Lecture 03. Introduction to Quantum Mechanics
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MannoseQuantenchemieChemieanlageMeeresspiegelMischenTiermodellModul <Membranverfahren>Hydroxybuttersäure <gamma->CHARGE-AssoziationMaischeInternationaler FreinameBukett <Wein>Systemische Therapie <Pharmakologie>DeprotonierungSetzen <Verfahrenstechnik>Physikalische ChemieMolekülmodellPeriodateElektron <Legierung>Konkrement <Innere Medizin>WursthülleDruckabhängigkeitElektronische ZigaretteNobeliumSubstrat <Boden>KernproteineFeuerWasserfallOrdnungszahlMeeresspiegelChemische EigenschaftMolekülRotwurstGummi arabicumSpurenelementBoyle-Mariotte-GesetzÜbergangszustandTiermodellAlkoholische LösungKrankengeschichteDurchflussAtomAtomorbitalBohriumKörpergewichtWasserstoffVorlesung/KonferenzComputeranimation
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MannoseLeucinQuantenchemieMalzDurchflussMethylmalonyl-CoA-MutaseMagnetometerBukett <Wein>AltbierSonnenschutzmittelQuellgebietSetzen <Verfahrenstechnik>AlterungErdrutschFarbenindustrieSeleniteQuerprofilKonkrement <Innere Medizin>HalbedelsteinPhosphoreszenzBukett <Wein>KrankengeschichteLavaKonvertierungMolekülSystemische Therapie <Pharmakologie>StereoselektivitätAtomInlandeisAzokupplungElektronische ZigaretteFülle <Speise>ComputeranimationVorlesung/Konferenz
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MannoseDifferentielle elektrochemische MassenspektrometrieMagnetometerDiazepamVancomycinBohriumTrihalomethaneKörpertemperaturErdrutschKrankengeschichteWursthülleElektronische ZigaretteKörpergewichtAzokupplungElektron <Legierung>WasserfallFunktionelle GruppePhosphoreszenzBukett <Wein>OberflächenchemieNobeliumMetallQuerprofilWasserSchmerzschwellePhotoionisationChemischer ProzessComputational chemistryNahtoderfahrungGradingSchönenComputeranimationVorlesung/Konferenz
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MannoseInsulinBohriumArgininVancomycinHydroxybuttersäure <gamma->PeriodatePolyp <Medizin>KaliumElektron <Legierung>OktanzahlFarbenindustrieSchmerzschwelleCalciumWursthüllePhotoionisationBlitzschlagsyndromEnzymkinetikExplosionBranntweinFunktionelle GruppeErdrutschComputeranimationVorlesung/Konferenz
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MannoseAdenosylmethioninDifferentielle elektrochemische MassenspektrometrieTrihalomethaneNatriumhydridEthylen-Vinylacetat-CopolymereHeck-ReaktionHydroxybuttersäure <gamma->CoffeinInternationaler FreinameThermoformenMagnesiumElektron <Legierung>Gangart <Erzlagerstätte>PeriodateTiermodellSchmerzschwelleAlterungKonkrement <Innere Medizin>PhotoionisationHalbedelsteinNahtoderfahrungQuerprofilSystemische Therapie <Pharmakologie>AusgangsgesteinMetallFülle <Speise>SenseComputeranimationVorlesung/Konferenz
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PhotoionisationVorlesung/Konferenz
Transkript: Englisch(automatisch erzeugt)
00:07
Okay, so today we're going to be talking about chapter one and this will take us about three weeks and up through the first midterm So chapter one covers everything involved in quantum theory or I shouldn't say everything But at least what we're gonna cover in this class for the most part
00:21
So we have a lot of things to cover. We're gonna start with just general properties of waves and electromagnetism because you need to have that as a backdrop to be able to talk about all the rest of the things and How we actually sort of build up an atom or how we think about atoms Now from that point we can kind of go on and we can start talking about the Bohr model
00:41
Which we've already been introduced to a little bit where you have the protons and neutrons and the nucleus and the electrons going around the outside But what we'll see is that this only really works for the hydrogen atom and other ions that have one electron So we'll start there and we'll talk about Many things there such as transitions and things of that sort at which point we can move on and talk about more complex systems
01:02
but within the hydrogen We can also then go on and talk about de Broglie wavelengths and quantum numbers and then from there We'll start talking about multi-electron systems atoms with more than one electron And this is where we can start really getting into the idea of quantum numbers and how electrons are actually distributed within an atom
01:21
whether we'll see that they don't actually orbit the nucleus in some sort of Circular pattern and we'll see exactly what that looks like and how we came about that That solution you may you may already kind of know s orbitals and p orbitals from your other classes We'll be able to finally see how those are actually derived and what those actually look like and why we know that's what they look
01:41
like We're going to cover a lot of different theories and principles. So I have them listed out here for you And we'll talk about each of those as we hit them So first a little bit of a history lesson for you. So this is important in the development of how these atom Models came to be so before
02:01
1900 or so we always thought of atoms and molecules is just these rebounding balls You can kind of think of them as billiard balls and three dimensions that they were just sort of bouncing around And we knew that there was more to it. We didn't exactly know how So this is the basis of theories such as ideal gas law, which we'll cover at the very end of this class
02:20
And it still works really well to describe certain phenomena We can still use it for the ideal gases because for the most part it works But this wasn't the whole story and evidence and kind of showed them that it wasn't the whole story so around 1900 Max Planck came along and this is when he was able to say well molecules and atoms
02:41
They're only emitting certain energies and we'll talk more about exactly what emitting energies mean and how that works in a little bit But that was a really important discovery because at that point there was they knew there must be something called quanta an amount of energy that you could have and This meant that there wasn't a continuous level of energy that these electrons must have some rules associated with them
03:03
And this turned physics upside down this they knew at this point that there must be something Massive that they weren't getting that was important to look at So we'll be able to sort of trace this line of thinking through the development of the different molecular models So we have the plum pudding model
03:21
Which was one of the really early ones they knew that there are some positive charges and some negative charges In the atom and they just didn't know how they were distributed So they were always trying to come up with how are what is these atoms look like? so in the plum pudding model exactly what it sounds like you have this sort of blob of Positive charge and then suspended in that blob of positive charge is all sorts of little negative electrons
03:46
So you can kind of think of it like a little raisin suspended in plum pudding But once plank 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
04:02
Rutherford kind of refined this quite a bit and said, okay Well, all of your positive charge is now in your nucleus He he went through and did an experiment that showed that all the positive charges in a very small space That didn't take up very much of the electron or very much of the atom So they knew that there must be something that later on would be called the nucleus at the time it wasn't termed that
04:24
Now then once quantization came about this concept of different energy levels that plank Discovered Bohr was able to take Rutherford's model and say okay now, let's refine it a bit more We think there's these energy shells and the electrons are in the energy shell Now this Bohr model is probably what you've you know, at least seen in high school
04:44
And we're gonna use this for a little while It's great for one electron systems, but after that it really breaks it down So in high school, you may have learned that you had two electrons circling the First shell and then eight and then eight and we'll see that there's some similarities to that in the later ones, too
05:10
Okay Now before we can talk too much more about atoms We need to have a backdrop of what waves and electromagnetic radiation is Because without knowing that we can't really go on with talking about hydrogen atoms and other atoms. So
05:26
First of all, what is electromagnetic radiation? Well, a lot of what we see in everyday life is concert is covered in this you can talk about any sort of light That we see or that even things like heat heat falls into the IR category
05:40
microwaves Sunlight any sort of light that you see from light bulbs X-rays these are just kind of a smattering of the of the different types but pretty much anything within this you couldn't count Radio waves is another one So there's lots and lots of types of electromagnetic radiation and we'll talk about that What makes each one of these?
06:01
Completely different here in a minute because obviously microwaves x-rays and sunlight and you know Fire heat doesn't all fall into the same category in our lives so Some things that you need to know about waves and need to be able to define and figure out from information I give you so you can we'll be talking mostly about transverse waves, but there's actually two different types
06:26
So the transverse waves is things you can think of light waves and all our EM radiation But maybe in real life You're better off tying it to thinking about things like guitar string or if I took a jump rope and I went like that And kind of made a wave out of it All of these would be transverse waves where you get this
06:44
crest and You can see that we have something called an amplitude which is how high it comes from the zero point And a wavelength which is from one peak to the other or really any point on the line to that exact same point later On and we'll talk about a few other things that we can calculate from this in a minute
07:01
Just so that you recognize that there are two types of waves while we're talking about waves and that they all have the same properties We can define all the same definitions. It's just a little bit different in look. We also have a longitudinal wave and We won't be talking about that much in this class. But in your physics classes, you'll talk about them as sound and pressure waves
07:21
So now a little bit more about transverse waves and exactly what you're gonna need to be able to know in this class So here we have just sort of a simpler picture of it. And once again, we see the amplitude and We see the wavelength Now we have something else and that's called new or Frequency, so this is not a V. It's new. It's kind of a squiggly V
07:44
and make sure you notice that because we'll be talking about both V and new in this chapter and Because could the computer fonts make them look very similar You're gonna have to know what they are based on context and that shows up in a lot of cases
08:00
So what new is is this kind of it's not a speed you don't want to think of it as speed But it gives a measurement of how much you can get from here to here how many cycles you can get in one second Sometimes that's a little bit hard to think about in terms of a wavelength But it's almost easier to think about in terms of spinning So if I take and I spin around in a circle and I do that once per second
08:23
That's my frequency would be one Hertz or one cycle per second same idea here If it gets from here to here in one second, that's one Hertz or one cycle per second And so that's how you want to think about frequency Now we can relate frequency and wavelength together because if you think about it the shorter the wavelength the more
08:44
the more Cycles you're gonna have in one time period and so because of that we can relate the two together Now they're related by C, which is the velocity right? That's in because we're talking about light We're talking about the speed of light here And so if we want to calculate new or we want to calculate weight or lambda or wavelength
09:05
We can go back and forth by using the speed of light in using this equation Now I kind of mentioned this off The the units for new or frequency is seconds inverse So that's one over seconds, or we can call that Hertz and the two are completely interchangeable
09:26
So, you know you get asked a lot. Well, do I have to know what Hertz means? Yes, because I can tell you well Here's the frequency in Hertz and if you don't know that that means cycles per second, you might have some problems So make sure you know that Now lambda or wavelength, which is your distance from one peak or one point on the wave to another
09:46
That's a distance. That's how far is it from one point to another so that's just in meters You'll see it done in nanometers a lot and that's because visible light tends to fall in that nanometer region And so because of that there's a lot of times where it's just simpler to say
10:03
550 nanometers than five point five times ten to the negative seventh And so you want to get really good in this chapter at converting to nanometers and converting between all your metric units So if you don't remember how to do that, that's you know all in the fundamental section Now one more backdrop that you need to have sort of in your mind about how electromagnetic waves work is that there's actually two
10:23
Components to this and in real research in real life. We can make use of both of those components There's an electric component and a magnetic component now You'll notice if you look at this and you can kind of see the blue and you can see the red That these are going to have the same wavelength and the same frequency
10:40
The only difference is is what axes are on if the electric field components on this axis Then the magnetic one will be on this one. So they're 90 degrees to each other So we're not going to do too much with this It's just you need to have this sort of in your background now because they're a way or an electromagnetic wave
11:01
They travel at the speed of light. And so here is the speed of light for you and we'll be using that quite a bit now Let's go back and talk a little bit about why all of those different Electromagnetic waves that I talked about are so different right? We had x-rays and microwaves and light and heat What makes all of those so different from each other?
11:24
So here we have the electromagnetic spectrum and I have it listed out from Or I suppose this figure has it listed out all the way now This little section right here is blown up so that you can see it because that's the visible wavelength That's so that you know, that's kind of special to us because we can see it
11:43
But what you'll see here is that you have your radio waves your infrared which is heat and then you're visible And then you're ultraviolet x-rays and gamma rays Now this shows you the difference right here You can see over in this section
12:01
You have a really hot or a really long wavelength and over here You have a really small wavelength or in other words. You have a really high frequency right here There's lots of cycles in one little area and a really low frequency here We haven't talked about how that's related to energy, but now we can a little bit and we can say well Okay as you increase
12:23
Wavelength you make the wavelength bigger you stretch it out You're gonna have a slower frequency and you're gonna have a lower energy. So things down here are really low energy Really low frequency and really long wavelengths So what makes radio waves different from something like x-rays which can we can actually use to visualize our bones is all in the frequency
12:44
or wavelength So we sort of went over this already, but let's look at it again as wavelength increases It's gonna take you longer to get from one cycle to the next which means what's gonna happen to your frequency It's going to decrease
13:01
Now let's look at this and say well, which has a greater frequency red light or blue light now frequency Isn't really listed on here but we know that frequency and wavelength are inversely related as Frequency gets or excuse me as wavelength gets bigger frequency gets smaller and vice versa So if you look at this you say which one has a greater frequency red light or blue light
13:25
It's going to be blue light now, which one has a greater energy we haven't done a lot of talking about how to calculate energy, but We can see that here
13:40
This is going to have more energy because you have a much faster or a much higher Frequency and a much lower wavelength and so your blue light will have it or higher energy Now does blue light have a greater speed we've said that it has a higher frequency and that it has a higher energy So now does it follow that it has a higher speed?
14:03
No, they all have the same speed right? It's all going to be the speed of light that doesn't change So all of them are going to have the same speed But the floss or the the frequency and the energy and the wavelength are all going to change now Even though I don't ask you to memorize this by any stretch
14:21
It is good to have a general idea especially in the visible range which ones are higher energy and it's good to know that things down here are a lower energy than things up here and There's an easy way to remember this. Thanks to this little comic by Foxtrot, so You have the you have the little kid who he's you know Kind of a smart genius kid in the in the comic and he walks into a store and he says do you sell?
14:43
ultraviolet blue Shopkeeper says well, excuse me. Well, what about regular violet blue? No Blue bull no green yellow orange. No, no, no Okay rats. I'll take a red bull So then he says I was hoping for something a little higher energy and then his friend says well
15:02
At least it was an infrared bull So, you know the joke being that we talked about red bull being full of energy Well, right is the lowest of the colors we can actually see we should really be looking for blue bull or ultraviolet blue or ultraviolet Now it turns out shortly after the first time I showed this comic go to my students told me that they actually do sell a blue Bull, I got all excited turns out is actually just blue raspberry flavored. So
15:25
Unfortunately, there's is not just a higher energy Okay, let's do an example exercise so We have a wavelength of green light from a traffic signal and we know that it's centered on 522 nanometers and we need to know the frequency
15:42
so When we look at this we know certain things You have to excuse some of the patterns my own computer crashed on me last night So it's been completely unchanged some of the the animations got messed up So we know this and when you're first starting out and doing a lot of chemistry problems it's a good idea to go through and write everything out that you know and
16:03
Put it in a little table so that you can fill into equations or maybe figure out what equation you need So this is sort of a good technique when you're first starting out to just write down Here's what I know that I think is going to be useful in this problem so you'll see here I have the speed of light written down and I have the wavelength that was given and then at this point I can kind of say well I need frequency
16:23
So I'm probably going to need to be using this equation So the first thing you want to do is this is a nanometers and this is in meters So we have to put them in the same unit Technically, it doesn't really matter what unit you put it in But in most cases it's best to convert to the SI unit or the base unit in this case
16:41
So the meters and so we do that. So we divide by 10 to the ninth some of you might say well Can I multiply by 10 to the negative ninth? I thought that's how I did it You can do that too. Either way is fine Whatever way you prefer and so we get this we get five point two two times ten to the negative seventh meters At which point now we have meters per second in meters and we can fill into here
17:04
So we fill in our speed of light we fill in our wavelength and we solve Now we need to check for sig figs and units always right you won't get all your points on your exam if you don't do That so we need to say well we have three significant figures
17:20
This is infinite. Don't forget that's infinite sig figs because it's a definition and So we put in speed of light to have three to match and so we're going to round to three significant figures Now notice I changed this from seconds inverse to Hertz Doesn't really matter if you do that or not you can put both of them or either one of them there either one is right
17:41
Just make sure that you know how that they're actually the same thing so that if I give you something in Hertz You know that you can just fill in Hertz into this equation and solve for lambda if need be Okay. So now let's do some more examples and we'll actually just work these over on the document camera for a change of pace
18:03
Okay So here we have the frequency of radiation from your microwave is a hundred and twenty gigahertz So we need to make sure we know what giga means So this goes back and tests all that that stuff that I asked you to study in the fundamentals chapter So we need to first convert that we can't have a hundred and twenty gigahertz
18:23
So we need to go ahead and change that Times ten to the ninth. So this is sort of the opposite. We now we have to multiply by ten to the ninth
18:41
now Something that's kind of useful to get used to doing here is I'm going to show you how I would actually write this conversion factor because I'm not you're not going to give this to me as an answer. You're going to use it in something else So rather than go through and type that into your calculator and risk making a mistake It's completely okay to just write out a hundred times
19:00
ten to the ninth Hertz and Then use that for all your calculations and it saves you a little bit of time a little bit of button pushing in a chance To make any mistakes when you're button pushing So now we look at our equation and we say well how How do we solve? for wavelength
19:20
So that was the version of the equation I gave you You'll have to look at your equation sheets to see what I give you on the exam But either way we just need to solve for lambda. So however, the equation is written We're going to solve for that So we can fill in our lambda equals C over nu wavelength equals the speed of light over frequency
19:43
And then we can fill in all our values and we can bring down Hertz here now Of course, you could never leave an actual answer in 120 times 10 to the ninth, but it's fine to fill it into an equation
20:03
and we get our answer and we check all our sig figs and I chose to use two here because we only had two here And so it doesn't matter how many I filled in for speed of light I needed to fill in at least two probably three would be better
20:23
I happen to fill in four but this sets up that we can only use two Okay, so now we have one more and now you're kind of getting the
20:40
That one's for next time We'll save that one from just a moment Okay, so this is a problem I have set up for you guys to do at home So I have the answers for you there, which isn't included in your worksheet So you may want to write that down and you're gonna do this one exactly like how we did that as extra practice
21:01
So now moving on a little bit you get a little bit more of a history lesson again We have Planck's quantum theory. So this is going to go into a little bit more of what Planck actually discovered So when he says that when solids are heated they emit radiation and we can see this to some extent in everyday life
21:21
We know maybe not lava in everyday life, but you know that lava glows red You know that if you turn on an electric heater, it's gonna go a little red, too And a light bulb of course and other lights Now they knew this before Planck. This wasn't something that was a secret or anything now
21:40
The difference was is they never could really explain it They could get close but whenever they would try to mimic the pattern of how Solids did this it always really messed up it either the the far on one side or the far on the other They could define they could figure out the middle and they could explain the middle using all of the atomic models But either at the UV or the IR areas, you know far out in the directions it would mess up
22:04
Now once Planck came along and said well, okay These molecules are not actually emitting a steady stream of light They're emitting energies at very specific or they're emitting light at very specific energies and that we're gonna name these quantum That changed things. So what a quantum is is the smallest quantity of energy and
22:23
That's going to have an equation and that's equal to Equals h nu or equals h c over lambda, whichever way you want to think about it, whichever way is useful So you want to think of this quantum as a little energy packet and it's the smallest energy packet So lots of things in life are going to be quantized
22:40
You don't want to think of this as some sort of weird concept. It's it's Not that bizarre when you think about it. So something you can think about in everyday life Our money system is quantized right? You can't really get less than a penny now, you know sure with modern accounting techniques They do things like that. But if you're talking back just trading cash money You're not gonna have less than a penny and so that's kind of a quanta, right?
23:04
You can't have half a cent in hand half a cent to someone else So just think of this as a the smallest unit of energy Now H is called Planck's constant and that's six point six two six times ten to the negative thirty fourth No, you don't have to memorize but yes
23:21
You'll probably have it memorized by the end of this chapter because you're going to use it so much And so this is just a constant that you're going to fill in to there that gets you to the answer that you need Okay. So now we have another example exercise So we talked about a green traffic light in our previous problem And we said that the wavelength was five hundred and twenty two nanometers or you know
23:43
Most of them were five hundred twenty two nanometers. We had calculated the frequency doing that now. I say find the energy So Once again, here's what we know we know see we know lambda And I went ahead and converted this right here. So we have it now. We also know this Now you may say well can I use e equals H nu too since I know nu we figured that out in the last
24:06
Problem sure you can in general You don't want to use things that you've already calculated once using that in another problems You can avoid it if you can't avoid it and you obviously have to that's fine but you don't want to have to If you can avoid it you want to because if you got nu wrong now, you're gonna get this one wrong
24:23
So we're gonna go back and we're gonna use free or lambda which was given in the problem So we have our equation And we can fill everything in planks constant just gets filled in as is so joules seconds We fill in C because that's just a constant. So we know that and then we can fill in lambda
24:42
Making sure that we match the units here and here Now it's always good when you're filling in these equations to make sure all of your units work So you can watch meters cancel here You can watch seconds cancel here and that leaves us with a unit of joules, which is an energy unit So everything should work out fine and we get three point eight one times ten to the negative 19th joules
25:06
So that is that we have our right unit and we have our energy. So that's the energy of a green traffic light Okay, let's do let's continue on with the problem that we were doing before Now we're gonna find the energy of our microwave
25:29
so this time we're given Hertz which means that we'll start from E equals H nu and We fill in H just as from the slides
25:44
Watching our units now. We have to fill in the hundred and twenty Of course, we can't just fill it in a hundred and twenty We need to convert this to Hertz and I'm gonna do it right right within the problem So I'll just multiply times ten to the ninth here and call it Hertz
26:01
So sure improper scientific notation once again saves some time and it doesn't hurt the problem at all Okay, so then we come down here we type that into a calculator We figure out how many sig figs we need
26:21
Now notice I took Hertz here and I cancel Hertz in seconds You know that that's one of those you want to keep in your head what Hertz means it really means inverse seconds It really means one over seconds, so that's going to cancel there Now let's round to the proper sig figs. So H doesn't matter This has two and so we need to round to eight point zero
26:44
Times ten to the negative twenty third joules. So now that we've done this Okay, we've seen that E is equal to H nu we've seen that we have H and that we have a hundred and twenty gigahertz and We've noticed that Hertz is equal to one over seconds. So that will cancel here and
27:05
We can go ahead and we can say well since E is equal to H nu we can fill this in With this now if we get this in our calculator We need to make sure that we still go ahead and figure out our sig figs. So we have two sig figs here
27:22
So we bring these two sig figs down. We have eight point zero times ten to the negative twenty third So just like what we did in the slides only with our other equation So now on the slides where I sent you home a couple of similar exercises to do And so go ahead and you can write down those answers if you need them
27:50
Okay So moving on with this idea of blackbody radiation now This is the idea that all of our solids emit some sort of light and you might say well, okay, that's fine
28:03
But when I look at you know this countertop, it's not emitting any light when I look at whatever It's not emitting any light And yet when you look at something like a heater or an electric stove or something of that sort now you start seeing red Light, so what's the difference between something that's just sitting and something that's glowing red-hot
28:20
Well kind of gave it away there right is glowing red-hot So that's because it's warm. The temperature is increased and that's why you start to be able to see the glowing Now if you look at something even warmer like the Sun or You know some some other stars out and about you're gonna get white light or you look at you know From the light bulbs you get white light
28:41
So what you're actually what the problem is is the reason we can't see all blackbody radiation is because it's not in the wavelength 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 affects what wavelength it's emitting So here we have a graph that this is intensity. This is wavelength. And so as your wavelength increases
29:08
Your air you have your wavelength over here and what these lines show you is the profile of what wavelengths are being emitted So if we have something at 3,000 Kelvin Arguably pretty warm. This will go ahead and it has this distribution. So you only see a little bit of light here
29:28
Most of it's sitting in the IR region now if you go up to 4,000 well Now you see a lot more light that's in the visible region your lambda max is still here and then here and then here so each one of these temperatures shows you where the distribution of
29:45
The photons are so what I'm what this graph means by intensity is how many photons or what percentage of photons? Have that wavelength so you can kind of think of it like your grade distributions that you're used to seeing How many people have an A? How many people have a B? How many people have a C?
30:01
Well, this is how many photons have this wavelength. How many photons have this wavelength? How many photons have this way? So it's 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 wavelength so we can see it So that's why we're able to see things glow hot the hot things glow
30:20
But we aren't able to see things at room temperature glow now If you look at an incandescent light bulb they glow they have about a 2700 to 3300 temperature range so Given this graph look at it for a second. Why do you think incandescent bulbs are so inefficient? We don't use them anymore because of this if you think about where would it its profile be its profile would be like here
30:49
right So when we look at an incandescent bulb most of it We can't see it's giving off plenty of light It's just most of that light is in this region Which is that region the region right below our visible spectrum would be the IR region, which we colloquially call heat
31:07
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's coming off as heat and so that's kind of useless to us We don't need to heat our houses with incandescent light bulbs. We want to light them with incandescent light bulbs
31:22
So something like a fluorescent bulb does a better job of lighting with less electricity because it falls into these higher ranges Okay, so another example exercise. So What is so in this case? Now we're looking at so Proxima Centauri our nearest star and it's a red dwarf star now
31:44
It's about 4.2 light years away, which we don't really need too much for this piece of information But we know that it has an average surface temperature of 3042 Kelvin So we're gonna work this problem a little bit backwards from what an actual astronomer would do which an actual astronomer would take and say
32:03
well, we have a We have this this wavelength spectrum They would have computers draw it out that can see all of the different wavelengths and They would find the temperature of the star in our case. We're gonna just work it this way, which is a little bit backwards So
32:20
We have this equation from the previous slide as far as why it's in millimeters It's just kind of the standard way of doing it. So when we find this We're going to end up with a millimeter value So we'll solve this equation for lambda max So in this case, I converted the the that constant that's in there to meters first
32:51
You could do it two different ways You could just fill in and then get your wavelength in millimeters and convert that or you can convert this to meters Either way is fine. And then for the sake of significant significant figures. There's also a zero there
33:09
Kelvin we fill in as is and we get this value
33:23
Now if we look at what region of the electromagnetic spectrum it is It might be a little bit easier to go ahead and convert this to nanometers just for the sake of looking at this Which comes out to be 952 nanometers So depending on how much you remember from the previous slides that we've done
33:43
This lines up right in the the near IR region is what we call it So it's near where we can see but it's still in the the IR region Which is right next to the red part of our visible spectrum, which is why when we look at a red dwarf That's where it gets its name from because the only light that we can see coming off it is red
34:02
And so we see it as red now sure there's this whole other profile It's in the IR region, but we can't see that and so to our eye We we just see it as a red and so that's where it gets its name from moving on to some more history
34:21
so throughout all of Modern ish history. I can't I guess you can't really call 300 BC modern But you know even back then there was some argument about what light really was and whether light is a particle or whether light is A wave. So what does that fall into? Well, so this kind of went back and forth back and forth as each group figured out what they figured out a little bit more
34:46
experimental evidence was that that was a little bit better than the last person's and sort of proved the last person wrong and Once we started getting into you know, this region now there started being really good experimental evidence either way
35:00
So it wasn't until Einstein came along and said hey you guys stop arguing. It's both So We're gonna go through we're gonna walk through and say well, why is light like a particle? Why is light like a particle and why is light like a wave and in see some of this wave particle? Duality that we call as we call it. So first of all, why is it a particle?
35:24
What can what treatment shows that it's like a particle? so We have something called the photoelectric effect and the idea of the photoelectric effect is that? You shine light onto a metal and when you do that you eject electrons
35:44
So the idea here is that you're you're and there's a lot of different rules for exactly what it can be But you're ejecting electrons from a metal surface with light So and I should also mention this is actually what Einstein won the Nobel Prize for so
36:01
In common culture, he might be best known for his theory of relativity But this this is what got him a Nobel Prizes, so it's it's you know is obviously very very important So now comes the part where that we sort of show its particle The energy of each photon has to be higher than what we're going to call the threshold energy
36:21
Which means that it has to each photon has to have a high enough energy or think about you know How is that related to frequency a high frequency? In Order to go ahead and eject an 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 blast it with as much intense light as possible
36:42
But if it doesn't have that minimum frequency, it's not going to eject an electron Now we call that minimum energy the work function So for example violet light can eject an electron from potassium But if you shine red light on it So remember a little comic with Foxtrot and you know, we know that our blue and our violet are higher energy than our red
37:01
So violet light can eject an electron from potassium, but it doesn't matter how much red light You're never going to get any so if you shine a little bit of violet light on potassium metal You'll get a little bit of electrons if you shine a bright violet light on it meaning more intense You're gonna get tons of electrons now if you shine the brightest red light you could possibly find on that potassium metal
37:23
You're still not going to get any electrons Okay, so what is the frequent the threshold frequency? How can we find it? Well, we can use e equals h nu to determine it and then you just have to take off the work function
37:41
So we'll do some examples of that in a minute So this this is one of the major things that show the wave particle duality of light Now if you want to do kind of a lab a computer simulated lab on how this works I would suggest going to this web page. They have a great simulation on it It works best if you play with it on your own rather than me showing you how to play around with it
38:03
So I'm gonna leave that for you guys, but you know go there and play around with it a lot It will really really help you understand on your homework and understand all the conceptual questions. I asked on the exam what's happening? So Consider that a homework assignment just like everything else
38:20
Okay, so now looking at this in a little bit more detail So this is the potassium example I had from before where I just sort of talked it through Now if you go through and you put in just enough energy to knock the electron loose So in other words, it's going to be exactly the energy of the work function. So
38:42
Just reminder work function is the lowest energy you need to eject an electron if you put on exactly that much It's not going to have any the ejected electron won't have any energy You're putting just enough energy in to knock it loose, but not enough to give it any energy at all
39:00
Now if the energy of the photon is higher than the threshold, so it's higher than just that work function Now all there's extra energy there. Where is the extra energy going to go? Well, it has to go somewhere and where it goes is into the kinetic energy of the ejected electron So if you increase the energy of a photon it increases the kinetic energy of the ejected electron
39:23
so Here if we look at this example Our red light our lowest energy of the three lights comes in and that's not at the threshold frequency And so that's not going to eject any electrons now if You put in green light that's high enough energy to go ahead and eject electrons and it's going to do so at this speed
39:48
Now, let's increase the energy again Into violet light so we get a much higher energy Now things to sort of note here and when you play around with that simulation
40:01
You'll note this to some extent too If you put in one photon the most energy or the most electrons you can get is one electron So if you want more photon or more 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
40:21
If you're below the threshold frequency, no photons are coming off at any speed. You're just stuck there You 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
40:41
Or I do that. I've just decreased the intensity of light I haven't changed the energy But I have decreased the intensity If I wanted to change the energy this light this light doesn't actually work because it's white light So there's there's a spectrum But let's say I had you know little flashlights here and I shined a red light if I want to increase the energy of the
41:01
Those photons I'd have to change it to blue light so Energy is very different from intensity Intensity is talking about total energy. So if I wanted to make a red light more intense Well, I turn on two of those same red lights if I want to make a blue light more intense I turn on two of those blue lights, but that doesn't speak to the energy of the photons
41:22
That's all about you can think of it as color if it's in the visible region It's what we see as color if it's in the non visible regions. The idea of color doesn't work so well So if we want to figure out this kinetic energy, it's what's left over after you take out the work function so we see h nu in here or
41:41
HC or lambda works too. That's our energy of a photon So the incoming photon and we just subtract out the work function we say, okay Well, there's a certain amount of energy of that photon that's going to be taken away It's going to be taken away and put into Actually knocking that electron loose. So we subtract the W and that gives us the kinetic energy
42:05
now What do we think happens if the intensity of light is increased but the frequency stays the same So remember we talked about intensity. We said it's just more and more and more light It's shining three bulbs instead of one bulb or ten bulbs instead of five bulbs
42:21
So if we increase the intensity are we increasing or decreasing number of photons? Well, we're increasing it right what our I see is being more bright means that more photons are hitting our eye And so increased intensity means more photons and the more photons you put in the more Electrons you're going to eject
42:46
so in that case You would get more just to restate that one more time as you increase the intensity you increase the number of photons thereby increasing the number of ejected electrons Okay, so let's walk through and do an example on the board with this. So we have calcium's work function
43:05
So now I've actually given it a number we call it a work function But in your guys's case It's always going to be a number that I'll either give you or I'll give you enough information for you to find it And I asked what is the minimum frequency of light for a photoelectric effect for calcium now
43:21
I could ask that a little bit differently. I could say what is the threshold frequency? I could ask you the energy I could ask you the threshold energy So make sure you know that term threshold that just means the minimum. I Could also ask you the maximum wavelength of light. So keep that in mind minimum frequency corresponds to maximum wavelength
43:42
Okay, so then I say calculate the kinetic energy and that's something that you're gonna see a lot in this chapter You're gonna you're gonna be doing two or three things with these equations working back and forth So we're gonna find the minimum frequency and then we're gonna find the kinetic energy of the electron if we now put this in so the work function
44:01
Will tell us the minimum frequency of light you need and then we can find the kinetic energy of that treatment problems, so I Wanted to put this in here like this because you'll you will see this in your book and you'll see this on the internet in Other random sources. So this is just another way of writing the work function. So don't think anything of that
44:21
I wrote it both ways so you can get used to seeing it both ways now If we look back on our last slide 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
44:42
We need to find frequency. We need to have kinetic energy, but we don't have kinetic energy, right? Well, we do What is the kinetic energy at the threshold frequency at the threshold frequency? Remember you're putting just enough light to knock the electron loose, but not enough light to actually give it any speed at all
45:03
So you're knocking it loose, but there's no speed or no velocity So your kinetic energy think back to your fundamentals, it's one-half MV squared So if there's no velocity, there's no kinetic energy. And so your kinetic energy is equal to zero and So because of that each new minus the work function is equal to zero
45:24
Well now we know H and we know work and we can just solve for new and so we end up with this So this is sort of the trick to making sure that you can find your threshold frequency
45:41
You have to remember that at your threshold frequency Your kinetic energy is zero and that's because your velocity or your speed is zero There's not enough energy in that photon to actually give the photo the electron any speed And so it's just going to knock it loose and it's not going to move anywhere and that gives you your threshold frequency
46:01
now we can go ahead and Also figure out our kinetic energy if we have this frequency of light So these are sort of the two of the main ways I can ask this question now we have this and We need to go ahead and find the kinetic energy
46:21
So we fill everything in we fill in our H we fill in the frequency that was given and We fill in our work function that was given and we get this Okay So one more Now notice in this question, we're taking it a little bit further. We're saying we have the work function for magnesium
46:46
We're calculating the minimum frequency of light required to eject the electrons. So that's the same thing We just did within we're calculating the kinetic energy if we change the frequency of light So again what we just did now, we're going to take it one step further though, and we're gonna say well
47:02
What about if we also want to know the velocity so that's sort of the extra step that we're going to do here
47:27
Okay, so we're gonna start the exact same way that we started in the last problem. So we start from Our kinetic energy equation and we remember that well at the threshold frequency our kinetic energy is equal to zero
47:51
So we can set that equal to zero which Now means that our new our frequency is going to be equal to W
48:02
Over Planck's constant so we can just fill those numbers in so we have this and Planck's constant
48:27
And we can get our number and of course you can write it in Hertz or you can write it in one over Seconds or you can write it in second inverse, whichever way you want to do it and you'll see your joules cancel
48:45
So that makes sense So that's our threshold frequency that answer is the first part or in other words to eject The electrons our minimum frequency our minimum energy our longest wavelength Now we can go through and we can do the second part What if now we're given a frequency of light of that?
49:04
what is our kinetic energy and Also our velocity our frequency Okay, so we go back to this equation again, you know draw a little line here So we know that we're starting a separate section. And once again, we're just filling everything in
49:30
So we fill in Planck's constant and we fill in our frequency and we subtract out our work function
50:08
Now that gives us our kinetic energy. So we fill that into a calculator and we solve
50:22
We get our kinetic energy But I also then asked you for one more thing. I said, what's the velocity? So now we can't quite end here. So this is kinetic energy Now we need to find the velocity
50:41
So in order to find the velocity we have to remember what our equation for kinetic energy is that we've used before So right now we've been using this equation because that's what works for this particular system but there's also the very general form of kinetic energy and that
51:05
is one-half and V squared and So we can go through and we can say well, okay now what is our velocity keeping in mind that it's an electron So if we know our kinetic energy and we know that that's equal to one-half now, what is M here?
51:31
Well M is our mass of an electron. So that's something that we would look up on an exam I would give it to you and then we would have V squared
51:47
Now notice this is one of those places that we get into the idea of we have both frequency and new and they're in one Equation, so make sure not to mess them up. This was new for the threshold frequency This was new for this frequency and this is V for velocity
52:03
So now we go through and we solve this and we get our velocity So that's sort of the other way that you'll be asked to do this on
52:23
Relatively regular basis and of course the backwards directions of all of those is fair game as well I can always give you the frequency and ask you for the kinetic energy and then ask you to use that kinetic energy to Solve for the frequency of light that was actually given
52:45
Now this comes up in your book And so I wanted to have you guys look at it a little bit and it comes up in your homework in it And I think it's good to always look at these graphically and see what's happening, too So in this graph we have three different metals and You can notice something about this. It's a linear right as you increase the frequency
53:05
You increase the kinetic energy and you do that linearly Now it's linear up until a certain point Or I should say after a certain point before that It's just zero So when you look at this in your book and you're asked questions on it
53:21
You can see that this is just zero until you hit this threshold frequency and at that point It's a linear relationship Now, what is that linear relationship? Well, we can look at the equation to show us that if We have this equation We can kind of look at it as y equals mx plus b, right?
53:43
So if we look at this as y equals mx plus b Where this is our X what is our M? Well, our M would be H so our slope here is H and So that's one of the places where you can sort of derive H out of and you can say, okay Well H is a constant that is going to be given to me
54:02
But it does come from somewhere and this is one of the places where it you're gonna be able to see it kind of Show up and you can actually graph it and you could find the answer so you're asked to do that at some point where you have to fill in a graph and you're given the incident wavelengths and you're given or the frequencies and you're given the Kinetic energies and you have to graph it and then you solve for the slope and then that's what gives you H
54:26
Okay, so that's what that's kind of gets us through the particle aspect of this so Keep this in mind as you're doing your homework that this is a good graph to have in your mind
54:42
It's going to increase as you increase the metals and that sort of wraps up the photoelectric effect and the sort of particle Aspects of this next time we'll go into more of the wave Interference and more of the ways that we can look at this and say okay Well light might be might act like a particle here, but it's definitely a wave too
55:02
And so there's there's experiments just like the photoelectric effect that we'll go ahead and show us that
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