![]() So we take the mass of an electron, 9.11 times 10 to the negative 31st and we multiply that by the velocity, 2.2 times 10 to the sixth, and we know there's a 10% uncertainty associated with the velocity, so we get an uncertainty in the momentum 2.0 times 10 to the negative 25. So we need to multiply all of that by point one. Sixth, and we know that with 10% uncertainty, The velocity of the electron is 2.2 times 10 to the So we would have the mass of the electron is 9.11 times 10 to the negative 31st. If there's a 10% uncertaintyĪssociated with the velocity, we need to multiply this by point one. Uncertainty of the momentum of that electron, so the uncertainty in the momentum of that particle, momentum is equal to mass times velocity. We just divide 10 by 100, so we get 10% is equal to point one. With a 10% uncertainty associated with that number. So the linear momentum P is equal to the mass times the velocity. And since we know the mass of an electron, we can actually calculate ![]() So the velocity of anĮlectron in the ground state of a hydrogen atom using the Bohr model, we calculated that to be 2.2 times 10 to the six meters per second. Alright, we also did some calculations to figure out the velocity. And this is just a roughĮstimate of the size of the hydrogen atom using the Bohr model, with an electron in the ground state. So two times that number would be equal to 1.06 times 10 to So if we wanted to know theĭiameter of that circle, we could just multiply the radius by two. Of the first energy level, is equal to 5.3 times 10 Here, there's a radius for an electron in the ground state, this would be the radius Radius for the electron, so if there's a circle To understand things like quantized energy levels. The Bohr model is useful, is because it allows us Is going this direction, so there is a velocityĪssociated with that electron, so there is velocity Negatively charged electron orbits the nucleus, likeĪ planet around the sun. Picture of the Bohr model of the hydrogen atom. Uncertainty principle to the Bohr model of the hydrogen atom. The position of a particle, the less accurately you know So another way of saying that is, the more accurately you know Uncertainty in the position, you increase the And so, what I'm trying to show you here, is as you decrease the In the position even more, so if I lower that to pointįive, I increase the uncertainty in the momentum, that must go up to eight. Momentum must increase to four, because one times four is equal to four. Uncertainty of the position, so I decrease it to one, so the uncertainty in the Two is equal to four, so I won't even worry about greater than, I'll just put equal to here. Of two for the position, and let's say you had an uncertainty of two for the momentum. Just extremely simplified, so let's just see if weĬan understand that idea of inversely proportional. Really simple numbers here, just so you can understand that point. Inversely proportional to each other: if you increase Of the two uncertainties must be greater than orĮqual to some number. It doesn't really matter that much, it just depends on how you define things. Number on the right side, and you might see somethingĪ little bit different in another textbook. So we have a constantĭivided by another constant. And that constant is Planck's Constant: h divided by four pi. Two must be greater than or equal to some constant. Uncertainty in the position, times the uncertainty in the momentum, so Delta P is uncertainty in momentum, the product of these So the uncertainty in the position, so Delta X is the Mathematical description of the uncertainty principle. If you know the momentum really well, you don't know the position. ![]() Velocity of that particle, and vice versa. You don't know the momentum, or you don't know the If you know where that particle is in space really well, Uncertainty principle, you can't know the position and momentum of that particle accurately,Īt the same time. Particle, the linear momentum is equal to the Mass times the Velocity. M, moving with Velocity V, the momentum of that Particle, let's say we have a particle here of Mass Heisenberg uncertainty principle is a principle of quantum mechanics.
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