I measured Planck's constant at home

0:00 Einstein is famous for his equation: E=mc^2.

0:02 But do you know that he actually won

0:04 his Nobel Prize for an equally important equation: E=hf?

0:09 This equation is famous for relating energy

0:12 and mass via a constant, the speed of light.

0:16 And this equation is quite similar.

0:18 It relates the energy of light to its color via another fundamental constant,

0:24 called Planck's constant.

0:25 Now, this equation kicked off the field of quantum mechanics,

0:29 and this constant is the constant

0:31 that determines the size of most quantum effects.

0:34 So as you can imagine, it's super tiny.

0:37 But in this video we're gonna do a simplified

0:40 version of the experiment that won Einstein his Nobel Prize.

0:44 And in the course of it,

0:46 we're gonna measure this Planck's constant, all using some LEDs.

0:50 This video is sponsored by KiwiCo, by the way, more on them later.

0:54 I do wanna clarify one thing first.

0:56 So Einstein didn't do the experiment himself.

0:58 He got the Nobel Prize for explaining an experiment that other people had done.

1:03 And of course, that experiment didn't actually involve

1:06 LEDs because these things hadn't been invented yet.

1:09 Instead, it involved shining light on various types of metals.

1:13 It did something very unexpected.

1:15 See, this is what they would've expected from the classical theory of light.

1:20 Light has energy in it, and the brighter the light, the more energy it's got,

1:24 and the way that energy manifests for a wave is in its amplitude.

1:28 The bigger it is, the more energy it has.

1:31 In fact, the amount of energy in light is proportional to the amplitude squared.

1:36 So for the energy of the light,

1:38 it doesn't matter at all what the wavelength is, just how big the peaks are.

1:43 The wavelength just determines the color, but the amplitude is the energy.

1:49 The thing light wants to do with all of that energy

1:52 is donate it to a charged particle like this electron here.

1:56 When the electron is all alone, it can receive any amount of light.

2:00 The more it gets, the faster it flies off,

2:03 but it's a little bit more complicated when the electron is bound up in a metal.

2:08 The reason the electron is trapped in the metal in the first

2:11 place is because it doesn't have enough energy to fly away.

2:14 For each metal, there's a fixed amount of energy that the electron

2:19 would need to break free when light shines on it.

2:22 That's the electron's opportunity for escape.

2:24 The electron doesn't mind what color it is,

2:28 as long as there's enough energy in the light to break it out,

2:31 the electron can escape.

2:33 The extra energy then might just go into how fast it flies off.

2:36 Only this story is what you would expect from classical electromagnetic theory,

2:40 and it turns out not to be right.

2:44 When you actually do this experiment, you find that color does matter.

2:48 When the experimenter shines low frequency light on the metal,

2:52 no electrons get released.

2:53 This is true, even if you shine the light very brightly,

2:57 meaning it has plenty of energy to give.

2:59 The electrons in the metal just don't seem interested in it.

3:02 On the other hand, if you have high frequency light, the electron does take it.

3:08 So what's going on?

3:09 Both types of light have the same energy.

3:12 Why does the electron ignore it in one case, but absorb it in the other?

3:17 Einstein had a really neat solution to this.

3:19 He said, what if the total amount of energy just depends on amplitude?

3:24 So both of these have the same amount of total energy,

3:28 but whenever light like this wants to give

3:30 some of its energy to, let's say this electron,

3:33 it's not just the total energy that matters.

3:35 There's also one other factor that you have to take into account,

3:38 and that is that the energy from this light is broken up into chunks.

3:43 These chunks of energy are called photons.

3:46 As you can see, the red light,

3:48 which has low frequency, also has very low energy photons.

3:52 Whereas the blue light, which has high frequency, has high energy photons.

3:57 So that's what E equals HF is actually referring to.

4:02 E is the energy per photon, and F is the frequency of the light.

4:07 So in other words, the color.

4:09 We can see that if the frequency is low, that the energy is going to be small.

4:15 Whereas if the frequency is high, then the energy is going to be quite big.

4:19 When light interacts with an electron,

4:21 instead of giving that electron all of the energy,

4:25 it gives the electron just one photon's worth.

4:28 So let's say we have a color of light that has really big photons.

4:32 And so if that one photon has enough energy to free the electron,

4:37 the electron will take that freedom.

4:39 Plus any surplus energy will just go into its kinetic energy.

4:43 On the other hand, we might have another color

4:47 of light shining with a lot less energy per photon.

4:51 Now the electron won't get enough energy to escape from one photon,

4:55 so it doesn't take any energy at all,

4:58 even though many photons may be raining down on it.

5:02 None of them are good enough.

5:04 So the genius of Einstein isn't that he came up with this equation himself.

5:08 In fact, plank had come up with a very similar equation,

5:11 which is why this constant is named after Plank and not Einstein.

5:16 But when Plank wrote this equation down to solve another problem,

5:19 which was called Black body Radiation.

5:21 He just thought it was a cute mathematical fact,

5:25 but he never thought that it corresponded to anything physical.

5:28 He knew that light is made out of waves and there is no quantization of light.

5:35 Whereas Einstein took this equation seriously,

5:38 he said that, okay, light might be a wave,

5:42 but there is a thing that's quantized and that is the amount

5:46 of energy it's allowed to transfer to another object that comes in chunks.

5:51 And that kind of quantization is what kicked off the field of quantum mechanics.

5:56 It's where quantum mechanics even gets its name.

5:59 So this was an incredibly important result.

6:02 I wanted to do a version of this experiment that was totally foolproof,

6:07 and that's when I came across this LED version of the experiment.

6:12 We're essentially going to do Einstein's experiment in reverse now.

6:15 So Einstein's experiment shone light on some metal,

6:18 and then that made the electrons inside of that metal flow,

6:22 which you can measure inside of a circuit.

6:24 But here we're gonna do the opposite.

6:26 We're going to make electrons flow.

6:29 And those electrons are going to make light.

6:32 So let's say this is our circuit for the LED

6:35 and we have our battery with some fixed number of volts.

6:38 That means that an electron that goes through

6:41 this battery has picked up two electron volts.

6:44 So electron volts is just a crazy unit of energy,

6:47 but it's very convenient because it lets you go straight from the voltage

6:51 of the battery to the energy that the electron will have.

6:54 So by the time it goes around this circuit and to the LED.

6:58 It will give that two electron volts to the LED and then go back,

7:03 but we wanna figure out what the minimum amount of energy is.

7:08 Two electron volts is more than required for this LED to turn on each

7:13 one of these LEDs only gives out a very specific color of light.

7:18 So in other words, the LED determines the frequency of the light coming out.

7:24 This LED needs a certain minimum amount of energy to make one photon worth,

7:31 and that minimum amount of energy is given by the equation E equals hf.

7:37 If this electron has enough to meet that bar,

7:42 then this LED can make some photons.

7:46 If the electron doesn't have enough to meet that bar,

7:49 then the LED ignores it and doesn't light up.

7:52 So if we can get to the point where

7:55 this electron has just enough energy to light up this LED,

7:58 then we've figured out what that minimum amount of energy is.

8:02 And so in other words, we've measured what E equals HF is,

8:06 but we already know what F is.

8:08 'cause that's determined by the color of this LED.

8:11 So we can figure out what H is.

8:14 So what do we do?

8:16 We actually want to decrease the electron's energy on the path.

8:20 So we could just add a resistor.

8:22 The resistor is going to use up a bunch of the electron's energy,

8:26 so it's going to come out the other side with much less.

8:30 Depending on the size of the resistor,

8:33 the electron's energy might have gone down to, let's say,

8:37 just one electron volt.

8:38 And so now when it goes to this LED,

8:41 it only has one electron volt worth of energy to give,

8:44 and so we can test if that is enough to turn on the LED or not.

8:49 We can keep testing this with either bigger or smaller resistors,

8:53 and eventually we're going to find some energy, which we'll call e.

8:59 Which is the exact minimum amount of energy to turn

9:03 this LED on, but because it's the exact minimum amount,

9:07 we know that it must be equal to hf,

9:10 where F is given by the frequency of the red light.

9:14 And H, we can now measure.

9:16 So that's the experiment we're gonna do.

9:19 We're gonna do that though,

9:21 using these adorable mini breadboards from this kit, from Keli Co.

9:25 As I rig up this circuit, I wanna tell you a little story.

9:29 So when I was 12, I did this unit about electricity in school

9:34 and for the project we had to like make a circuit or something.

9:39 And I made this little, um, board game where there were a bunch

9:43 of like switches and you have to click things.

9:46 And I, I don't even know if it was fun to play,

9:49 but it was so fun to make and I learned so much.

9:52 And I remember at the end of that experience that I told everyone I wanna be

9:57 an electrician because I didn't really know that there

10:00 was such a thing as being a physicist.

10:02 But what's kind of crazy is that like all these years later,

10:05 I kind of fulfilled my childhood dream.

10:08 And it all started with a very simple little

10:12 experiment like this, a toy that I helped co-create,

10:15 and that's what I really love about Kiwi Co.

10:18 Every month Kiwi Co sends your kids a crate that they can use to make a project.

10:24 Then they can play with that project for the rest of the month.

10:27 I know how valuable that kind of exploration was for me,

10:30 and so I'm really excited for kids in the future to be able

10:34 to do these kind of experiments for themselves and learn things by doing,

10:39 for engaging projects that spark a passion for stem.

10:42 I think you'll really love Kiwi Co.

10:44 Click the link in the description or use my code

10:47 looking glass for 50% off your first kit at Kiwico.com/looking glass.

10:52 Okay, so look at what I made.

10:55 This little breadboard is actually the exact

10:57 same circuit as the one we drew here.

10:59 All that's happening is we have the battery pack and this here is the resistor,

11:05 and as you can see, it works.

11:09 But this is a very small resistor right now,

11:12 and so the energy of the electron is pretty close

11:15 to the two electron volts that it would've gotten from the battery.

11:20 We want a stronger resistor in here so that eventually there's

11:25 not enough energy to turn on the LED if we can

11:29 just keep trying different resistors until we get to the exact

11:33 point where this LED no longer turns on, then we'd be done.

11:37 But that is a lot of work.

11:39 Um, and so instead I bought this special little thing.

11:43 This is called a variable resistor.

11:45 So if I turn this little knob,

11:48 then it turns up the resistance from zero all the way to 1 million.

11:54 This is zero resistance, and then that is higher resistance.

11:57 So we wanna find the exact point where there's not enough energy to make light.

12:03 I think that might be it.

12:06 Let's see.

12:06 It's still a tiny, tiny little flicker of light.

12:10 Turn the resistance up a bit more.

12:13 I'd say that's off.

12:14 Okay, so now we're gonna use a multimeter to figure out how much energy this is,

12:20 this exact point where there's no longer enough energy to make.

12:25 Which should roughly be equal to hf.

12:28 The way we're gonna do it is we're going to measure the voltage across the LED,

12:32 but that's okay because there's a very simple way

12:35 to convert the voltage here to the energy the electron has.

12:39 All we have to do is whatever voltages is, let's say it's like 1.5 volts,

12:46 then the energy of the electron is equal to 1.5 electron volts.

12:52 So as long as we measure the voltage.

12:54 We know how much energy the electron lost as it moved across this LED,

12:59 so let us indeed measure that voltage.

13:02 Oh, nice.

13:03 1.5.

13:04 1.54.

13:05 The frequency of red LEDs like this is

13:10 typically around 4.7 times 10 to the 14 hertz,

13:15 and so dividing the top number by the bottom number would give us.

13:22 Planck's constant, but it'll only give

13:24 us one estimate of Planck's constant, right?

13:27 We have all these different LED colors,

13:28 so why don't we just do the same experiment for all of them

13:32 and then we'll see how good our estimate of Planck's constant is.

13:35 Okay, so the green LED is on.

13:38 Let's turn it off.

13:40 Okay.

13:41 That look like it was off.

13:43 Um, why is this happening?

13:48 Okay, so at this low level of resistance, this green light is still on.

13:55 It's very faint, but you can just about see that it's still not off.

14:03 I didn't get it.

14:04 Um, that doesn't make sense.

14:07 Okay.

14:08 Let's see.

14:09 Why is it 1.9?

14:11 It shouldn't be 1.9.

14:13 I am definitely doing something wrong.

14:16 I don't understand this.

14:17 I feel like this is going the opposite way than it should.

14:22 Okay, so it's a different day.

14:24 In fact, it's several days later because

14:27 when I was trying to do this experiment,

14:29 I kept getting a very unexpected result.

14:31 I thought this experiment was foolproof, but apparently not for me.

14:37 You see what happened was every time I turned down the voltage,

14:40 I'd still be able to see just a tiny little bit of light.

14:44 It never kind of turned off at some point.

14:47 Um, well, I looked into it and it turns out that that is

14:51 actually fairly easy to explain and I will tell you about that.

14:54 But after I answered that question for myself,

14:57 I had more and more questions about LEDs and P junctions,

15:01 and now I've learned much more than I thought there was to know.

15:05 So I think that's gonna have to be a separate video about LEDs.

15:09 But for now, let's just go back to the picture that we were using,

15:11 because that is more or less correct.

15:13 What we said before was that this electron goes around

15:16 this circuit with a certain amount of energy provided from the battery,

15:21 and it's able to dump that energy.

15:24 Into light at the LED and then go back less energetic.

15:29 If the electron has an energy of hf, then yeah,

15:33 it will definitely have enough energy to make some red light.

15:36 But what happens when the electron's actually

15:38 picked up less than that amount of energy?

15:41 Then surely there's no possible way

15:43 for the electron to go through and make light.

15:46 But this is where I was going wrong.

15:49 Actually.

15:49 There is, you see, there is the energy that the electron gets from the battery,

15:53 but there's always a small amount of thermal energy in any system,

15:57 and so this electron just has a certain amount of that that may be

16:01 enough with the small amount of energy gets with the battery to make light.

16:06 And so sometimes the electron will get enough energy from the thermal energy.

16:10 Plus the energy from this battery to make

16:13 light even if there's no battery whatsoever.

16:16 It's possible for this to happen.

16:19 In fact, apparently LEDs.

16:21 Emit about 20 photons per second,

16:23 even when they're not attached to anything else.

16:26 So this is why no matter how much I turned down the energy,

16:29 there was always a little bit of light,

16:31 and our eyes are insanely sensitive to light.

16:34 So even when it was very low, I was still able to discern it.

16:39 But it is still true though that.

16:41 If the energy drop across this LED is equal to HF or greater,

16:45 that there is gonna be much more light being produced.

16:50 So what we're looking for is the voltage where you transition

16:52 from a background amount of light to a very significant amount of light,

16:56 and that voltage at that transition is what solves this equation.

17:00 So let's do the experiment.

17:02 Okay.

17:03 So somewhere in there.

17:04 You can see that the transition doesn't happen at exactly one point.

17:09 It kind of, there is like a little bit of leeway in that transition.

17:13 So I'm not a hundred percent sure where to put it.

17:16 So maybe what I'll do is I'll record sort of a low number and high number,

17:21 like here's the high number.

17:23 Okay.

17:23 I reckon that's the low.

17:25 1.8 to 1.86.

17:26 Okay, I'll go ahead and do that for all the other ones.

17:31 1.8 5.9.

17:31 All right.

17:32 So I've done it for all of these except for the blue one because,

17:37 um, this battery was a bit too weak to like fully turn on this LED.

17:41 Now, what I would do if I was a good experimental scientist

17:44 is that I'd find out the frequencies of all of these LEDs.

17:47 And then I would plot these data points on a graph,

17:51 and from the gradient you would be able to figure out what plank's constant is,

17:55 and that would give you by far the best results.

17:59 But.

17:59 I'm not gonna do it.

18:01 I'm not gonna do it because, well,

18:03 mostly because I'm lazy and it would involve a little bit of work.

18:07 So let me explain.

18:08 Figuring out the exact frequency of this light is a little bit tedious.

18:12 And so instead I'm going to cheat,

18:14 I'm gonna use the fact that at least for this red LED,

18:17 I know exactly what the frequency is,

18:19 and from that I'll be able to use this threshold

18:22 voltage and figure out at least one estimate of Planck's constant.

18:26 I have no idea how accurate that's gonna be, but let's find out.

18:30 All right, so that's the frequency.

18:31 The threshold voltage is somewhere in there.

18:33 Let's rearrange to get H.

18:35 We're hoping that this is gonna be approximately equal

18:38 to 6.63 x 10^(- 34) meters squared kilograms per second.

18:47 Let's see.

18:49 This is an incredibly tiny number.

18:51 I would be happy just to like roughly get into the same order of magnitude.

18:57 So let's put in first our low threshold value

19:00 and see what we get for H or from Alpha

19:03 is really good for these kind of calculations

19:05 'cause it like deals with the units for you.

19:09 So let's see.

19:11 Okay, so that's crazy.

19:12 The number we were going for is this, and what

19:15 we actually got was 6.73 x 10^(- 34), basically.

19:21 Very, very accurate.

19:24 That's, that's crazy.

19:26 Okay, let me just try the high threshold

19:32 number to see if that was better or worse.

19:36 So that one would've given us this, which.

19:39 Yeah, it's a little bit worse, but still very, very close to the real thing.

19:44 Okay, so it turns out that you can measure this fundamental quantum constant

19:50 that is absolutely tiny and is what sets the scale for quantum mechanics,

19:57 um, using a single LED fairly accurately.

20:01 That's crazy.

20:01 This was a really fun experiment and it

20:05 went a lot better than my experiments usually go.

20:08 So thanks for joining.

20:10 And by the way, if you are interested in Kiwi Co, the link is in description.

20:15 Thanks very much.

20:16 Bye.