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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
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everything but at least we're going to cover in this class for the most part so in a lot of things to cover where you start with just general on properties of we've been electromagnets as long as you that as a backdrop to be able to talk about all the rest of things and how we actually sort of build up in Panama how we think about Adams now From that point we can kind of go on which insert talking about the model which is married that introduced a little that we have the protons and neutrons the nucleus and the electrons going around the outside but will see is that this only really works through a hydrogen atom in other at ions they have 1 electron so will start there will talk about many things there such as transitions in that sort at which point we can move on and talk about more complex systems but was then the hydrogen at that we can also meant a lot to talk about the Brawley Way links in quantum numbers and then from there will start talking about almost high electron systems Adams more than 1 electron and this is where we can start really getting into the idea of quantum numbers and how electrons actually distributed in Adams whether it will see that they don't actually ordered the nucleus and some sort of them circular pattern that will see exactly what that looks like and how we came about that that that solution you may very kind is no lesser roles of your bills from the other classes finally see how those are actually drive models actually look like and why we know that's what they look like how we're going to cover a lot of different theories and principles so I have a listed out here for you and and we'll talk about using those as we have done so 1st solo that a history lesson for you this is important in the development of how adamant on models came to be so the foreign 1900 ourselves we always thought of atoms and molecules just rebounding balls even higher than women's billiard balls in 3 dimensions that they were just sort of bouncing around and we knew that there was more to it from meaning that the knowhow so this is the basis of the an ideal gas flow which will cover the very end of this class but it still works really well to describe certain phenomena we could still use it for the ideal gasses because for the most part it works but this wasn't the whole story and evidence and can show them that it wasn't the whole story so around 1900 him along and this is when he was able to say Well molecules in Adams only admitting certain energies and talk more about exactly what immediate and how that works a little better but that was a really important discovery is about .period there was that the new there must be something called quanta amount of energy that you can have In this meant that there wasn't a continuous level energy that these electrons must have some rules associated with them and this turned physics upside down this new at this point that there must be something massive that they weren't getting that was important to look at so it will be assorted traces line of thinking through the development of the different molecular models so we haven't plum pudding model which was 1 of the really early once they knew that there are some positive charges negative charges but in the heart ministers how they were distributed so they were always trying to come up with how are going Arabs look like the plum pudding model since would sounds like you have a sort of blob of positive charge and then suspended in that while positive charges all sorts of little negative electrons and having that little raises suspended and company but and once plan came along and said well energy is quantized there must be something else happening that was when they said well there must be something else going on what it kind of refined this quite a bit and said OK well all the positives charges nongenetically winter ended an experiment that showed that all the positive charges very small spaces that didn't take up very much in the electric urgent very much of the atom so you know that there must be something that later on when called the nucleus at the time it was determined that no fewer than ones quantities Xinhua came about this concept a different energy levels that plank discovered poor aggressive advances OK knowledge find it a bit more we think there is the energy shells and the the electrons in the energy shops now as bore models probably what you've Williams and at least 1 in high school on and really uses for a little while it's great for 1 electron systems but after that it really breaks down so In high school you may have learned that you had to electrons circling the 1st shell and then ate and ate and will see that there some similarities to that In the later ones don't before can talk too much more about our homes we need to do have a backdrop on what really is an electromagnetic radiation is because without knowing that we can't really go on with talking about hydrogen atoms than other atoms so 1st of all what is electromagnetic radiation while a lot of what we see in everyday life is concerned it is covered in you can talk about any sort of light that we see with even things like the he falls into the IR category microwaves sunlight and like that you see from light bulbs and Xrays of the the kind of a smattering of the of different on tights but pretty much anything within this you can count on radio waves is another 1 so there's lots and lots of types of electromagnetic radiation and we'll talk about that what makes each 1 of these is completely different here in a minute he obviously microwaves Xrays and some in Neil fire he does all fall into the same category lights self since Iranian Nobel waves media wielded defined and figure out from information I give you so you can the world is talking mostly about transverse waves but there is actually 2 different types so the transverse waves as things beginning of light waves are you radiation but maybe in real life you're better off tying it to thinking about things like the pasta or if I took a jump rope and I would like that I encounter made aware of it out all these would be transverse waves where you get this crest and you can see that we have something called an amplitude which is how high it comes from the 0 . on N O wavelength switches from 1 peak to the other early and point underlined that exact thing .period later on and will talk about a few other things we can calculations and that just so that you recognize that there are 2 types of waves while we're talking about waves and that they all have the same properties on which define all the same definition is just a little bit different look we also have a longitudinal wave and we will be talking about that much in this class playing the physics classes of talk about them is found in pressure waves now let more transverse waves exactly when you're going to be a in this class so here we have just sort of a simpler picture of it and once again we see the amplitude and it we see the wavelength now we have something else and that's called New or frequency so this is not of the it's new it's kind of a squiggly views on initiating notice that because we will be talking about the end in this chapter and because could the computer fonts make them look very similar EU have to know what they are based on context and that shows up in a lot of cases so what new this is kind it's
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not a speed you don't think of it as speed but it it's a given measurement of how much you can get from here to here ,comma cycles in 1 2nd in command of little hard to think about in terms of a wavelength but it's almost easier to think about in terms of spending so if I had taken a spin around the circle and I knew that once per 2nd that's my frequency would be 1 her saw 1 cycle per 2nd same idea here if they get from here to here in 1 2nd that's 1 hurts 1 cycle per 2nd and that's how you want to think about frequencies now we can really frequency wavelengths together because we think about it the shorter the wavelength the more of the more cycles during having 1 time period and so because of that we can relate the 2 together now they're related by C which is the last year that in because we're talking about light we're talking about the speed of light here and so if we want a calculating new were like calculate layer Landauer wavelength we can go back and forth by using the speed of light in using this equation no I can mention there of the units for new or frequency is 2nd and burst so that someone over seconds or we can call the courts and the 2 are completely interchangeable so irregular will do I have to know what hurt last because I can tell you will hear the frequency in hertz and if you don't know that means cycles per 2nd may have some problems so make sure you know that now or wavelength which is your distance from 1 peak hour 1 point under our waved to another at the distance that's how far is it from 1 point to another so that's just in years you'll see eminently a lot and that's because of the little light tends to fall in that manner meter region and sold because of that there's a lot of times work is just simpler to state 515 animators then fiveway fight inside the 97 and so you want to get really good in this chapter converting the Mountaineers encouragement volumetric units so if you remember how to do that that's the all the the fundamental section no 1 backdrop that you need to have sort of in your mind about how electromagnetic waves work and that there's actually 2 components to this and in real research in real life we can make use of both of those components there's an electrical components and a magnetic components now you'll notice if you look at this meeting kind of see the blue and agency the right that these are going to have the same wavelength and seeing frequently the only differences is what actually are are if electric field components on the sexiest and the magnetic will be on this 1 so the 90 degrees to each other so we're not going to do too much when they're on it's just you need to have the sort of your background now because they're away as an electromagnetic waves they travel at the speed of light and so here is the speed of light fuel will be using that quite a bit now let's go back and talk a little bit all why all those different electromagnetic waves that I talk to are so different Xrays and microwaves and light heat what meets all of those so different from each other so here we have the electromagnetic spectrum and I have a listed out from the other I suppose this figure has a listed out all the way and now this little section right here is blown up so you can see it because that's the visible wavelength that's so that you know that kind of special to us because we can see a boy you see here is that you have your wheat radio waves near infrared which is seats and then you're visible and then your ultraviolet Xrays and gamma rays now this shows you the difference right here you can see over in this section you have a really hot for a really long wavelength In over here you have a really small on other words even really highfrequency hearing here there's lots of cycles of 1 little area and a really low frequencies we haven't talked about how those related to energy but now we can little that it we can say well over as you increase wavelength you make the wavelength bigger stretching out here in House lowerfrequency and have a lower energy something down here really low energy really low frequency in a really long wavelengths so what makes radio waves different from something like Xrays which can we can actually used to visualize the bones is all in the frequency a wavelength so we sort of went over the side but let's look at it again as wavelength increases it's going to take you longer to get from 1 cycle to the next which means what's going to happen year frequency it's going to decrease now let's look at this and say Well which has a greater frequency red light on light no frequency of listed on here but we know that frequency and wavelength are inversely related as frequency gets isn't wavelength gets bigger frequency gets smaller embrace 1st so if you look at this user which 1 has a greater frequency red liar or blue light it's going to be polite now which 1 has a greater energy in which will allow time calculi energy but we can see that here this is going to have more energy because you have a much faster and much higher frequency much lower wavelengths and so your blue light will have a higher energy now there's good have a greater speed we said that it has a higher frequency and that I have a higher energy so now does it follow that I had a higher speed no they all the same speed right it's all going to be the speed of light that doesn't change so all of and have the same speed of but the floss the the the frequency and the energy and the wavelength of all going to change now you know and I don't ask you memorize the spice extract it is good to have a general idea especially in his law and which ones are higher energy and it's good to know that things down here are lower energy things appear and there's an easy way to remember this things to this little comment by the Foxtrot so he had said he had a little kid who he's no kind of smart genius kid in the in the comic and he walks into a store and he says you sell ultraviolet blue has shop uses lots to see what was about regular viable now Bloomberg also no green yellow orange No no no the wrath of the the rebels still he said I was hoping for something a little higher energy and his friends along the northern infrared ball so you know the joke being that we talk about rebel being full of energy will run the lowest of the Kowloon actually see we should really be looking for global a ultraviolet air ultraviolet will now turned out shortly after the 1st summation of this comic assumes told me that they actually do sell global and all excited turned on his actions as blue as briefly so and unfortunately there is is not just a higher energy but let's do an example exercise so that we have a wavelength of green light from a traffic signal and we know that some and 520 animators and we need to know the so when we look at this we know certain things that excuse similar patterns I'm
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computer crashes last nite so it's been completely unchanged so that the animations that myself so we know all of this in when you're 1st starting out and doing all I can assure problems that's a good idea to go through and write everything out that you know it and put it in a little tables so that you can Fillinger equations are many things that we services firm good technique your 1st starting out as right down here is what I know that things could useful in this problem the had the speed of light rain down and I have a lot wavelength that was given and then at this point I can kind as they I need frequencies I'm probably going to need to be using this equation so the 1st thing you want to do is a and this is years so we have to put them in the same unit technically it doesn't really matter what unit you put an end but in most cases the best to convert to the SI unit the base unit in this case of leaders and so we do that we divide by candlelight Sony might still carry multiplied by 10 of the 1995 about how I did it you can do that you either way is fine whatever we prefer and so we get this week 5 . 2 2 times tendinitis at which point now we have meters per 2nd in meters and we fell into here so we fell in the speed of light we fell in our wavelength and we solved now we need to check for saying things in units always Israeli Mongolia .period reexamined don't do that so we need to say Well we have 3 significant figures of this is infinite and don't forget that influencing things because the definition and so we put in speed of light have 3 to match and so Oregon around 2 3 significant figures no notice any change to this from seconds and Versteher it doesn't really matter if you do that or not you can put both of them 1 of them there either 1 is right just make sure you know how that they're actually the same thing so that I can do something hurts you know that you can just fill in hurts into this equation land don't do some more examples and will actually just work really is over the top camera for a change of pace but so here is the frequency of radiation from my choice 120 day there so we need to make sure we know again so this goes back and pass all that stuff that I asked you to study in the fundamentals chapter so we need to 1st convert that we can't have 120 gigahertz so we need to go ahead and change that times 10 to the nite so this is sort of the opposite of what we now have to multiplied by 10 the nite now something that's kind of useful to get used to doing here then I will show you how I would actually like this conversion factor because I'm not not going to give this to me is the answer to use it and something else so rather than go through and type and calculator risk making a mistake it's completely OK to just read out 100 times 10 to the 9 Turks and use that for all your calculations and this save little this time a little bit buttonpushing and a chance to make any mistakes when you're buttonpushing now we look at our equation we say Well how old how do we solve for Wembley so that was originally of the equation I believe you have you have to look at the equation she says he wouldn't give you an example but even way we just need to solve for land so however the equation is written for himself for that so we can fill in areas let land wavelength equals the speed of light over frequency any can fill in all our values and we can bring on hurts here now cost you can never leave an actual answer in 120 times 10 the nite Bruce Fein a filet equation and we get our and we check our things and I chose to use to here because we only had to here and so it doesn't matter how many have filled in for speed of light and needed to fill in at least 2 probably 3 would be better I happen to fill in for but this sets up that we can only use to the so now we have 1 more and now you're kind of during the head section but I wanted extend the will say that was be just a moment of it so this is a problem I have set out for you as you at home so I have the answers for you there which is included in your worksheet so you may want to write that down in you knew this was exactly like how we did that extra practice I have seen now working on a little bit differently a little bit more a history lesson again we have links quantum theory so this is going to a lot more what playing actually discovered so when should this she says that when solids are heated they emit radiation and we can see this to some extent in everyday life we will mean a lot in everyday life being know that lava glows red you know that if you turn on an electric heater it's good goal little Red too and a late of course another lights now the knew this before applying this wasn't something that was a secret or anything now the difference was that they never could really explain it could the close the whenever they would try to mimic the pattern of how solids did this it always really messed up at either that thus far on 1 side and find the other they can define they could figure out the middle and they can explain the millions in all the time I was very happy but either the Uvira the IRA areas you know far out in the direction it would mess up now once I came along and said well OK these molecules not actually mean a steady stream of light the remaining entities that very specific and their meeting light at very specific energies and that were going in these quantum that changes things so what quantum is is the smallest quantity of energy and that's going to happen equation and that equal to eagles each new or E equals HC Orlando whichever way you want to think about it is useful so you 1 thing the squanders little energy package is the smallest energy package sold lots of things in life are going to be quantized on you don't want to think of this as some sort of weird concept it's it's not that desire we think about it says something you can think about everyday life we are among system is quantized straight you kingdom village less than a penny now we assure with modern accounting techniques they make you things like that but if you're talking back just training cash money on you not to have less than a penny and select kind panel quantum right you can have half a cent in hand half a cent to someone else so I just think of this as a the smallest unit of now h is called planes constant and that 6 . 6 2 6 times 10 negative 34 no you don't have to memorize but yes probably haven't memorized the Indians chapter can during his itself much and so this is just a constant that you're going to fail and have their that gets you to the advances that you need up to now we have another
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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
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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 MakeAWish 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
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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 redhot 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
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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
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the summer history still throughout all of this the modern issue historymaking 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 computersimulated 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 foreignregistered 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
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prior to that I just decrease the intensity of like I haven't changed the energy
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that I have decreased in intensity if I wanted to change the energy of light this light of actually work because white light so there's there's a spectrum but let's say I had me a little flashlights shined a red light by 1 increase the energy of those photos I'd have to change it to blue light so energy is very different from intensity intensity is talking about the whole energy so if I wanted to make a red light more intense well I've turned 2 of those same red like if I want make a blueline 110 determined to all those bullets but that doesn't speak to the energy of the photo and that's all about it and think of it as color within the visible region it's what we see as color if it's not visible regions the idea of color doesn't work so well so if we want to figure out this kinetic energy into what's left over after you take up the work so we see age new in here for HC Rolando works to that the energy of the photons up to the incoming photons and we just subtract out the work function we say OK well there's a certain amount of energy that photon it's going to be taken away it's going to be taken away In cut into on actually knocking out electron loose so we subtract the W and that gives us the kinetic energy now what we think happens the intensity of light and increased but the frequency stays the same so remember we talked about intensity we said it's just more and more and more White it's shining 3 balls instead of 1 10 of the 35 balls so if we increase the intensity are we increasing and decreasing number well we're increasing where I see as being more bright Nunavut more they're hitting eye and so increased intensity means more photons and the more false you put in in the morning light turns your going to inject so in that case of you would get more just to reshape our time as you increase the intensity of the increase in photons thereby increasing the number of ejected electron I'm so let's walk through and do an example on the border tests so we had calcium work function so now I've actually given a number we call it a work function that endured as this case is always going to be a number evaluating did you all given enough information for you to find it and ask what is the minimum frequency of light for a photoelectric effect for Council now I can ask that a little bit differently I could see what is the threshold frequency at asking the energy a classy the threshhold energy arm some McShane electoral threshold that just means the minimum I can also ask you the maximal wavelengths of light so keep that in mind minimum frequency corresponds to maximally of so that is a calculate the kinetic energy and that's something that you're going to see a lot in this chapter here you know you're going to be doing 2 or 3 things in these equations working back and forth so we're going fundamental frequency and they were going to find the kinetic energy of the electron if we now put this and so the work function will tell us the minimum frequency of light you need and then we can find the kinetic energy of the general problems so I want to put this in here like this because you you will see this in your book and you'll see used on the Internet and other random sources so this is just another way of writing the work functions so don't think anything of that and I wrote it both ways you can use to sing of it's now if we look back on our last flight we know that we're going to need this equation but we don't have something we're missing something so if we have our work function and we need to find frequency need to have a kinetic energy but we don't have kinetic energy right well we do what is the kinetic energy at this threshold frequency at the threshold treatment during the reporting just enough light to not philatelists but none of light actually any speed so you're knocking in a loose but there is no spirit no velocity so you're kinetic energy think back your fundamentals and onehalf and the squared so there's no velocity there's no kinetic energy and so kinetic energy is equal to 0 and so because of that each new minus the work function is equal to 0 well now we know H and we know work and we can Salford and so we end up with so this is the sort of the trick to making sure that you can find a threshold frequency you have to remember that at your special frequency in the kinetic energy 0 and that's because your velocity speed is 0 there's not enough energy in that fulltime to actually give the fellow the electron any speed in so it's just that Annapolis a loose and it's not gonna move anywhere and that gives you your threshold frequency now we can go ahead and also figure are kinetic energy if we have this frequency of life so leaders of the 2 of the main ways I can ask this question and now we have this parents we need to go ahead and find the kinetic energy so we sell everything and we fell in H we fell in the frequency that was given and we fell our work function that was given and we get so 1 more now knows this question we're taking a little bit further were saying we have the work function for magnesium were calculating the minimum frequency of light required to reject the electrons so that's the same thing we just stayed with were calculating the kinetic energy if we change the frequency of flights so again what we just did now arena take it 1 step further them and we're going to say Well what about is we also 1 of the lost so that sort of the extra step that we're going to do here the story start the exact same way that we started in last problem so we started from are Connecticut energy equation and we remember that while at the threshold frequency are kinetic energy is equal this so we can
47:52
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 onehalf 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 onehalf 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
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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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Quantenchemie
Metadaten
Formale Metadaten
Titel  Lecture 03. Introduction to Quantum Mechanics 
Serientitel  Chem 1A: General Chemistry 
Teil  03 
Anzahl der Teile  23 
Autor 
Brindley, Amanda

Lizenz 
CCNamensnennung  Weitergabe unter gleichen Bedingungen 3.0 Unported: Sie dürfen das Werk bzw. den Inhalt zu jedem legalen und nichtkommerziellen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen und das Werk bzw. diesen Inhalt auch in veränderter Form nur unter den Bedingungen dieser Lizenz weitergeben. 
DOI  10.5446/18968 
Herausgeber  University of California Irvine (UCI) 
Erscheinungsjahr  2013 
Sprache  Englisch 
Inhaltliche Metadaten
Fachgebiet  Chemie 
Abstract  Chem 1A is the first quarter of General Chemistry and covers the following topics: atomic structure; general properties of the elements; covalent, ionic, and metallic bonding; intermolecular forces; mass relationships. Index of Topics: 0:00:17 Quantum Theory: Structure of an Atom 0:01:50 The Birth of Quantum Mechanics 0:03:17 Development of Atomic Models 0:05:09 Electromagnetic Radiation 0:06:11 Properties of Waves 0:07:25 Transverse Waves  Frequency 0:10:16 Electromagnetic Waves 0:11:23 Electromagnetic Spectrum 0:20:59 Plank's Quantum Theory 0:27:52 Black Body Radiation 0:34:19 Light: A Wave or a Particle 0:35:29 Photoelectric Effect 