properties of light um so we typically talk about two natures of light or two two ways lights trap light travels uh wave nature of light is one so that's that means that light looks like a wave you can kind of see the wave up here in the top of the picture um where they come really close together those are that's called high frequency where they're really far apart that's called low frequency and the electromagnetic spring spectrum ranges from gamma rays which is the high frequency all the way down to radio waves which is like the lowest frequency and then right here in the middle we have light this is our visible light spectrum and um you can see that the wavelength so that's the distance between like the peaks so the wavelength for a high frequency is really short and then wavelength for a low frequency is really long and so based on the wavelength it gives us a specific color so that's these numbers that you see down here below the visible light part where it says 400 500 600 and 700 nanometers that's where or based on the wavelength of the light wave we see a specific color so we use this in um things like space science to figure out um you know how far away a star is what what elements are present in the star we can use light waves based on their wavelength we can view a color we can determine their wavelength we can then determine their frequency and then determine their energy which is kind of like the end goal so we can go all the way from color to energy which we'll do in calculations um later so this is the these are some of the constants that you need i guess are some of the variables that you need to know in order to be able to do the equations so c lowercase c is the speed of light that's a constant 3.00 times 10 to the 8 meters per second if you google that constant you're going to get like 10 2.9978 um so we're just going to use three in this class 3.00 times 10 to the 8 meters per second and wavelength is this lambda symbol here um which is like i said before was the distance between the same points on the wave and then frequency again that's how often it occurs and we use the f you sometimes see frequency as a v also um so if you see that don't turn to get confused i think your book uses the f but if you see a v that also means frequency wavelength is measured in typically nanometers we convert it to meters because speed of light is measured in meters so we do a conversion there so that our units match and then a frequency is measured in hertz which is the same thing as one over seconds so there's actually no numerator unit to just a denominator unit which also works out again because we have seconds up here in the speed of light so this is the equation speed of light equals wavelength times frequency and you can see here all those variables are defined this picture down here in the left corner is just sort of like a condensed version of what you saw on the last slide um so c again is speed of light and then there's the constant wavelength is that symbol that it's called lambda but it's that like symbol um meters nanometers basically distance is how we measure it and then um frequency remember i said before it was the f like up here in this first picture sometimes you see it as that v and that's measured in hertz which is again is the same thing as one over seconds and then here's an example calculation calculate the wavelength for light at a frequency of 5.4 times 10 to the 14th hertz so given the equation we were we know speed of light light we know c because that's a constant and then the next uh thing we're putting in is f which it told us the frequency and then we're solving for the lambda variable by dividing the um 3 times 10 to the 8th by the 5.4 times 10 to the 14th so you should put that in your calculator and make sure you could get the 5.56 times 10 to the negative 7 you should pause it now and do it that way you know how to use the exponent button in your calculator if you don't put it incorrectly you're going to get instead of negative seven you'll get something like a positive like in the 20s or um weird stuff like that so again i would pause it right here and put that in your calculator and make sure you can put the exponents into your calculator properly and get that answer the other nature of light is particles so sometimes we say that late that light travels as a wave and then sometimes we say that it travels as photons which are little packets of light so little particles and um there's a the theory of wave duality that basically says that light travels as a particle and a wave that it kind of does both um and the i guess the science community community has sort of um accepted that answer there's a lot more to it um and there's definitely people on both sides um but that's sort of the conclusions that's made because there's not really a way to prove one or the other actually there's ways to prove both um which is why we say light has a duality um nature so the way that we proved that it was a particle um is that is the photoelectric effect so basically when you shoot light at a um at like a piece of metal uh there is because those are are uh quantized energy so quantized means like definite and defined little packets of energy they can hit that metal and then knock electrons off or we call that ionize the electrons we call it quantized because it's the quantum energy it's the minimum energy needed to lock to knock those electrons off the plate and a wave couldn't do that but a packet of energy a quantized packet of energy could so that's our photoelectric effect the other equation we need uh to solve for energy so we saw before we saw the speed of light equation this is the energy equation so e equals h f or equals h v again that frequency variable sometimes differs sometimes it's f and sometimes it's v and h is the planck's constant so in that other equation we had c as a constant which was the speed of light in this equation we have h which is planck's constant 6.626 times 10 to the negative 34 joules times seconds so both of those units are in the numerator and then that equals the energy energy we measure in joules which we get the joules from the planck's constant and then if you remember frequency is measured in hertz which is one over seconds so when you multiply those together it divides out and you're left with joules as your as your unit for energy uh so einstein is kind of the person who said that light has a wave and particle duality that uh it can behave as both a photon and a wave the bohr model of an atom measures energy corresponding to each wavelength so that means that basically every time we see a jump from one energy level to a net to the next we get a specific wavelength and from that wavelength we see it as color and so from that color we can calculate the amount of energy using our two equations uh so that jump this is the bohr's model of an atom where where energy exists as energy levels and as the electrons jump from one energy level to another um depending the direction they go so if they fall in that means they're going to emit light if they go up like to energy level from like two to three then they're absorbing energy so to get to a higher energy level you have to absorb energy and then to fall down to lower energy levels you emit energy and so when that happens we can see a color from the color we can determine the wavelength and then we can use the c equation the speed of light equation to calculate the frequency and then we can take the frequency and plug it into our other equation and the energy equation to find uh the energy of that photon of that electron so here if you mash both of those those equations together we get e equals h which is planck's constant times c which is the speed of light divided by wavelength we can do this because frequency exists in both of the equations so notice there's no frequency in this final equation that's it's basically making the previous two equations equal to each other um by saying they're both equal to frequency and then merging those equations and solving for e so again in this final equation where we have e equals hc over lambda and here's all the variables c and planck's constant are both sp are both constants so you would either need to have the energy value or the wavelength value to solve and i will do some of those examples in your notebook