quantum mechanics in chemistry teach us something incredible if you take a metal and you shine light onto that metal with the right frequency you can actually get electrons in the surface atoms of the metal to be ejected from the surface now there are some conditions that need to be met for this experiment to work for example the energy of the light that you fire at the metal needs to be greater than the minimum amount of energy required to eject electrons from the metal this minimum amount of energy is called the work function of the metal and it varies depending on what metal you use so if the the energy of the light that you utilize is smaller than the work function of the metal no electrons will be ejected from the surface however if the energy of light is stronger than the work function for the metal then electrons will be ejected from the surface and not only that but any excess energy of light that you have will go into the kinetic energy of the electrons basically meaning that a much stronger light energy will cause the electrons to move even faster so that's the entire idea of this light experiment which is known as the photoelectric effect this is the equation for the photoelectric effect that basically says if we take light of the right energy and shine it onto a metallic surface we can actually free an electron from that surface so we'll start with the far left side of this equation this is kinetic energy kinetic energy is dependent on speed or velocity so basically if you have your electron up here and it moves really fast it has a very high velocity then you're going to have a high kinetic energy this piece of the equation is literally just the energy of the photon itself this last piece of the equation is the work function and the work function tells you the minimum amount of energy that you need in order to free an electron from the metallic surface so so to sum things up this equation is basically saying that if we take the energy of the light itself or the photon and then we subtract off the minimum energy that we need to free an electron from this surface the remaining energy of this difference will go into the kinetic energy of the electron now if the energy of the photon is not strong enough to overcome the work function then the electron is not going to be freed at all so that's the basic idea of the photoelectric effect so here we have this red light and this light is shining onto a metallic surface the photoelectric effect says that if we have light with the right energy we can actually get an electron to escape from the metallic surface we are given the energy of the light that we are shining onto this metal and we are given the work function of the metallic surface notice how the light energy is less than the work function that means the energy of the light we are shining is not sufficient to free an electron but that's not what this question is asking this question is asking if we up the intensity of light can we free an electron Quantum mechanic says that the light being fired at this surface is delivering all of its energy in Little Wave packets known as photons and if we were to increase the intensity of light all we would do is shine more photons onto this surface notice how even with more photons being fired at the surface each Photon still has an insufficient amount of energy so that means even with a greater intensity of light we still will not be able to free any electrons off this metallic surface so the answer to this question is no I want you to picture yourself in a physics lab and in this physics lab you do some kind of light experiment that tells you the kinetic energy of a moving electron now what you want to do is derive a formula that will tell you the velocity of the moving electron after it has been freed from the metallic surface all you need is the formula for kinetic energy most physics textbooks will tell you that the equation for linear kinetic energy is 1/2 mass time velocity squared since we're looking for the velocity of the electron let's see if we can solve for the Velocity in this equation so the first thing I'm going to do is multiply two on both sides to get the two and the 1/2 to cancel on the right I'll then divide both sides of the equation by the mass to get the masses to cancel on the right from here the last step is to square root both sides of the equation to get the square and the square root to cancel on the velocity this will give us a formula that looks like this now the mass of this formula is just going to be the mass of an electron so if you have the kinetic energy you can calculate the velocity of these Quantum particles this equation right here will give you the speed of a photo electron which is a Quantum particle formed from the photoelectric effect if the kinetic energy for this photo electron is 7.2 * 10 -20 je what is the speed of the photo electron so to solve this problem let's use this equation so we have that the speed of the photo electron is going to be the square < TK of 2 multiplied by the kinetic energy which is given to us as 7.2 * 10 -20 Jew now what I need to do from here is divide this entire thing by the mass of an electron now you can look up the mass of an electron online for me though I actually have this number memorized so I'm just going to put it in here it's 9.11 * 10 to the - 31st kilg so now that you have all the numbers plugged into this equation what you want to do is take this entire quantity and throw it into a calculator if you plug everything in correctly you should get a speed of about 397,000 m/ second so this Quantum particle is moving very fast