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# Lecture 03. Introduction to Quantum Mechanics

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on a system they were going to be talking about Chapter 1 and this take us about 3 weeks after the 1st midterm so Chapter 1 covers everything involved in quantum theory version
example exercise so we talked about a green traffic light in previous problems said that the whaling was 522 anatomy deserve you know most of them were factor in 20 generators we calculated the frequency doing that now I say find the energy so once again here's
what we know we know seeming a lander I am and I went having converted the straight here so we have it now we also know that now you may still can use eagles each new to this and that no new we figured that out in the last problem sure you can in general you don't want use things that you've already calculated once using that and other problems you can avoid it if you can avoid you obviously have to that's fine but you don't want to have to go on if you can avoid it you want to position that new round Nigeria persona somewhere in the back of Oregon industry Rolando which was given in the problem so we have a equation it's Valerie thing and planks constant just filled in as this so jewels seconds we feel in because that's just a constant so we know that and then we can fill in land of making sure that we matched the units here and here now it's always good when you're filling in these equations to make sure Olivier work so you can watch meters cancel here you can watch seconds cancel here and that leaves us with the unit of jewels which is an energy unit so everything should work out fine and we get free . 8 1 times 10 needed maintenance jewels so that is that we have a reunion and we have a energy so that the energy of a green traffic lights but let's dualistic continue on with the problem that we were doing before now we're going to find the energy of our Make-A-Wish so this time were given Hertz which means it will start from equals H. New and we fell in age just as from the slides watching the units now we have to fill in the 120 of course we can just fill in 120 when he did convert this to hurts and I'm going to write right within the problems so I'll just multiply times 10 the nite here in color hurts so sure improper scientific notation once again same sometime in doesn't hurt the problem at all OK so then we come down here we take that into account he later we figure out how many saying things we need now as I seriously Council Hertz in seconds unit that's that's 1 of those you wanna keeping your head were hurts means really means in the 2nd it really means 1 over seconds so that's going to cancel now was thrown to the proper thing thinks so age doesn't matter this has to and so we need to round 2 8 . 0 times 10 to the needed 20 3rd jewels Sinaloa done this Of
that we've seen the illegal Agent we've seen that we have H and we have 120 gigahertz and we noticed that the bill the 1 over 2nd so that will cancel here and we can go ahead and we can say Well since equal that each new we can fill this In best now if we get this in our calculator need to make sure that we still go ahead and vigorous includes so we had to sing things here so we bring these usage figures down with it . 0 times 10 to the negative 20 3rd so just like what we did and slides only with the other greater so now on the slides with I sent you home a couple of similar exercises to in so go ahead and you can write down those answers you knew them so moving on with this idea of a black body radiation this is a good idea that all of our solid from slaughter of light and you may say Well OK that's fine but when I look at field was counted 190 million your light when I look at whatever it's not admitting any light and yet when you look at something like year or electric stove or something of that sort now you start seeing red light so what's the difference between something that's just sitting in something that's glowing red hot well can you give away their right and glowing red-hot so that's because there's more the temperature has increased and that's why you start to be able to see the glowing now you look at something the water like the signed a word you know some some other stars Allen about wearing a white light only look at from light bulbs to get white light so what you're actually what the problem is the reason we can't see all black body radiation because it's not in the way link that we can see Our eyes only see certain wavelengths and we don't see wavelengths until it hits certain temperature so that means that the temperature effects of what we've link emitting so here we have a graph that this is the intensity of this is wavelength and so as your wavelength increases the year area in the wavelength over here in what is the line show you is the profile of what we links are being emitted so if if you something 3 thousand :colon arguably pretty warm this will go ahead and has distribution so you only see a little bit of life here most of it sitting in the IRA regions now if you go to 4 thousand now you see a lot more like that in the visible region Yolanda Max is still here and here and here so each 1 of these temperatures shows you where the distribution of the photons are so what I know what governing by intensity is how many photons are what percentage of photons have that wavelength you kind of thing Gilligan during distribution that you're used to seeing how many people had a how many people have to be harmed if you will have a seat will this is how many photons have this wavelength from the photons have this with a family photo 1st says the same idea and you can see as it gets hotter and hotter and hotter and hotter it moves over more and more into the visible wavelengths so we can see it so that's why we were able to see things global hot the happenings "quotation mark we are unable to see things at room temperature now if you look at an incandescent light bulbs think all they have a ball a 27 102 33 100 on temperature range Seoul did graph look at it for a 2nd why do you think incandescent bulbs are so efficient and don't use them anymore because of if you think about where or what it profiled in its profile would be here right now so I look at an incandescent bulb most of it we can't see it getting off with plenty of light as most of that life is in this region with that region the region right along with the most spectrum would be the IRA debt which we colloquially called heat so most of the electricity that we put into an incandescent bulb is coming off in a region of the spectrum that we can't see it coming off his seat in so that's kind useless to us we don't need to heat up our houses with the insulate the want like them with incandescent light bulbs so something like a fluorescent involved there's a better job awaiting with less electricity because it falls into these higher ranges think another example exercise so I what is
it so in this case now we're looking at approximates Centauri on Eurostar is a red dwarf star now it's about 4 . 2 light years away which we don't really need to much for this piece of information but that we don't have an average surface temperature of 3 thousand 42 Calvin Soriano work this problem a little bit backwards from what actual astronomer would do which natural stronger would take and say Well we have 80 of them have this this and linked spectrum would have computers with dried out that concealed the different wavelengths and they would find the temperature of the staff and argues worries work at this way which is a little bit occupants so we have this equation from the previous slide so far and wide in MM is so just kind of the standard way of doing it so when we the that I invest we're going to end up with the mm value so we will solve this equation for landmarks so in this case I converted the dead that constant that's in their 2 meters 1st you could do it to the ways you could just fill in and get your wavelength in mm over back or you can convert DM either way is fine In the end for the sake of significant a significant figures is also 0 Calvin we fill in as it is and we yet the study now if we look at at what region of the electromagnetic spectrum that as it might be a little bit easier to go ahead and convert this to nanometers just for the sake of of looking at this which comes out to be 952 anatomy so depending on how much you remember from the previous slide that we've done this lines of right in the new year region is what we call it so it's near where we can see that it's still and that the IRA region which is right next to the right part of the visible spectrum is why when we look at a Red Dwarf that's where it gets its name from because the only like that we can see coming off it is wrapped in so we see it as red now sure this was hardly the profile as in the arid and we can see that and so too are I mean we just see it as a writer and so that's where it gets its name from you
the summer history still throughout all of this the modern issue history-making can really call for interview the modern but we'll even back then there is some argument about what life late really was and whether light is a particle or other light years away if so what is that fall into well so in this kind went back and forth back and forth as each group figured out what they fear a little more experience experimental evidence was that with a little better than the last person inserted for the last person and that when she started getting into you know this regional there started being really good experimental evidence either way so it wasn't until I signed came along and said Hey you guys stop arguing it's both so reading of Oregon walk through and say Well why as light like a particle of wisely light like a particle and why and light like a weight in the sea of this we've particle duality that we call as we call it the 1st of all why is the particle What can want treatment shows that it's like a particle so we have something called the photoelectric effect in the idea the photoelectric effect is that you shine a light on to a and when you do that you reject the lecture so the idea here is that you're you're it and there's a lot of different rules for exactly what it can be but you're injecting electrons from a metal surface With the light so and I should also mention this is actually lines and won the Nobel Prize for so doing in incoming calls free may be best known for his theory of relativity but this this is what got him a Nobel prizes so it's it's is obviously very very important so now comes apart and that we should a show its particle the to each photon has to be higher than what we're going to call the threshold energy which means that it has set each photon has to have a higher energy or think about warehouses related frequency a high frequency in order to go ahead and ejected electron if you don't have that per photon it doesn't matter how many photons you shine on it you can just you know blasted with as much intensely is possible but it doesn't have that minimum frequency it's not going to electric now we call that minimum energy the work functions simpler example violet light can eject electron from the Casteel but if you shine red light on its remember a little comment was foxtrot and you know they're blue in a violent are higher energy ride so my liking jet electron from potassium but it doesn't matter how much red light you're never going to get so if you shine a little bit of Bilal a on potassium out to be a little bit of electrons if you shine a bright violet light on its meaning more intense period tons of octopus now if you shine the brightest red light you could possibly find on that potassium you're still not going to get any electric so what is the frequent those social frequently how can we find it what we can use equalization you to determine it and then you just have to take off the work functions so will do some examples of that in a minute or so this and this is 1 of the major things that show the wave particle duality of light now if you want to kind of allowed a computer-simulated land on how this works I would suggest going to this webpage they have a good rate simulation on it all it works best if you play with it on your own rather than me showing you how to play around with it so I'm going to leave that for you guys but you go there and play around with the latter will really really help you understand your homework and understand all the conceptual question last Sunday exam what's happening so considering that a homework assignment just like everything else so now looking at this and a little bit more detail so this is the potassium example I had From the foreign-registered have talked it through no if you go through in you put in just enough energy to knock the electron so in other words it's going to be exactly the energy of the work function so just reminder work function is the lowest energy you need to reject electron if you put on exactly that much it's not going to have any this ejected electron won't have any energy company just enough energy into knocked loose but not enough to give it any energy at all now if the energy of the photons higher than the threshold so it's higher than just that work function now all of there's extra energy there where the extra energy going go well it has to go somewhere and where goes into the kinetic energy of the ejected electron so if you increase the energy of a photons it increases the kinetic energy of the ejected electron so here if we look at this example a red light are lowest energy of the 3 lights come then and that's not at the threshold frequency and so that's not going to reject any electrons now this year putting green light that's high enough energy to go ahead and Egypt electrons and it's going do so at this speed now as increasing energy began into violet light so we get but much higher energy now things to sort of note here and when you play around that simulation you'll note this to some extent you if you put in 1 photon the most under the most electrons you can get is 1 electron so if you want more the moral ejected electrons you have to put in more photons just increasing the energy isn't going to make more photons come off it's just going to make them come off with a higher speed if you're below the threshold frequency no on the coming off at any speed you're just stuck the need to make sure you know the difference between intensity and energy so the difference in intensity and energy is if I take these lights and I do that
prior to that I just decrease the intensity of like I haven't changed the energy
set that equaled a 0 Rich now means that are little new were frequency is going to be equal the W or Planck's constant so we can just fill those numbers in so we have this and thinks constant here we their number and of course you can write it hurts reading writing in 1 over 2nd Street can 2nd in 1st whichever way you want to do it and use your jewels Council so that makes sense so that the threshold frequency that answers the 1st part or in other words to reject the electrons are minimum frequency a minimum energy and longest wavelength now we can go through it in the 2nd part what is now were given a frequency of light of that what is ah kinetic energy and of also are of loss there a frequency but so we go back to this equation again you draw little lying here so we know that we're starting a separate section and once again were just filling everything and so we fill Planck's constant then still end their frequency we subtract other work functions now that gives us a kinetic energy so we fell that into a calculator and we solve we get our Connecticut energy but also the nasty for 1 more thing I said What's the velocity soon now we can't quite here so this is kinetic Andrzej now we need to find the velocity so in order to find a lasting we have to remember what equation for kinetic energy is that we use before so right now we have been using this equation because that's what works for this particular system but there is also a very general form of kinetic energy and that's is one-half and he squared In so we can go through region a while OK now what is our velocity keeping in mind that it's an electrical so if we know our kinetic energy and we know that that's equal the one-half no 1 is any here will and there is a mass electron so that's something that we would look up on an exam I would give it to you and then we would have the square no notices is 1 of those places that we get into the idea we have both frequency and new and they're in 1 equation so make sure Santomassimo of this was new Florida threshold frequency this was new for this frequency in this is the 1st so now we go through and we solve them and we had our losses so that's 1 of the other way that you will be asked to do this on our relatively regular basis and of course the backwards directions of all of those is fair game as well as you know we give you the frequency and asking for the kinetic energy and the nasties that kinetic energy 2 months after the frequency of light that was actually get now this comes up in your book and so I wanted told had you as look at it a little bit your homework in it and I think it's good to always look at these graphically and see what happened to so in this graph we have 3 different models and you can notice something about this is a linear right as you increase the frequency you increase the kinetic energy if you do that linear now In the last year up until a certain point of urged Tuesday after a certain point before that it's just 0 so when you look at the Senior Bowl opinion ask questions on it you can see that this is just 0 until you hit this threshold frequency and at that point it's a linear relationship now what is that linear relationship while we can look at the equation to show us that if we have this equation which EnCana look at it is why Golden explores the right so if we look at this as white gold and Max plus where this is the axis 1 is a N well R and would be H slow periods H In so that's 1 of the places where you can sort of deride each out of and you can say OK what age is a constant there is going to be given to me but it does come from somewhere in this is 1 of the places where if you're nearly over the CIA kind show up and you can actually grafitti could find me and I'll say you're asked to do that at some point we have to fill in after you're given the incident wavelengths near Yuma area frequency you're given the arms kinetic energies and you have to grant and then you sold for the slope and that's what gives you each so that's what that's going to get this the rule of the particle aspect of this so keep this in mind as you do your homework that that this is a good guy after having your mind it's going to increase as you increase the analysis and that sort wraps up the photoelectric effect and the sort of particle aspects of us next time will go
into more of the wave interference in 1 the way that we can look at this and say all will light might leave my acts like a particle here but it's definitely a wave to end is so there's there's experiments just like the photoelectric effect that will go ahead and show us that
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