Trapping An Electron In a Box

electrons are always moving whizzing around in electrical wires and Sparks and jumping from one orbital to the next in atoms but what if you could take a single electron and confine it within a box what would it look like what color would it be and what would happen when you release it from that box wo look at that look at that sparkle I'm going to put this ball in a box and give it some energy so it bounces around it can be found anywhere within the box with equal probability when I check where is so if I take some Ste frames with this bouncing around in slow motion you'll see that there's not any place in the box where it has higher probability of being but something weird happens when the particle and the Box get smaller so if we were to shrink this ball and box down to only a few nanometers then every time we try to check where the ball was we would find that there are certain spots where we usually find it and there's certain spots where we never find it if I made a 3D graph about the probability of finding the particle in a certain spot in the Box it would look like this the darker areas are the areas where I'm likely to find it and the lighter areas are where I never find the particle when I check where it is in the Box suddenly this particle that used to just act like a ball in a box that could be anywhere when I checked where it was suddenly has these nodes where it's usually found and never found if I graph these probable locations of the ball in one dimension it would look like this it looks exactly like a wave so when small particles are trapped in a small box they start to look like waves instead of particles in 1929 the French physicist Lou de Broger proposed that since light showed particle and wav like Behavior perhaps any particle could show the same type of behavior this equation is known as the de broglia wavelength equation it relates the momentum of a particle to its Associated wavelength so the more momentum a particle has the smaller the wavelength so for our particle in a box when we give it more momentum it has a bunch more nodes within the box and with this equation we can see why when we had a macroscopic ball in a big box it was equally probable to be found anywhere within the Box because the distance between the nodes and the high probability areas were so squished together that it was just completely smooth throughout the whole box so you couldn't even see the Peaks and valleys in your probability locations before we continue when life gets harder than quantum physics it's nice to know that there's help out there so I want to take a minute to thank the sponsor for this video better help these last few years have been difficult for everyone and one of the most important things you can do in times like this is to focus on your mental health better help is the world's largest therapy service and it's a 100% online with better help you can tap into a network of over 30,000 licensed and experienced therapists who can 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you ever confine an electron to a tiny nanometer sized box and if so how could you even check that it's really acting like a wave Inside the Box well it just so happens that I have a bunch of tiny little partic in this case electrons trapped in some tiny boxes these are my particles in a box so believe it or not this is regular table salt that has no dyes or additives in any way to make it this orange color but the reason it's orange is because it's been blasted with gamma rays from a Cobalt 60 Source yep tastes like salt on the bottle here it says this was exposed to 300 kilor RADS of gamma radiation that is a law of radiation those are the levels you get inside nuclear reactors so it's far beyond the lethal dose for humans but luckily it itself isn't radioactive after it's been blasted with radiation and we're going to use this to test out this quantum theory regular sodium chloride looks like this it has sodium and chloride ions in a regular pattern but if you take this sodium and blast it with gamma rays then some of these gamma rays will knock electrons off the chlorine ions these chlorine atoms will find another chlorine atom and make a chlorine molecule that just hangs out in the crystal lattice but the electron that got knocked off get stuck where the chlorine atom used to be it's trapped by these sodium atoms surrounding it they're all attracting it equally so the electron is literally trapped in a box of sodium ions and it can't go anywhere these trapped electrons are called f-centers or farb centers where farb is German for color in this case it gives the salt an orange color but why would trapped electrons have an orange color like this well it's because the trapped electrons can only exist at certain frequencies within the cube for example if I shake a string that's trapped within a certain length it can only resonate at certain frequencies if I try to shake it at some other frequency then it doesn't absorb that energy but it will only absorb frequencies that match its resonant frequency well the electron does the same thing within that box it's trapped as a wave and at its base energy level so the only only energy it can absorb is if it has the right frequency to knock the electron up to its next energy state in this case blue light can knock it up to its next energy state so the electrons are absorbing bluish light from the white light in the room and when you remove blue light from White Light it makes orange light so we're seeing this orange light so it looks orange if the tiny box that the electron is trapped in had a different size it would be able to absorb different frequencies of light and resonate at different energy so if you take other salt and trap electrons in their lattice then they'll absorb different colors of light in fact if you make a graph of the colors of light that these different crystals absorb when you've irradiated them to make these f- centers then you'll find something beautiful it exactly matches what would be expected from the wave properties of the electron trapped within these different sized boxes in one of the very few equations you can solve analytically in quantum mechanics the wavelength of an electon versus the size of box is given by this equation the prediction for the first excitation of an electron in a box versus the size of a box is the dotted line here and the circles are the actual values taken from Maximum absorbed light in these different irradiated crystals it's amazing to see that these crazy predictions from quantum mechanics actually match what we see in the real world so these truly are electrons trapped in a box and in our case because of the size of the box they're orange now these electrons have been trapped in these boxes for a long time and they'll stay trapped for several years but if we can heat up the salt hot enough then the electrons will eventually get enough energy that they'll escape the box and find their way back to the chlorine molecules and when that happens they'll release their energy as visible light so let's watch what happens when I drop the salt on this hot plate whoa look at that look at that sparkle so I'm just dropping grains of it onto the hot plate and it's sparkling that is so cool okay let's do a bunch at once wao look how long that's glowing so when I turn the lights on you can see what this looks like see how the salt has just turned white now so as I dropped the orange salt on it it turns white so we've released all the electrons now so it turns back into its regular translucent color let's see if we can do it with just a bit more light here and see if we can see the color change with the light coming off of it oh you can look at that oh that's [Music] cool see how it gets brighter and then turns to White so you can see this magical Sparkle as I drop the salt on the hot plate as the electrons are released from their box where they've been imprisoned for years that is so cool can't you just hear the electrons thanking me from freeing them from their Eternal [Music] prison and thanks for watching another episode of the action lab I hope you learned something if you haven't subscribed to my channel yet remember to hit that subscribe button so you can see my latest videos when they come out and thanks for watching and we'll see you next time [Music]

Channel: The Action Lab

Views: 214,545

Keywords: quantum physics, quantum mechanics, electron in a box

Id: 4bQ0oe4FCzk

Length: 9min 46sec (586 seconds)

Published: Fri Jun 14 2024