in this video we're going to talk about Planck's Constant and black body radiation now you might be wondering what is black body radiation well any object with a temperature above zero Kelvin is going to emit some form of electromagnetic radiation as the temperature increases the energy of that radiation will increase as well so imagine if you have a metal and you heat the metal as the temperature of the metal goes up eventually you'll notice that the metal will have a reddish glow to it and as you continue to heat up the metal as the temperature increases it's going to appear yellow and then maybe even wide-ish whenever you increase the temperature of an object the molecules in that object will vibrate with more energy and the oscillations of the electric charges in those molecules can emit electromagnetic radiation so let's say you have an atom let's say this is a hydrogen atom this is the first energy level the second energy level let's say this is the third energy level when an electron in this atom when it absorbs energy it can jump to a higher energy level now when that electron returns to its original state or if it drops to a lower energy level it's going to emit electromagnetic energy and so as these electrons as they oscillate back and forth they can absorb any mid electromagnetic energy now the energy that is carried by a photon is a multiple of this value HF so we're going to put an N where n is an integer H is the Planck's constant f is frequency the frequency is measured in hertz or S to minus 1 and H is Planck's constant which is 6.626 times 10 to the negative 34. joules times seconds now this equation tells us something very important and that is that the energy of a photon is quantized it can't it's not continuous it can only have discrete values so it can't be just any value but it's a multiple of HF it can be one HF it could be two HF 3hf but nothing in between that so the energy of a photon can only exist in discrete values it can't take any value so thus we could say that energy is quantized now let's work on some problems calculate the energy of a photon with a frequency of 4 times 10 to the 14 Hertz so we could use this formula to get the answer so we're only dealing with a single Photon so n is going to be one Planck's constant that's 6.626 times 10 to the negative 34. and this is joules times seconds the frequency is 4 times 10 to the 14 Hertz and hurts is seconds to minus one or one over seconds and so we can see the unit seconds will cancel and this is going to leave behind the unit joules and so the energy is going to be 2.6 five times ten to the negative 19 joules so that's the energy of this particular photon now what is the energy of a red photon with a wavelength of 700 nanometers whenever light has a wavelength of about 700 nanometers it's going to appear red now in order to do this one we need an additional formula the wavelength of light times frequency is equal to the speed of light so what we need to do first is we need to calculate the frequency the frequency is the speed of light divided by the wavelength and the speed of light which is the same for all types of electromagnetic radiation in a vacuum is 3 times 10 to the eight meters per second the wavelength is 700 nanometers and a nanometer is 10 to the minus 9 meters so the unit meters will cancel given us the unit 1 over seconds which is frequency in hertz so 3 times 10 to the 8 divided by 700 times 10 to the negative 9. that's going to give us a frequency of 4 .286 times 10 to the 14 Hertz now that we know the frequency we can calculate the energy of the red photon so since we're only dealing with a single Photon and is one and then we have Planck's constant and then we have the frequency 4.286 times 10 to the 14 but I'm going to write 1 over seconds for the unit so I got 2.84 times 10 to the negative 19. joules so that is the energy of a single red photon that's how you can calculate it now let's work on one more problem what is the energy of five blue photons with a wavelength of 450 nanometers so this problem is very similar to number two the only difference is we have an N value of five so let's begin by calculating a frequency the frequency is going to be the speed of light divided by the wavelength that's 3 times 10 to the eight in meters per second divided by 450 nanometers or 450 times 10 to the negative 9. meters so we're going to cancel the unit meters just like we did before so this works out to be 6.67 times 10 to the 14 Hertz so now that we know the frequency let's calculate the energy of the photon so e is equal to n h n is 5 since we're dealing with 5 photons five blue photons H is always going to be the same planes constant that's not going to change so that's just a number you're going to have to commit to memory and we have a frequency of this value so 6.67 times 10 to the 14 times Planck's constant times 5 will give us this answer so the energy of the five blue photons combined is going to be two point two one times 10 to the negative 18. joules so now you know how to calculate the energy of a single Photon or a group of photons if you know the frequency of the photons or their wavelength