 The previous video covered the founding theory of pure rotational spectroscopy. This uses microwave radiation to excite quantized molecular rotations. We also saw some of the equations for how to calculate the energy of these rotational levels and how they can be expressed in terms of the rotational constant B. If we work out the energy levels of rotations in terms of B, we see a clear structure. Energy levels are further apart as the rotational constant number J increases. To connect this with what we see in the pure rotational spectrum, we need to consider that B is a very small amount of energy. So it's quite easy for molecules to jump from low rotational states to higher, faster rotational states using only a small amount of heat so that dozens of rotational states can be occupied just at room temperature. Because so many energy levels are occupied, near enough every excitation from one level to the above will be visible in the microwave spectrum. Each of these transitions increased by the equivalent of 2B as the rotational quantum number increases. The result is a regular progression in the microwave spectrum where each peak is 2B apart. Remember that because B is an energy, it can be expressed in a number of different waves, joules, frequency, wavelength and wave number. So let's unpack wave number just a little bit. Now wave number is measured in reciprocal centimeters or per centimeter. And that sounds a little bit strange until you understand the question that that unit is asking. Instead of asking how long is the wavelength, it's asking how many can fit into a fixed length. So wave number per centimeter is asking how many wavelengths fit in per centimeter. For a microwave, that's a couple of dozen at most. To clarify the notation here, we normally use omega for rotational frequencies and omega with a tilde on top to represent wave number. This tilde also crops up on the rotational constant to clarify that it's measured in wave numbers and also on the speed of light to clarify that we want the speed in centimeters per second. Converting to wave numbers is as simple as 1 divided by wavelength. They're the inverse of each other. But remember, this inversion won't magically convert to the right unit. You need to make sure you're in centimeters and then invert. If you end up in per meter, you'll be out by a factor of 100. So you'll need to divide by 100 or multiply by 100. But I'm not going to tell you which is which. I want you to remember that definition of how many waves fit into a fixed length. If so many fit into a meter, how many fit into a centimeter? This brings us back to something said in the first video. All of these measures are interchangeable because they're all measures of the same thing, energy. We're just changing how we express it. Converting between wavelength and wave number is a straightforward inverse relationship, providing you match the length unit. But there are many other relationships, which is why I really don't recommend memorizing equations here. So instead, think in the units. If you need to convert from or to energy in joules, you need Planck's constant as that's joule seconds. If you need to convert between the time and length domains, you need the speed of light, that's meters or centimeters per second. Doing it in stages can help too. Going from energy to wavelength via Planck's constant and the speed of light in two steps gives you two simple calculations to check. We'll keep on top of units throughout this course, but that concludes our deviation to it from now. Just be comfortable with the concept of wavelength, but how many waves fit into that centimeter? Because they're used very extensively in the next part of the electromagnetic spectrum, the infrared.