 So let's try this Heisenberg uncertainty Example it says an electron is moving at a speed of eight point zero times ten to the six meters per second If the uncertainty in measuring the speed is one point zero percent of the speed Calculate the uncertainty in the electrons position and then the mass of an electron is nine point one one times ten to the negative thirty one kilojoules, okay, so The first thing you're going to want to do is well calculate the Uncertainty in the electron speed, okay, so it gives you these two Numbers here and from that you need to figure out what delta u is, okay, so We're going to say delta u It's going to be this measurement uncertainty okay so the measurement uncertainty Percentage though. We need to put it in a ratio. Okay, so it's actually the ratio of that measurement uncertainty so one percent is going to be 0.010 1.0 percent And we'll multiply that by 8.0 times 10 to the six meters per second Okay, so one two So this is going to be well the uncertainty and this is eight point zero times ten to the fourth meters per second like that so The next thing you want to do is figure out. Well, what's the uncertainty in the momentum, okay? Because there's a couple more equations that you're going to dump this information into So the next equation you need to remember is that uncertainty of the momentum equation so delta p equals the mass of the thing that you're measuring times That uncertainty in the velocity, which you just figured out here. Okay, so you've got the mass over here And remember momentum is going to be in kilograms meters per second So those are good units and so those are the units that you're going to get so So the mass 9.11 times 10 to the negative 31st kilograms Okay, so you have to have that in kilograms 8.0 times 10 to the fourth meters per second So let's figure out what that number is. So I get 7.3 times 10 to the negative 26 kilogram meter person Okay So it wanted the uncertainty in the position of this electron though not in its momentum Okay, so how do we do the uncertainty in position? Well, it's another equation that we have to have memories, okay? so Do you remember this equation? No, I'm not even gonna mention Okay, so On the top up here is H. There's Planck's constant. Remember Planck's constant? Yeah, okay 4, 5 On the bottom times Delta momentum, okay, you remember it now Okay, so well Planck's constant remember that has to be given to you. Okay, so that's going to be 6.626 Times 10 to the negative 34 Joules seconds Okay The other thing you want to remember Is the conversion factor? one joule equals One kilogram meter squared per second squared But I like to rearrange this to say Take these second squares and put them up here. So we've got one joule second squared equals one Kilogram meter squared, okay? So it's just it'll be easier So let's just do this now. So we've got Planck's constant so 6.626 Joules seconds And we're going to convert that because remember this momentum is in kilograms meters per second So we're going to convert those joules to those other units, okay? so What did we say one? Joules second squared equals one kilogram meter squared We're going to divide that all by a four pi and then that change in momentum or the uncertainty of momentum and that's going to be 7.3 times 10 to the negative 26 Kilogram meters or one second Like that, okay So let's just confirm remember this is going to be uncertainty in position, right? So that's going to be where we'll want meters, okay, or a length unit, okay? So let's just make sure we got that So we cancel Joules Kilograms kilograms Meters and one of the two meters Seconds and one of the two seconds and then seconds and the other second. Okay. What are we left with just meters? Okay, and those are good lengthy So now it's just a matter of doing the plug-and-chug so Hi I'm actually going to put this into picometers. Okay, so it'll look like a normal number So this is going to be the two sig figs So seven point two times ten to the negative ten meters