Scientists have tried to create a setup that will be ideal or close to ideal black body and the way they did that was by creating what is called a cavity. So let's suppose that we have some kind of a cavity with metallic walls inside. Imagine that this is some kind of a cavity with metallic walls inside, but it has some kind of a hole on its surface, a very small hole on its surface. If this is the kind of a construction we have and some kind of an external incident radiation falls on this hole, then after undergoing successive reflections on the inner surface, we can for sure say that this kind of an incident radiation will be near perfectly absorbed by this cavity. So if we have this kind of a construction, all the incident radiation that is falling on this particular cavity having this hole on the surface will absorb all the radiation falling on it. Now therefore, this kind of a setup would be a near ideal black body setup. So then we can use this setup to study the black body radiation. How? Because if we have this setup, this hole essentially would behave like a black body. So now if we heat this kind of an object to some kind of a temperature, then the walls would start emitting radiation. The inner walls will start emitting electromagnetic radiation or thermal radiation. If we increase the temperature of this kind of an object sufficiently, then this thermal radiation would also approach the visible spectrum of the electromagnetic radiation. And now if the cavity gets filled with thermal radiation that is being emitted by these kind of inner walls, then some portion of those radiation will also come out. And this radiation that is coming out, this tiny portion of radiation that is coming out from the cavity, this can be studied to give us an idea about what is the nature of the black body radiation spectrum. So this is the clever technique that was used by scientists to create a setup that would be an approximately ideal black body that emits radiation by virtue of its temperature. And then we can study the black body radiation spectrum to get us an understanding of what the nature of this radiation is for all kinds of objects. So if we have that kind of a black body in thermal equilibrium with its surroundings, which means that it radiates as much energy as it absorbs so that the temperature of that black body is a constant and we study the spectrum of the radiation coming out of that black body, then we get something very, very interesting, something that looks like this. So here I have a 2D graph where the x-axis represents the frequency of radiation and the y-axis represents what is known as the spectral energy density, which means the amount of energy per unit time per unit surface area that is being emitted by the black body cavity for a given range of frequency. Now let us try to study the different kinds of experimental observations that we are interested in. The radiation has a very well defined energy distribution. To each frequency there corresponds some kind of an energy density that is completely independent of the chemical composition of the body or the shape of the body but only depends on the temperature of this body. So this is our first observation that we get this kind of a very much well defined continuous energy distribution. The second observation is kind of very simple, it is just the nature of the graph itself. So for example, the energy density per unit time or the power that is radiated by the black body for some fixed interval of frequency is very small for low values of frequency but it increases rapidly as frequency increases, it reaches a maximum for some fixed value of frequency we are going to call that mu max and then decreases continuously for further increase in frequency and approaches 0 as frequency tends to infinity. This is a very very simple sort of a graph representing a very simple observation but we will see how difficult it is to explain it later on. There are some additional observations associated with this. So let us go to the third observation which is known as Stephen Boltzmann law. You see we are only studying the amount of power radiated by the black body for some fixed interval of frequency. What about the total amount of power radiated by the black body? So if I sort of trace the area under the curve, if I trace out the area under this curve, let's suppose I am interested in this entire area then this area would give us the total amount of power that is radiated by the black body for all frequency range at a given temperature. It was found experimentally in 1879 by Stephen and later on derived theoretically in 1884 by Boltzmann therefore known as the Stephen Boltzmann law that this total amount of power emitted by a black body at a given temperature is actually directly proportional to the fourth power of temperature. That means if I have multiple black bodies or if I change the temperature of a given black body and look at how this kind of a distribution changes, we will see that the area under the curve increases by a proportionality of fourth power of temperature. So let me draw couple of more graphs corresponding to different temperatures. So you see here the shape of the graph remains more or less similar but the size of the graph increases with increasing temperature. So for example let's suppose initially we had the black body at a temperature of T1 and then we increase the temperature to around T2 and then we increase the temperature further to T3 such that T1 is less than T2 which is less than T3 in that situation the black body spectrum of these three distinct bodies at different temperature would look something like this such that the area under the curve which is a total power emitted by the black body would be directly proportional to the fourth power of temperature. This is known as the Stephen Boltzmann law and the proportionality constant sigma is known as the Stephen Boltzmann constant. It has a value of 5.67 into 10 to the power minus 8 watt per meter Kelvin to the power minus 4. This is a very interesting experimental observation related to the black body radiation. Now if you notice the different temperatures and the peak of the black body radiation and how it is shifting to the right then you would see that with increase in temperature the peak associated with the black body radiation spectrum is also shifting towards increasing frequencies right that would give us what is known as the fourth experimental observation which is known as Wayne's displacement law. The Wayne's displacement law simply tells us that if we associate with the peak of the black body spectrum some kind of a frequency value because the peak of the black body spectrum is associated with some fixed frequency right I am going to call this new max. So new max is the frequency at which I get the peak of the black body spectrum for one body for another body the peak might lie somewhere else for the third body the peak might lie somewhere here. Now the Wayne's displacement law tells us is that the peak associated with the black body spectrum corresponds to a frequency which is directly proportional to the temperature. So with increase in temperature the frequency corresponding to the peak of the black body spectrum also increases linearly. This is the nature of the Wayne's displacement law sometimes in some books the law is specified in terms of wavelength we can also obtain that. So what is frequency? Frequency is nothing but the speed of light upon wavelength. So if I look at the distribution instead of with in terms of frequency but in terms of wavelength then I can associate some wavelength corresponding to the peak of the black body spectrum then we have c upon lambda max is equal to I can say let us suppose or proportional to temperature in that situation if we introduce some kind of a proportionality constant then lambda max times t is equal to the proportionality constant and this proportionality constant is known as the Wayne's proportionality constant and the value of this proportionality constant is 2.89 into 10 to the power minus 3 meter Kelvin. So the Wayne's displacement constant or the proportionality constant basically gives us an idea about how the frequency and the temperature are correlated. You see if you are reading different kinds of books you will see different kinds of black body radiation spectrum distribution. In some books they give us energy density versus frequency in some books they might give you a little bit of a different looking graph which is energy density versus wavelength. So if you are looking at that particular graph you would see that instead of the black body spectrum shifting towards the right in those graphs where the x axis is wavelength the black body spectrum will be shifting towards the left because frequency is directly proportional to temperature so with increase in temperature frequency increases but wavelength is inversely proportional to temperature. So essentially with increase in temperature the entire black body spectrum shifts towards higher frequencies or lower wavelengths alright. So these are some experimental observations of the black body spectrum. We have the Stephen Boltzmann law, we have the Wayne's displacement law and of course we have this kind of a distribution that graphically looks something like this. Now if we have some sort of a phenomenon in physics the purpose of physics is to come up with an explanation that is what a scientific theory is right. The whole purpose of physics is to come up with an explanation to explain why things are the way they are. So when we are studying the thermal radiation that is being emitted by objects or the black body radiation we want to explain why it is the way it is. Now classically speaking it is not really that difficult to explain why objects would radiate energy. This is because objects have heat contained within them right. No object is at zero temperature, every object has some amount of heat contained within them. What is the meaning of heat? Heat means the atoms, the molecules they have some kind of a vibration going on right. So atoms have charged particles like electrons so if a charged particle like an electron is vibrating then that vibrating charged particle would emit electromagnetic radiation. So if an object is at a certain amount of temperature all the particles that make up the object has some kind of a thermal agitation going on and they are emitting radiation and that radiation is nothing but the black body radiation we are studying. So conceptually it is not very difficult to explain but what about the specific nature of this graph? What about the specific nature of these expressions? Can we explain that classically speaking? That is where the interesting journey begins. You see classically based on our understanding of classical thermodynamics, classical electromagnetic theory, many scientists tried to explain the specific nature of a graph that the power emitted by a black body for a fixed width of a frequency increases, reaches a maximum, decreases goes to zero, now that was very very difficult to do. In fact that led to the ultraviolet catastrophe or the failure of classical physics in explaining black body radiation which is where Max Planck came and gave some different idea or different way of looking at this particular experiment which we are going to call the Planck's postulate which would give us the starting point of something very fundamental about how matter and radiation interact with each other. In classical physics radiation can be emitted in a very continuous fashion but in quantum physics it is not like that but we will reserve those discussions in the coming lectures. In the next video lecture I am going to talk about a very specific classical explanation which is the Rayleigh-Jean's law. I am going to show you how based on classical considerations we can actually derive an expression to calculate the black body radiation and we will see whether that explanation correctly predicts this kind of a spectrum or not and then we will take the discussion forward. So this is all for today black bodies and black body radiation spectrum and their experimental observations. I will see you in the next video. Thank you so much. Take care. Bye bye.