 In the first video we looked at absorption of light by electrons, now that wasn't meant to be an exhaustive treatment of electronic spectroscopy by any stretch of imagination, but it was meant to get across the idea of quantisation, the idea that light comes in, discreet individual chunks. Now that means light can't be broken down, photon must be absorbed or not absorbed, you can't absorb part of a photon and discard the rest, you can't jump up partway between two energy levels and then wait for some more energy to come along, it's really all or nothing. But how else can we know that's the case, and to understand that we have to flip this on its head a bit and ask about light being emitted by objects. We tend to associate heat with infrared light, and that's because at most temperatures that we experience, hot things emit infrared light, it can be seen in thermal imaging cameras for instance, and we can't see it with our own eyes because it's too little energy to actually initiate that chemical reaction we need to see light. But it's not the end of the story, the reality is that all objects really do emit light at all frequencies, but just in different amounts, and just depending on how hot it is, that begins to change the frequencies. So if we begin to heat something up to sometimes hundreds, maybe thousands of degrees, suddenly that's no longer infrared light, it becomes visible and we can begin to see it. The main model we have to describe the submission of light is blackbody radiation. Here the graph's x-axis frequency and the height is the amount of light emitted. There's a characteristic curve to it. There's no light of zero frequency because that's not really possible, and very little light of a high frequency and high energy, with a peak in between that varies with temperature. Blackbody radiation is also a key proof of quantum mechanics because the best prediction made by classical mechanics, with a continuous and non-quantised energy, is painfully wrong. The best prediction shows an infinite amount of high frequency light being emitted at every temperature, which is clearly on-sense and doesn't happen. We should probably unpack the term blackbody a little bit more. The Sun, for instance, is a near-perfect blackbody emitter, but you wouldn't necessarily call it black. Blackbody in this sense refers to the fact that it would absorb all light perfectly equally across the whole spectrum, and it would only ever emit light based on its temperature. So it's in effect really a colourless emitter or a colourless body, but blackbody has stuck. Now the best way to model this system is to think of a small box, but with a hole cut inside. That means that any light going in would be bounced around and absorbed, and the only light that would ever come out is what's actually produced by the radiation inside that object. The model considers how many different wavelengths or frequencies could bounce around inside the box, and how many different ways they can arrange. There are more ways to fit in high frequencies, so there should be more potential light at higher frequencies. There's a few different ways of formulating exactly how much, but it's proportional to the frequency squared. This part of the model is the same in the classical and the quantum picture. The next part of the blackbody model asks how probable it is we will find a photon of a particular frequency, and it's that probability that changes between classical mechanics and quantum mechanics. So if we start with the first part of the function that tells us how many frequencies there are, we can clearly see it increases with frequency. And in classical mechanics, the probability, the next bit, is simply multiplying by Boltzmann's constant times temperature. You'll recognise KT from various thermodynamics equations, but that's it. That's the final formula. You find that intensity of light just increases with frequency. So as the frequency increases, as the energy increases, it just goes up and up and up. In fact, you should find an infinite amount of light being emitted at an infinite amount of energy, which is clearly nonsense, it's mad, and it doesn't happen. So this model must be wrong. So around the turn of the 20th century, Max Planck made a slight change to this part of the equation. If you assume Planck's relation between energy and frequency and apply some statistical physics from there, you can create a different distribution of energy within the blackbody emitter. This is a more complicated formula, and you don't need to memorise it or know its derivation. But it is important to show that that probability has the frequency dependence, and the resulting curve matches experiment perfectly. In this model, and in reality, the peak intensity of the blackbody emitter varies with temperature. The hotter the object, the more light emitted, and the higher its average frequency. Objects at room temperature emit in the mid and far infrared regions, but emit no visible light. This is why we need thermal imaging cameras to see most warm or hot bodies. But as temperature increases into the hundreds or thousands of Kelvin, we start to see it, first as a faint red glow around 2000 Kelvin, before moving further and further into higher energy regions. So that's just a little bit of background physics and information, but it is really important to the development of quantum mechanics. Planck's insights truly changed the way we thought about lighting matter forever.