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so today we're gonna do an electromagnetic calculation problem we've got Sally Ann and Doc Brown here to help us out if we have any troubles here we go so we're gonna try to find the frequency of purple light with a wavelength of 410 nanometers so the first thing you're gonna need to do is write down your variables and your constants to figure out what you're trying to solve for so the first thing is that we know what lambda is lambda is wavelength and it's 410 nanometers we also want to solve for frequency which is nu and that is our question mark and that is gonna have the units of Hertz or per second is the same thing or you can write it as second -1 all those are identical to each other you always have the speed of light constant which is three point zero zero times ten to the eighth meters per second some people do is two point nine eight and that's fine also you can also realize that you have the constant Planck's constant which is six point six two six times ten to the negative 34 joules times second we also could try to solve for energy but that's not in this problem at this point if we did it would have the unit of joules over here what I'm going to do is write down your equations that you can use to solve for wavelength frequency and speed of light and energy for any type of electromagnetic radiation moving at the speed of light so we've got speed of light equals lambda times nu which is wavelength and frequency you've got another one where energy is equal to Planck's constant times frequency and the last one is putting those two equations together which is Planck's constant times the speed of light divided by wavelength or lambda so the first I'm going to do is look at what I'm given and then look at my equations and decide which one's gonna help me solve for in this case frequency and the answer is this one but it's not written in a form that I can use directly so I have to isolate for the variable that I'm trying to solve for and in this case it's the frequency so I'm gonna divide both sides by lambda and I get a new equation that says lambda on the bottom and speed of light on the top is equal to frequency so I'm ready to plug my numbers in however I have one issue if I put in the speed of light on the top which is 3 to the 8th meters per second on the bottom I need my unit down here to be in meters and currently right now I have nanometers so I have to convert from nanometers to meters so to do that I have to use a metric conversion that if I were to draw an entire meter stick and this was 1 meter what you have to realize is that a nanometer is 1 billion parts of a meter so what most people do is say that that's 1 times 10 to the ninth on nanometers and it equals 1 meter so you have this conversion that we're gonna need because we have to have meters in our formula so I'm going to take my 410 nanometers and I'm going to convert it to the correct metric unit which is meter and again 1 meter is a billion nanometers and so I have this then with the right type of scientific notation and I can plug that into a calculator show that I'm I did this correctly I have it sort of memorized so you're gonna take and have 410 and you're gonna divide it by 1 ee and then 9 and so again if it's not in the right scientific notation in this calculator you can hit second and then the 5 and then it puts it as 4.1 to the negative 7th and that's good because I actually don't have a significant figure here that 0 is a trailing zero and so really there's only two significant figures who ever measured this it's somewhere between 414 nanometers this is the range and it could be as small as 405 nanometer so we're saying there's only two significant figures so that's gonna be fine to keep it that way 4.1 times 10 to the minus seventh now when I plug this into my calculator I don't have to use that exponential notation key correctly you can type in the point zero zero e e8 if you want to press it'll see that it'll just get rid of the zeros divided by four point one seven and so my calculator says this is the answer so that's seven point three one seven zero I'll just keep that times ten to the 14th and then the answer is Hertz or again per second and the reason why is meters will cancel and we'll have just that Hertz or per second left as the unit but I don't have the proper number significant figures I can only keep to that one has three this one has two and you can keep the least when you're multiplying and dividing so this would be then the final answer with significant figures and the appropriate unit you