in this video we're going to focus on a few problems that asked to find the wavelength and the frequency of a photon so let's start with this one calculate the wavelength of a photon that has a frequency of 2.5 times 10 to the 12 hertz so what equation do we need perhaps you've seen this one c is equal to lambda times nu now c is the speed of light lambda represents the wavelength in meters and nu is the frequency in hertz so the wavelength is going to be the speed of light divided by the frequency the speed of light you need to know it's 3 times 10 to the 8 meters per second the frequency is 2.5 times 10 to the 12 hertz which is the same as seconds to the minus one or one over a second so basically we just need to divide these two numbers and so you should get 1.2 times 10 to the negative 4 meters and so that's all you need to do in order to get the answer now sometimes you may need to convert it to a different unit because this number is pretty small so let's convert it to micrometers how can we convert meters to micrometers what is the value of one micrometer micro represents 10 to the minus six so one micrometer is 10 to the negative six meters you can take this number and move it to the top by changing the exponent from negative six to positive six so this is equivalent to one point two times ten to the minus four multiplied by ten to the positive six and when you multiply by a common base you need to add the exponents so negative 4 plus 6 is 2. so the answer is 1.2 times 10 to the 2 micrometers now 10 squared is 100 and 100 times 1.2 is 120. so the wavelength you could say is 120 micrometers so if you have a multiple choice test your answer may be in meters or it could be in a different unit micrometer so you might have some conversions with these problems as well just be ready for that now let's move on to number two what is the frequency of a photon that has a wavelength of 1.5 times 10 to the negative 8 meters so go ahead and try that problem so starting with this equation we need to solve for the frequency so nu is equal to the speed of light divided by the wavelength the speed of light is going to be the same it's 3 times 10 to the 8 meters per second and when using this formula the wavelength has to be in meters which it's already in meters so now we just got to divide these two things so 3 divided by 1.5 is 2. now what's 10 to the 8 divided by 10 to negative when you divide by a common base you need to subtract the exponents so you take the top exponent which is positive eight and subtract it by the bottom one which is negative eight eight minus negative eight is the same as a plus eight so that's 16. so the answer is 2 times 10 to the 16 hertz so that's the frequency of this photon and you could type it in to make sure that we do indeed have the right answer which it is that answer now what about number three what is the frequency of a photon that has a wavelength of 350 nanometers so let's use the same formula the frequency is the speed of light divided by the wavelength but this time the wavelength is not in meters it's in nanometers which means we need to convert it to meters so how do we go about doing that it turns out that all you need to do is replace nanometers with 10 to the minus 9 meters and it's going to work out if you want to write it out here's what you can do start with what you're given and know that one nanometer is equivalent to 10 to the minus 9 meters so these units will cancel and all you have is 350 times 10 to the minus 9. so you just got to replace this with 10 to the minus 9 meters and the speed of light is not going to change in a vacuum it's constant however when light passes through a different material let's say water or through diamond the speed of light does change it decreases but in pure empty space in the vacuum it's three times ten to the eight meters per second so the frequency is going to be 8.57 times 10 to the 14 hertz or seconds to the minus 1. so this is the answer for this problem number four determine the wavelength of a photon that has a frequency of 95 megahertz so to calculate the wavelength we know it's the speed of light divided by the frequency now let's convert megahertz into hertz so what is the value of mega a megahertz is basically a million hertz mega represents 10 to the sixth so what we have now is 95 times 10 to the sixth hertz so that's the frequency so now that we changed a unit we can plug it in to the equation so let's go ahead and divide these two numbers so you should get 3.16 meters so that's the wavelength of a photon with that frequency now here's a question for you what happens to the wavelength of a photon as the frequency increases so we know that wavelength is the speed of light divided by the frequency notice that the frequency is in the bottom of the equation which means it's inversely related to the wavelength so as the frequency increases the wavelength decreases and vice versa so as the wavelength increases the frequency decreases so these two are always going to be inversely related to each other and so that's all you need to know about photons and relation between wavelength and frequency when one goes up the other goes down now what if you're given the energy of a photon how can you calculate the frequency the equation that relates the energy of a photon to the frequency is this equation the energy of the photon is basically the product of planck's constant represented by the symbol h multiplied by the frequency now the value of planck's constant is it's 6.626 times 10 to the negative 34 joules times seconds so if you wish to calculate the frequency it's simply the energy of the photon divided by planck's constant so it's going to be 3.5 times 10 to the minus 18 joules divided by 6.626 times 10 to the negative 34 joules times seconds so as you can see the unit joules will cancel leaving the unit one over seconds which is equivalent to the hurt or hertz so let's divide these two numbers so the frequency is going to be 5.28 times 10 to the 15 hertz and so that's how you can calculate the frequency of a photon given its energy now this is going to be the last problem determine the wavelength of a photon with an energy of 4.3 times 10 to the negative 19 joules what we're going to do in this problem is just like before we're going to calculate the frequency first and once we have the frequency then we're going to calculate the wavelength so the frequency is going to be the energy divided by planck's constant so it's 4.3 times 10 to the negative 19 joules divided by 6.626 times 10 to the minus 34. so for the frequency you should get 6.49 times 10 to the 14 hertz so now that we have the frequency let's go ahead and calculate the wavelength now we know that the wavelength is going to be the speed of light divided by the frequency so that's 3 times 10 to the 8 meters per second divided by 6.49 times 10 to the 14 hertz so you should get 4.62 times 10 to the negative 7 meters now let's go ahead and convert this to nanometers so keep in mind one nanometer is equivalent to ten to the minus nine meters so i'm going to take this and move it to the top so then it becomes four point six two times ten to the minus seven times ten to the positive nine and negative seven plus nine is two so it's four point six two times ten to the two nanometers and we know 10 squared is 100 so 100 times 4.62 is 462 nanometers so that's the wavelength in nanometers this is the answer you