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Heisenberg's Uncertainty Principle

Pearson
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Heisenberg's Uncertainty Principle is one of the most important and fundamental principles in our understanding of atomic theory. However, Heisenberg's Uncertainty Principle is also very difficult to get a conceptual understanding or a physical feel for how to use it and how it gets expressed in real chemical systems. So, Heisenberg's Uncertainty Principle is often expressed mathematically in terms of this equation. Where "delta x" represents the uncertainty in position "delta p" represents the uncertainty in momentum and the product of those two always has to be greater than or equal to Planck's constant "h" divided by "4π". So, in this case if you know the position well, then you can't know the momentum very well or the velocity and vice versa. If you know the momentum or the velocity well for a particle, you're not going to know the position very well. But again, how does that get expressed in real physical systems? So, in this case we're going to demonstrate this using another virtual experiment in Virtual Chemlab. Where we're going to perform the two-slit diffraction experiment. In the two-slit diffraction experiment, we have a laser. And this laser we're able to tune or adjust the wavelength to anything that we want. In this case we've adjusted it to 500 nm. And we can also control the power or the intensity of the light coming out of the laser. We have here a two-slit device. Now this is virtual it's actually difficult to do this in a real experiment. But in this case we have two infinitely long splits spaced in this case 3 μm apart. Or 3 times 10 to the minus 6 meters or 3 times 10 to the minus 3 millimeters. And we're going to detect the light using this video camera. So in this case this video camera, the output of this video camera is going to be shown here in this screen as well. So in this case we a 500 nm light The intensity is 1 nW or considerably pretty high going through two slits that are spaced at 3 μm, and we're going to see what happens here. In this case you notice that there are these light spots and dark spots. This is caused by constructive and destructive interference. What is the cause of this dark spot region right here? We can understand constructive and destructive interference in terms of light waves. So if we assume the light coming out is a wave, you can think of constructive interference or these light regions as where the light adds together and gives us an enhanced brighter signal and the dark region is where the light comes together and subtracts or one wave subtracts from another and gives us a dark region. So you can see that this is pretty clearly we can treat light as a wave. It behaves like a wave. It gives us diffraction patterns, it gives us constructive and destructive interference. But now the question becomes what's going to happen if we change the intensity of the light? What if we turn it down and we only have a single photon at a time going through the two slits? See, remember when we had a lot of light, we had lots of photons and we can imagine those interacting with each other. But what's going to happen if I turn down this laser and I only get one photon at a time in the slits? What's going to change, if anything? So let's go do this experiment and see what the answer is. We're going to turn down the intensity of our laser and turn it down to 100 photons per second. So imagine that we have a single photon in the slits at a time. So imagine we have a 100 photons in a line coming through the slit at any one time but only one photon is in the slit. So there's nothing for it to interact. We see something quite different. We don't see a diffraction pattern and we see these individual photons hits on our detector screen here. So notice that you can't predict where any one photon is going to hit. It could be here, it could over there. You can kind of see that they're congregated in the middle, ut there's no real way to predict where each photon is going to hit when we have individuals. So perhaps the answer is that we have a very different experiment now because we only have single photons in the slits. Let's go do something virtual and let's save where all these photons hit the screen. So we'll click on that persist button and save where it hits. And you notice that over time you start building up and you start seeing a diffraction pattern again. So that's really interesting. We only have a single photon in those slits at a time. But how do we get diffraction, if it has no other photons for it to interact with? Will this is another expression or a better expression of Heisenberg's Uncertainty Principle. Notice that we had single photons we couldn't predict where it was going to go, our uncertainty was very high in the position because we knew the wave length, so therefore we knew its momentum because we knew the wavelength, so therefore we knew its momentum well so we knew the momentum but we didn't know its position so we couldn't predict where that photon was going to hit. But if I save over time and get good statistics. So I have lots of photons saved over time then I can start seeing what that pattern is going to be and I'm going to get that diffraction pattern. In the first experiment when I had high intensity I had lots of photons lots of statistics. My statistics were high, my probability was high so I could see a diffraction pattern. So both experiments turned out to be the same, one was just an expression of Heisenberg's Uncertainty Principle and that I didn't know its position. So when it comes to the atom, same idea when we have a single atom with a few electrons floating around it we don't know, we don't have good statistics, we can't predict where that electron is going to be, so we talk about probability. But when we have lots of atoms and lots of interactions going on, we have great statistics and so our predictive ability is better.
Heisenberg's Uncertainty Principle is one of the most important and fundamental principles in our understanding of atomic theory. However, Heisenberg's Uncertainty Principle is also very difficult to get a conceptual understanding or a physical feel for how to use it and how it gets expressed in real chemical systems. So, Heisenberg's Uncertainty Principle is often expressed mathematically in terms of this equation. Where "delta x" represents the uncertainty in position "delta p" represents the uncertainty in momentum and the product of those two always has to be greater than or equal to Planck's constant "h" divided by "4π". So, in this case if you know the position well, then you can't know the momentum very well or the velocity and vice versa. If you know the momentum or the velocity well for a particle, you're not going to know the position very well. But again, how does that get expressed in real physical systems? So, in this case we're going to demonstrate this using another virtual experiment in Virtual Chemlab. Where we're going to perform the two-slit diffraction experiment. In the two-slit diffraction experiment, we have a laser. And this laser we're able to tune or adjust the wavelength to anything that we want. In this case we've adjusted it to 500 nm. And we can also control the power or the intensity of the light coming out of the laser. We have here a two-slit device. Now this is virtual it's actually difficult to do this in a real experiment. But in this case we have two infinitely long splits spaced in this case 3 μm apart. Or 3 times 10 to the minus 6 meters or 3 times 10 to the minus 3 millimeters. And we're going to detect the light using this video camera. So in this case this video camera, the output of this video camera is going to be shown here in this screen as well. So in this case we a 500 nm light The intensity is 1 nW or considerably pretty high going through two slits that are spaced at 3 μm, and we're going to see what happens here. In this case you notice that there are these light spots and dark spots. This is caused by constructive and destructive interference. What is the cause of this dark spot region right here? We can understand constructive and destructive interference in terms of light waves. So if we assume the light coming out is a wave, you can think of constructive interference or these light regions as where the light adds together and gives us an enhanced brighter signal and the dark region is where the light comes together and subtracts or one wave subtracts from another and gives us a dark region. So you can see that this is pretty clearly we can treat light as a wave. It behaves like a wave. It gives us diffraction patterns, it gives us constructive and destructive interference. But now the question becomes what's going to happen if we change the intensity of the light? What if we turn it down and we only have a single photon at a time going through the two slits? See, remember when we had a lot of light, we had lots of photons and we can imagine those interacting with each other. But what's going to happen if I turn down this laser and I only get one photon at a time in the slits? What's going to change, if anything? So let's go do this experiment and see what the answer is. We're going to turn down the intensity of our laser and turn it down to 100 photons per second. So imagine that we have a single photon in the slits at a time. So imagine we have a 100 photons in a line coming through the slit at any one time but only one photon is in the slit. So there's nothing for it to interact. We see something quite different. We don't see a diffraction pattern and we see these individual photons hits on our detector screen here. So notice that you can't predict where any one photon is going to hit. It could be here, it could over there. You can kind of see that they're congregated in the middle, ut there's no real way to predict where each photon is going to hit when we have individuals. So perhaps the answer is that we have a very different experiment now because we only have single photons in the slits. Let's go do something virtual and let's save where all these photons hit the screen. So we'll click on that persist button and save where it hits. And you notice that over time you start building up and you start seeing a diffraction pattern again. So that's really interesting. We only have a single photon in those slits at a time. But how do we get diffraction, if it has no other photons for it to interact with? Will this is another expression or a better expression of Heisenberg's Uncertainty Principle. Notice that we had single photons we couldn't predict where it was going to go, our uncertainty was very high in the position because we knew the wave length, so therefore we knew its momentum because we knew the wavelength, so therefore we knew its momentum well so we knew the momentum but we didn't know its position so we couldn't predict where that photon was going to hit. But if I save over time and get good statistics. So I have lots of photons saved over time then I can start seeing what that pattern is going to be and I'm going to get that diffraction pattern. In the first experiment when I had high intensity I had lots of photons lots of statistics. My statistics were high, my probability was high so I could see a diffraction pattern. So both experiments turned out to be the same, one was just an expression of Heisenberg's Uncertainty Principle and that I didn't know its position. So when it comes to the atom, same idea when we have a single atom with a few electrons floating around it we don't know, we don't have good statistics, we can't predict where that electron is going to be, so we talk about probability. But when we have lots of atoms and lots of interactions going on, we have great statistics and so our predictive ability is better.