Heisenberg Uncertainty Principle

now, the physicist Werner Heisenberg theorized that the velocity and position of an electron cannot be calculated simultaneously, meaning that you might know the velocity or speed oven electron as it's traveling. But you won't know what's position, and conversely, you might know where it's located. But you wouldn't know how fast it's moving now related to an electron. Be hitting both as a wave, and a particle is a reason for this issue. We're going to say here that the velocity or speed, often electron, is related to its wave nature. Remember, light energy can move in the form of a wave, and we're going to say that the position, often electron, is related to its particle nature. Again, Some say that light energy can be seen as just a cluster off particles known as photons. Now this relationship, we call it complementarity, where electrons can be seen as either particles or waves, but not both simultaneously. And that's the reason why you can't know both the velocity and position of an electron at the same exact time

with the inability to determine both the velocity and position of an electron, comes the Heisenberg uncertainty principle. Now here we're going to say that it can be broken down in terms off uncertainty and momentum and then the uncertainty principle formula itself. Now we're going to say mo mentum can be described as mass in motion. Here. We're going to say that Delta P equals R uncertainty and momentum, and here it's in units of kilograms times meters over seconds. We're going to say here that are uncertainty in position. Delta P equals M times. The M here is just the mass in kilograms of our electron. And then v here represents the uncertainty and it will be Delta v the uncertainty in our velocity. Now, with this, we go on to the uncertainty principle formula itself. Now here it's going to say it's used when given the uncertainties in position and momentum. So here what's going to be that Delta X, which is our uncertainty in position in terms of meters times Delta P, which we just said is the uncertainty in our momentum. Remember, this could be further expanded by substituting in mass times, uncertainty and velocity and then h is Plank's constant, which is 6.626 times 10 to the negative. 34 jewels times seconds. Now one additional thing. Remember that one? Jewell is equal to kilograms times meter squared over second squared. That would mean that Jules Times seconds equals kilograms times meter squared over second squared times s so one second will cancel with one second here. So this is equivalent to also saying kilograms times meter squared over seconds. So keep that in mind. When it comes to Plank's constant, the units can either be in jewels, time, seconds or kilograms, times meter squared over seconds.

in this example we're going to talk about the uncertainty involved with a neutron. Here, it says calculate the uncertainty in momentum off a neutron moving at 6. times 10 to the seventh meters per second. The massive a neutron is given as 1.67510 times 10 to the negative 27 kg. Alright, so remember uncertainty in momentum is Delta P here we're giving the speed in which it's moving. So this is our uncertainty in velocity and here they're giving us the mass of the subatomic particles. So m remember, uncertainty in momentum equals mass in kilograms time the uncertainty in velocity. So here that's gonna be 167510 times, 10 to the negative, 27 kg. And then we're gonna plug in the uncertainty in the velocity. This is the Onley speed in which they give us. So we assume that is our uncertainty and velocity. So here, when we plug that in, we get one point 01 times 10 to the negative, 19 kg, times meters over seconds. Here are answer has 366 at the end to match the three Sig figs that we see here in 6.0