 Let's do this Heisenberg uncertainty principle problem. It says the velocity of an electron and a hydrogen atom is 2.2 times 10 to the 6 meters per second. If we assume that the velocity is known to within 10 percent then what is the uncertainty in the electrons position within the hydrogen atom? Okay, so in order to do this you have to remember some of these formulas. Okay, so the first thing you're going to be looking for is the uncertainty in the velocity. Okay, so they give you the uncertainty in the measurement. They say it's 10 percent. Okay, so the uncertainty in the velocity is just going to be the measurement uncertainty times the velocity itself. Okay? And what we're going to be figuring out is the minimum uncertainty in position. That's why we're setting everything equal. So if you look back in the book it'll always, it'll give you these greater than less than something. So don't worry about that. Okay? So here, so this measurement uncertainty, it's not a percentage. It's that ratio. So we're gonna have to divide that by a hundred percent. So we'll get back. Okay? Times 2.2 times 10 to the 6 meters per second. So I can do that in my head, thankfully. So 2.2 times 10 to the 5th meters per second. Okay? So now because we're looking for eventually the uncertainty in the position. We don't know what that is, but in order to figure out that we need to figure out the uncertainty in the momentum first. Okay? It told us, or I have to give you the mass of the electron. It told us we were working with an electron. Electron's masses are 9.11 times 10 to the negative 31st kilograms. Okay? So you're going to want to have these numbers in our units in kilograms. Okay? So what does that mean? Well, what you'll find, well, let's just go with this. Okay? We'll see when Planck's constant comes. We're gonna have to do some conversions of units. Okay? So let's figure out the momentum now. Okay? So the momentum equation, do you remember that? Mass. It's the uncertainty in the velocity. Okay? And that's what we just found up here. Okay? The mass, remember, has to be in kilograms. So, sweet, we got it in kilograms. Okay? So, okay? So when I do this to two sick bigs, it's 2.0 times 10 to the negative 25 kilogram meters per second. Is that what you got? Oh, sorry. That's all right. Is that what you got? Just blanket him. It's all right. It's all right. Okay. So anyways, now we found the momentum. We're gonna have to remember our last formula that we're gonna use for the uncertainty measurement. Okay? Do you happen to remember that formula? So let's write it out together. Doff, change it, x equals what's on the top? H. And then? 4 pi. Change in momentum. Okay? Yeah, so they might say mass times uncertainty. Is change x times change of p greater than or equal to? Yeah, this is the same. Like I said, we're not using the greater than or equal to. Okay? So this we're doing the minimum uncertainty, which is all you really need to be. Okay? So then I'll just do this plug and chuck. Okay? So since we're kind of falling off the edge here, I'm going to erase this part and then just write it in here. Okay? Is that fine? Did you write this step down? You got it? Okay, wonderful. So I'm gonna just write these numbers down so I don't forget them. So I guess I don't need this one. Okay? So I'm going to erase this now. We're going to do the uncertainty in x now. Okay? So in order to do this, we're going to have to have planes constant, which is given to us 6.636 times 10 to the negative 34th joules seconds. Okay? So notice that's in joules, right? Well, we're going to have to convert joules to the kilogram meter squared per second squared. Okay? So if you recall, right, let's just write that over here. One joule equals one kilogram meter squared over one second squared like that. Okay? But I like to just equate these two things and say put the second squared up here. Okay? So multiply both sides by second squared. So we're going to have one joule second squared equals kilogram meter squared. It'll make it easier on us. Okay? So, well, let's just plug in. So 6.636 times 10 to the negative 34th joules seconds like that. Okay? But we want to convert our joules, right? So let's use that conversion. One joule second squared one kilogram meter squared like that. Okay? At the bottom four pi and then multiply by our momentum. Okay? So what do we have? 2.0 times 10 to the negative 25th kilogram meters per one second like that. Okay? So why did I do it this way? So I could cancel out all of these. Okay? So remember, this is change in position. So position, that's going to be like a length or something. Okay? So hopefully we get meters when we're done. Okay? So let's cancel our units. Joules cancels with joules. Seconds cancels with one of the two seconds. Right? Kilograms cancels with kilograms. Meters cancels with one of the two meters. Seconds cancels with the other seconds. We're left with meters. Okay? So that's good because that's what we wanted for the units of position. Okay? So and what I get is 2.6, because it's the two sick things, times 10 to the negative 10 meters. But let's put this in picometers so it'll be units that are a number that kind of, you know, looks nice. Okay? So remember for every one meter, there's one times 10 to the 12 picometers. Okay? So meter cancels with meter. So what do we get? 260 picometers. So that would be the uncertainty in the position of this electron. Okay? So just go through those steps. Probably the biggest problem will be to remember those ones. Any questions on this? Okay, wonderful.