 before starting spectroscopy properly we're going to cover some very basic physics and before starting that we're going to start with units and dimensions so a dimension is one of the seven basic physical quantities that we can measure these include length time mass and temperature is the most common while things like force and energy are actually derived from these so seeing what these derived quantities are made of and how they can then combine is known as dimensional analysis so we can multiply units together and the quantity changes for instance mass multiplied by speed leads to momentum we can also divide units so in this case a force spread over or divided by an area leads to pressure but through dimension analysis we can also show that energy divided by volume leads to the same thing incidentally this is why what the PV part of the ideal gas law is getting out as both sides here are equal to energy more generally than multiplying and dividing we can integrate and differentiate quantities this is fairly straightforward calculus but is a more powerful concept to talk about because values can change continuously an obvious example is speed speed is the first derivative of your position with respect to time or the gradient at any point and because there is a different speed at each point that could generate a new graph to where the y-axis is the gradient of the other if we keep on to differentiating with respect to time we get distance speed acceleration and then some additional quantities with various non-standard names which are occasionally useful but they're here mostly to show that we can keep on doing integration and differentiation to these qualities here now an important set of relationships that we'll come across in understanding spectroscopy and quantum theory will be the relationships around energy of the base unit here is mass length squared and per time squared or time speed squared which is equals mc squared if you want to remember it now because the base using here includes time and space as dimensions we could integrate or differentiate across time and space dimensions separately we'll ignore mass for now because there isn't too much interesting down that avenue now the relationship between energy and force is the integration and differentiation with respect to distance this may sound counterintuitive because if you push for it really long time it feels like you're expending a lot of energy but if something sits still on a surface it exerts its downward force due to gravity and the surface exerts an equal upward force but no energy has been used there because there's no movement there's no exchange of kinetic and potential energy which we'll get onto later this fact is clearly reflected in the units and the dimension analysis we can also fill out a few more of these qualities and quantities by differentiating and integrating in different dimensions and again we can keep going although not every combination is physically meaningful and some do have more than one use meaning or interpretation also note that because speed is made of both time and space dimensions integrating and differentiating with respect to speed would be a step diagonally along these quantities now practically this only works in a really straightforward way if your units match and so far all of these have been in standard s i units these are internationally agreed on and standardized meters seconds kilograms and so on other units exist and could be combined but then you need to be really careful that you're what they match up when you're calculating by hand so tapping in numbers purely because you've memorized equations and haven't thought about units will give you the wrong answer and it's not always as obvious as say miles divided by hours is the same as meters per second but what we'll see later is that the rotational constant b which is a measure of energy and that energy can be expressed as a wave number or reciprocal centimeters but if you get that speed of light as meters per second instead you end up with reciprocal meters two orders of magnitude out from what you expect even worse if you don't convert molecules mass to kilograms and that's a very common error and stick in atomic mass units instead you'll get complete garbage out the calculation just won't work or at least its physical significance will be a little weird now if you lay out your units correctly and rehearse your equations before you do any calculator tapping however you won't necessarily have this problem so pay attention to your units and use them properly