AP Chemistry Light

Hello, and welcome back to Educator.com, and welcome back to AP Chemistry.0000

Today, we are going to begin our discussion of elementary quantum mechanics.0005

We are going to begin with a discussion of light and the general behavior of light--things like frequency, wavelength...some of it is properties.0011

This is, for me personally, really an extraordinary, extraordinary topic.0021

For those of you that are chemistry majors and physics majors, you have some really, really amazing things to look forward to, because when you take your course in quantum mechanics in the next couple of years (probably in your junior or senior year), it really is an extraordinary, extraordinary class.0027

It's very, very unusual in the sense that particles--they just don't behave the way you expect them to.0044

It is all very, very counterintuitive, and yet it's all very, very beautiful.0054

It begins with our discussion of probably the most ubiquitous thing in our life, which is light.0058

Now, I have to warn you: this particular topic and the next couple of chapters that we are going to discuss (which is going to consist of bonding, basic bonding theory, other bonding theory)...we run the risk of actually saying too much when we discuss some of these things.0066

And it is interesting: these are some of those topics that, by saying too much about them, you actually end up causing some confusion.0087

Now, I am hoping that we don't actually fall into that trap, so if it seems like some of the things that I'm saying are just sort of...I'm dropping them, dropping them, dropping them, there is a saying in a lot of science: "Much of science seems to be difficult to understand; it's just a question of getting used to it."0094

So, if there is something that you can't completely wrap your mind around, don't worry about it: the more we discuss it, the more problems we do--you will actually get used to it, and you will sort of become accustomed to it, and understand it sort of from the back end, as opposed to from the front end.0111

That is just the nature of some of the things that we are going to be discussing.0127

With that, let's just sort of jump in and see what happens.0130

OK, so a fancy term for light: you all know what light is, at least from your daily experience with it; a fancy term for light is electromagnetic radiation.0134

Let me write that down: A fancy term for light is electromagnetic radiation.0146

So, yes, light is a form of radiation; so when you are exposed to light, you are being exposed to a type of radiation.0165

Now, electromagnetic: well, that is because electricity and magnetism are actually two sides of the same phenomenon.0173

Two sides of a coin: electricity and magnetism are not separate things--they are actually different aspects of the same force, the electromagnetic force.0180

Light is energy; OK, energy travels in waves.0192

Any time you see, let's say, a wave on an ocean--what you are looking at is energy that is being transmitted through the medium of water.0208

That is what it is: if there were no energy being transmitted through the water, the water would just be like a swimming pool.0220

But, there is energy being transmitted through that water, and that energy takes the form of a wave.0226

Well, electromagnetic radiation is a form of energy; light is energy, and it travels in waves.0231

These EM waves have different energies, and in a minute, I will actually draw out the electromagnetic spectrum, so that you can see the different types of light that make up this thing that we call electromagnetic radiation.0241

These EM waves have different energies, but they all travel at the same speed, which happens to be--well--the speed of light...because that is what light is: light is electromagnetic radiation.0265

The symbol is c, and it is equal to 2.99x10⁸ meters per second (or 186 thousand miles per second)--very, very, very fast.0287

OK, now, waves have 3 things: they have speed; they have something called frequency; and they have something called wavelength.0303

Wavelength is pretty descriptive--it's the length of the wave.0321

Frequency--a little bit less descriptive, but we will define what it means in just a second.0324

Speed, we have already dealt with; it is the speed of light; so c is the speed of light.0330

Every type of electromagnetic radiation travels at the same speed: radio waves, x-rays, gamma rays, ultraviolet light, infrared...all of these things...microwaves...they all travel at the same speed.0338

It is their frequency and wavelength that distinguishes the different types of light.0350

Visible light, the light that we see, is a very narrow band, a very small part of the electromagnetic spectrum; it travels at 186,000 miles per second, 3 times 10⁸ meters per second.0355

OK, so let's draw out some waves here: so let's draw out a broad wave, and let's draw out something that is a little less broad, something like that.0367

OK...actually, I'm going to carry this wave out a little bit further.0377

A wavelength is exactly that: it is the length of one cycle: top of the wave, bottom, top of the wave--it's repeating--top of the wave, bottom, top of the wave; top of the wave, bottom, top of the wave.0381

This thing is called the wavelength, and its symbol is lambda--the Greek letter lambda--and that is the standard symbol for wavelength.0399

It is the length of a wave, usually from crest to crest; I mean, you can measure it any way you want, but the crest to crest is usually a good reference point.0413

You can go trough to trough--that is fine--but it's just the length of one wave.0423

OK, so let's see here: let me actually redraw these: so we have one, and then there we go; so let's do this again.0429

This is lambda; that is wavelength; and this is another lambda--this is another wavelength; so notice that this wavelength is actually smaller.0445

Well, so lambda is equal to the wavelength, and it has units of length.0457

It's exactly what it sounds like: sometimes it's expressed in meters; sometimes it's expressed in nanometers, centimeters...whatever the problem at hand seems to require.0470

Because we will be using mostly 3x10⁸ meters per second (it's the speed of light), we will be using the unit of length as a meter; but the problem might ask it in nanometers; you just have to learn to convert it.0480

So again, we have to watch our units in all of science, but particularly in quantum mechanics.0494

A frequency...well, I'm going to make this symbol: this is a symbol, the Greek letter nu (the Greek letter for n).0500

It looks like a v; it is not a v; my nus are probably a little different than most other people's nus--most people just sort of do it that way.0509

I don't like that: the reason is because I don't like to confuse it with velocity.0516

It happens sometimes, because velocity shows up--the letter v does show up in quantum mechanics; so it can be a little bit confusing if you are not careful.0521

This is called the frequency, and I will explain what it is in just a second: it is the number of cycles per second.0531

A cycle is just a repetition.0542

The unit of frequency is called a hertz, and its unit is per second, or usually, s^-1.0550

It is actually cycles per second; you can think, if you will, for those of you that are familiar with trigonometry, radians per second--because again, remember, a radian is just going around a certain number of times.0561

You are going through a cycle; but this cycles part, we usually don't put in there; we just say "per second," so 13 hertz is 13 cycles per second.0571

That means, in every 1 second, the wave goes through that many cycles.0582

Well, a cycle is exactly what you think it is: it is the periodic motion of the wave.0586

So, in this case, from here to here is one cycle.0590

It is 1, 2, 3, 4, 5; so let's say, in this case, if this were a time length of 1 second, this would be like 1 cycle; this would be like 1, 2, 3, 4, 5; so this would be 1 hertz and 5 hertz.0600

That is the thing: the wavelength is the length of a wave from crest to crest of the wave; the frequency is the number of those waves--number of cycles that actually happen per second.0617

OK, so now we have a relationship between these two--a very, very important relationship.0633

The speed of light is equal to the wavelength, times the frequency of the particular type of light that we are talking about.0639

Another way of expressing this is: equals c over lambda.0647

It doesn't matter which one you actually use; you are going to be using it in both forms; I tend to remember it (I personally) as this: Nu equals c over lambda.0653

Notice that nu and lambda (frequency and wavelength) have an inverse relationship.0662

In other words, if the wavelength gets longer--gets bigger--the frequency gets smaller.0685

As the wavelength gets smaller--shorter--the frequency increases.0696

You can see that from the picture: this is a long wavelength, small frequency; this is a very short wavelength, high frequency.0704

Per second: one wave passes per second; in one second, five or six waves pass per second.0717

The wave is smaller here; the frequency is greater.0725

That is the relationship: so, a profoundly important relationship here.0729

Now, let's go ahead and actually draw out the electromagnetic spectrum and see what it is that we are looking at.0734

I'm going to do it this way--that is that, and I have this over here...this is going to be wavelength, and I'm going to use units of meters; and this is going to be frequency, and it is going to be in units of hertz (or per second).0742

This is the EM spectrum; OK, so let's go ahead and do 10, 10^-2, 10^-4, 10^-6, 10^-8, 10^-10, 10^-12...all right, I guess we can stop there.0760

Let's go here: 3x10⁸, 3x10¹⁰, 3x10¹², 3x10¹⁴, 3x10¹⁶, 3x10¹⁸, and 3x10²⁰.0795

Radio waves are somewhere around here.0829

Radio waves have a wavelength of about 10 meters, so each wave of a radio wave is about 10 meters long.0832

Its frequency is about 3x10⁸ hertz--not bad.0840

TV is somewhere around there--a little bit shorter; microwaves--microwave radiation is on the order of about 10^-3--that is how long it is in terms of meters, so .001 meter--that is how long a microwave is.0850

And its corresponding frequency is just about there, so 10^-4; here we are talking about infrared radiation, and let's see: let's go over here to about 10⁸; we have ultraviolet radiation.0875

We have x-rays just about here, and we have gamma rays just about here.0895

So you notice: radio waves, microwaves, infrared, ultraviolet, x-ray, gamma ray: the wavelength is getting shorter.0903

As the wavelength gets shorter, the frequency gets higher; that is the inverse relationship: notice--short wavelength: the more energy that wave has, the more powerful it is, the more damage it will do.0911

So, shorter wavelength--more damage; higher frequency--more damage.0928

OK, visible light fall in this range, just about here.0936

I'm going to magnify this: somewhere in the 10^-6, 10^-7...so I'm going to go ahead and expand that.0944

What you have is 1, 2, 3, 4, 5, 6; 1, 2, 3, 4, 5, 6; red, orange, yellow, green, blue, indigo, and violet.0956

Here, you are looking at about 7x10^-7 meters and 4x10^-7 meters.0970

So, all of this electromagnetic radiation--all of this is light.0982

This little region in here, between waves that have a wavelength of about 4x10^-7 meters all the way up to 7x10^-7 meters--that is the light that we see; that is visible light.0987

It is a form of radiation; it is part of the electromagnetic spectrum; in other words, the light that we see is an electromagnetic phenomenon.1003

It travels in waves, and this is the range of wavelengths for these.1011

Red is about 7x10^-7 meters; violet light, 4x10^-7 meters.1016

Smaller wavelength for higher frequency; it's more powerful.1024

Ultraviolet--that is what gives you the sunburn; so the radiation that we experience from the sun is actually in this range.1029

Ultraviolet and infrared: infrared is heat; when we feel heat, we are actually feeling infrared radiation--radiation that is electromagnetic in nature, and the wavelength of that light is on the order of 10^-5, 10^-6, things like that.1038

That is all that is going on here: this is the standard electromagnetic spectrum.1055

OK, so let's do an example...yes, I guess we can do it on this page: not a problem.1060

Example: OK, the red colors you see in fireworks is due (oops, hey, look at that--we have our crazy lines back again! OK) to the emission of light at around 650 nanometers (so here we gave it to you in nanometers) from strontium ions whose electrons have been excited to higher energies, then have fallen back down to lower energies to release the excess as light.1068

OK, so any time you see a firework, and you see the red part of the firework (whatever that happens to be), what you are seeing is a strontium ion whose electrons are...basically, we explode things; and when we explode them, that energy--the ions--it actually kicks up the electrons in the strontium ion to a higher energy level.1171

Well, it doesn't like being up at the higher energy level; it falls back down automatically--it's a spontaneous process for it to fall back down.1195

When it does that, that excess energy that it absorbed to rise--it actually gives it off as light; and the wavelength of that light is 650 nanometers, which happens to fall in the red range.1201

There you go; OK, so let's see: Calculate the frequency--that is our...1219

Well, this is nice and easy: so we said that nu equals c over lambda; it equals 2.99x10⁸ meters per second, over 650 nanometers (nano- is 10^-9, so we can just write 650x10^-9 meters).1236

When we do this, we get: a frequency is equal to...see, watch: meter cancels with meter; you end up with: on the bottom, it's 4.6x10¹⁴s, which is 4.6x10¹⁴ hertz: that is the frequency of the red light that you see in fireworks.1263

OK, so now, let's move on to our next phase; and again, we are just going to sort of throw out some ideas.1291

We are not going to get into too much explanation about it; a lot of the explanation will sort of come in the process of our discussion.1300

A lot of the really detailed explanation will come in courses that you take later on; so we are going to, in some sense, ask you to take this stuff on faith.1307

And it has actually worked out pretty well, because we enjoy the life that we enjoy around us: that has confirmed the fact that this stuff actually is true.1315

OK, so energy can be gained or lost in discrete units only, and that unit is hν, where h is the Planck constant (and that constant is 6.626...this has been determined experimentally...times 10^-34 Joule-seconds; not Joules per second--Joule-seconds).1323

OK, and nu, as you know, is the frequency of the light of that energy; that is the frequency of electromagnetic radiation emitted or absorbed.1382

Emitted...I can't remember whether it's 2 t's or 1; oh, well--it doesn't matter.1406

OK, emitted or absorbed: so energy...we think of energy rising continuously or dropping continuously; as it turns out, it doesn't happen continuously.1412

It is very, very small, and it seems continuous, but energy moves in a stair-step fashion.1423

It doesn't go like this: it is not continuous--it is discrete; when energy rises or falls, it makes little jumps.1435

So, you have a certain amount of energy; the next amount of energy that you can have is actually a full unit up; or the amount of energy you can lose is a full unit down.1445

There are no in-between; it is discrete; it is not complete--it is not a continuum, like the real number line.1459

The real number line--if you were to put your finger anywhere on the real number line, you will always hit a real number.1467

As it turns out, energy is not like that; it is very, very discrete quantities; energy goes up in discrete units.1472

Now, this unit is very small; it is based on the particular frequency and this Planck constant, which is 10^-34; so it's true--from our perspective, it is so tiny that it actually looks continuous.1479

But it is not continuous; it is discrete, and that is what is important.1495

OK, so once again, let me rewrite that: the energy is Planck's constant, times the particular frequency--very, very important.1500

OK, so let's do another example: let's go to Example 2.1512

OK, for the previous strontium salts (or strontium ions, I should say...well, salts, because the actual material that we use in fireworks are the salts, but salts are made of ions, so...let me write this out a little bit better; I think I'm getting a little loose here), what is the increment of energy at that frequency?1521

OK, so we calculated a frequency of 4.6x10¹⁴ hertz (so I will write inverse seconds, hertz).1578

We want to know what kind of energy is associated with that red color in the fireworks.1591

Well, the increment of energy is equal to h times the frequency, which is equal to 6.626x10^-34 Joule-seconds, times 4.6x10¹⁴ inverse seconds.1598

Second, second, inverse second, and inverse second cancel, leaving me with Joules--energy!1626

That increment of energy--that is why I have this Δ; when we speak about an increment, I am just taking (in this particular case) the initial as 0.1633

It is equal to 3.05x10^-19 Joules.1645

Now, that is not a lot, but it is still a particular increment: so, in other words, if I have a unit of energy...so let's say I'm a ground level of energy--let's just call it a base level--the next rise in energy is 3.05x10^-19.1656

If I add a little bit more energy to that, it is not going to go to 4.06, 5.1...it is going to go to 6.1x10^-19.1673

And then, it is going to go to 9.15x10^-19; any jump that it makes in energy is going to happen according to this increment; that is it--nothing in between.1684

And, if that energy level is not available to it, guess what: it is not going to make that jump; that is the whole idea--that these are very, very specific jumps, based on the particular frequency of light.1696

That is pretty extraordinary: you think that, OK, let's say if I'm at 3.05x10^-19 Joules of energy, can I add just a little bit more heat to make it go to 4?1707

The answer is no, you can't, because it won't do that; it will stay at 3.05.1718

And then, when it reaches its threshold, it will jump to 6.10, and then 9.15, and then 12.20; that is the idea.1725

It jumps in discrete units.1734

OK, so let's see what else we have here: so let's play around with some of these equations that we have introduced, and one that you actually are familiar with, that we are going to go ahead and just use here.1737

We said that the energy is equal to Planck's constant times that; well, we also know, from Einstein's relationship, that energy equals mass, times the speed of light squared.1754

Let's go ahead and put ν=c/λ; so now, we are going to sort of combine all of these.1771

Well, energy--so we have mc²=hν; so m, which is mass, equals hν/c²; well, ν equals c over λ, so this is equal to hc/λc²; the c's cancel; h/λc.1777

OK, now, wait a minute: what is going on here?--this refers to energy; energy refers to waves--energy is about waves; mass has to do with particles.1812

Particles have mass; waves have energy; this is suggesting that (these are constants here) light of a certain wavelength--of a certain frequency--actually has a mass.1822

As it turns out, it does.1843

We call this particle, if you will, of light--this particle--we call it a photon.1849

It is light, which we know is a wave; and yet, it actually behaves like a particle in certain circumstances; so the energy of the photon of light is equal to hν.1861

This is not just the energy, but it is the actual energy that is associated with this particle, when I see the particle as some energy, or I have energy that I can actually convert to a mass, based on this.1876

Light--electromagnetic radiation--has a particle-like quality associated with it, and you can actually assign it a given mass.1890

That mass comes from this relationship.1901

OK, so now, let's see if we can take it a little bit further.1905

We have: a wave can behave like a particle.1913

Well, it begs (well, that is not a question; we know that) the question "Can a particle behave like a wave?"1925

OK, can a particle behave like a wave?1933

In other words, can a particle have a wavelength?--can it have a frequency associated with it?1943

Well, guess what: the answer is yes, it can.1948

OK, so let's mess around a little bit more here: so we have this relationship, m=h/λc; well, what is c?--c is just a velocity (right?--it's a speed; we call it c, but it's just a velocity; it is meters per second).1951

So, there is a real-world analog to this for things that are not travelling at the speed of light; it's exactly what you think it is--just replace this speed with a velocity.1968

Mass equals Planck's constant, over wavelength, times velocity (I'll just put vel).1982

Well, if I rearrange this, guess what happens: I end up with λ=Planck's constant, over the mass times the velocity.1990

Well, mass times velocity is momentum, for those of you who have taken physics; if not, don't worry about it; you can just do mass times velocity.2002

Now, stop and think about what this is saying: this is saying that, if that I have a certain mass something, like a truck, moving at a certain velocity; if I take the mass of the truck, multiply it by its velocity (the speed at which it is moving), and if I take Planck's constant and divide by that, I actually have a wavelength associated with the fact that it is moving.2009

So, it actually can display wave-like characteristics.2030

Now, for large objects (like a baseball, a bowling ball, a truck, an asteroid...), the mass of these objects is so massive that the wavelength is virtually buried; we don't actually notice the wavelength.2035

But, as it turns out, as the mass gets smaller and smaller and smaller, when you get down to the level of neutrons, protons, and particularly electrons and smaller particles, the wave-like properties actually start to manifest in really, really strange and beautiful and clear ways.2055

In fact, the whole idea of electron microscopy is based on the fact that the electron is not just a particle, but it actually behaves like a wave.2072

If it didn't, we wouldn't be able to use the electron to actually see the things that we see.2080

That is the whole idea; so let's go ahead and do an example.2085

This is Example 3: We want to compare the wavelength of an electron travelling at 5.0x10⁷ meters per second, and a 4.50 gram bullet going 950 meters per second.2093

OK, so we are going to use this equation, which is called the de Broglie equation (after a Frenchman named Louis de Broglie): it actually gives us the wavelength associated with a certain mass moving at a certain velocity.2131

We have an electron that is travelling at 5.0x10⁷ meters per second (very, very fast), and a bullet, which is 4.5 grams, and it is going 950 meters per second (also very, very fast).2151

We want to see what the wavelength is associated with that; what is the wave-like property of that particle?2164

OK, so let's go ahead and calculate the wavelength of the electron: so it is going to be Planck's constant, 6.626x10^-34 Joule-seconds...oh, actually, we can't use the Joule here; we have to remember...2169

Here is why: we have to make sure that our units actually work out; so this is going to be lambda; our unit has to be in meters.2188

So, if we recall, the Joule is a derived unit: the Joule is equivalent to kilograms-meter squared per second squared.2196

So, a Joule-second is equal to kilogram-meter squared per second (right?--Joule-second--the second on top cancels one of the seconds down below).2208

That is the unit; so it is going to be kilogram-meter squared per second; now, that means that mass has to be expressed in kilograms, because kilograms (the units) have to match.2227

The mass of an electron (when we look it up in a table) is equal to 9.1x10^-31 kilograms (it's actually in the back of your book).2241

The speed is 5.0x10⁷ meters per second.2253

Here we go: kilogram cancels kilogram; meter cancels 1 meter; second cancels second; sure enough, we are left with a unit of meter; so everything works out just fine.2258

Well, the wavelength of the electron happens to be 1.45x10^-11 meters.2268

And, if you want to take a look, that is on the order of the length of the wavelength of an x-ray--which is actually going to be important in just a minute.2282

So now, let's go ahead and do the wavelength of the bullet: so the wavelength of our bullet is equal to 6.626x10^-34 kilogram-meter squared per second, divided by the mass (which, again, has to be in kilograms, so...) 4.5 grams is 0.0045 kilograms; and we said it's travelling at 950 meters per second--very, very fast.2293

Second cancels second; meter cancels one of the meters; kilogram goes with kilogram; and what you end up with is 1.5x10^-34 meters.2331

There you go: you have a bullet that is a standard bullet, 4.5 grams; it is travelling at 950 meters per second; there is actually a wave associated with the energy that...2345

I'm sorry, it's not a measure of the energy of the bullet; that is different; that is kinetic energy (one-half the mass times velocity squared); this is different.2358

This is--the bullet--instead of thinking about it as a particle travelling through space, we are thinking about it as a wave travelling through space.2369

Now, that wave does damage; it does damage as a particle; but there is a wavelength associated with it.2381

The reason that we don't actually experience that wavelength, or some of the properties associated with this wavelength, is because the mass of the bullet is so big, and this is so immeasurably small, that it goes virtually unnoticed.2387

However, it does prove that (it goes to show that) a particle does have wave-like behavior, just like a wave (which is pure energy) has particle-like behavior.2402

This is the great--I don't know what to call it--the great unique thing about quantum mechanics--that, as you get smaller and smaller and deal with smaller particles at the atomic and molecular level, are you talking about a wave?--are you talking about a particle?2415

What is going on?--are you talking about pure energy, or are you talking about actual mass?2433

Well, both: they are just different sides of the same coin.2437

So, let's make some observations, and we will go ahead and close off this discussion.2442

1.45x10^-11 is on the order of the wavelength of an x-ray--is on the order of the ϣ of x-rays.2448

As it turns out, shooting a beam of electrons...2468

Now, an x-ray is a wave; it is light; it behaves as light, and light has certain waves behave in certain ways that particles don't.2477

All of classical physics is based on the fact that waves behave one way; particles behave another way.2491

So, now, shooting a beam of electrons at a crystal gives a similar pattern to the diffraction pattern seen when x-rays strike the crystal.2499

When you shine x-rays at a crystal, the spaces in between the crystals actually take the light (which is in the form of x-rays; you know what light is--our general term--we are not talking about visible light), and it actually diffracts it, and it gives you a particular pattern.2544

Well, that pattern is unique and tells you what the structure of the crystal is.2562

That is how we get molecular structures for all of the biological molecules that we actually know what they look like--we actually crystallize them; we shine x-rays at them.2567

Well, here is what is interesting: this diffraction pattern is characteristic of waves--not characteristic of particles; particles don't do this; waves do this.2575

Diffraction is a wave property, not a particle property.2584

Well, check this out: when I take a beam of electrons (which are particles--we know that they are particles), and we shine them at the crystal, guess what happens.2587

We get the same diffraction pattern; that is very, very odd--that confirms the fact that particles behave like waves.2595

So, a particle (which, in this case, is the electron) behaves like a wave.2605

OK, so this was our general discussion: I'm going to go ahead and stop the discussion here.2621

The next time, we will go ahead and pick it up with a discussion of electrons in atoms, with an introduction to real quantum mechanics, and talk about electrons and how they behave.2626

But, I definitely wanted to get a good foundation, here, for light, how it behaves, the idea of wavelength, the idea frequency, and the idea of energy being quantized.2639

The big word is "quantum," and that just means packet--the Latin word for a little package.2651

The idea is that energy is quantized.2660

Energy rises and falls in discrete units; it does not rise or fall continuously, like some functions that we are accustomed to seeing.2663

It is very, very discrete; it is a stair-step function, is what it is.2675

With that, thank you for joining us here at Educator.com.2679

We'll see you next time; goodbye.2682