Heisenberg Uncertainty Principle - Video Tutorials & Practice Problems
Get help from an AI Tutor
Ask a question to get started.
Heisenberg's Uncertainty Principle tries to explain the potential duality of an electron behaving as either a particle or wave.
Heisenberg Uncertainty Principle
1
concept
Heisenberg Uncertainty Principle
Video duration:
1m
Play a video:
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 of an electron as it's traveling, but you won't know its 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 hidden both as a wave and a particle is a reason for this issue. We're going to say here that the velocity or speed of an electron is related to its wave nature. Remember, light energy can move in the form of a wave, and we're gonna say that the position of an electron is related to its particle nature. Again, some say that light energy can be seen as just a cluster of 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 the reason why you can't know both the velocity and position of an electron at the same exact time.
2
concept
Heisenberg Uncertainty Principle
Video duration:
2m
Play a video:
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 of uncertainty and momentum and then the uncertainty principle formula itself. Now we're gonna say momentum can be described as mass in motion. Here we're gonna say that delta p equals our uncertainty and momentum, and here it's in units of kilograms times meters over seconds. We're gonna say here that our uncertainty in position delta p equals m times v. M here is just the mass in kilograms of our electron, and then v here represents the uncertainty and it would be delta v, the uncertainty in our velocity. Now with this, we go on to the uncertainty principle formula itself. Now here it's gonna 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. Now remember, this can be further expanded by substituting in mass times uncertainty and velocity. And then h is Planck's constant, which is 6.626 times 10 to the negative 34 joules times seconds. Now one additional thing, remember that 1 joule is equal to kilograms times meters squared over seconds squared. That would mean that joules times seconds equals kilograms times meters squared over seconds squared times s. So one second, we'll cancel out one second here. So this is equivalent to also saying kilograms times meters squared over seconds. So keep that in mind when it comes to Planck's constant. The units can either be in joules times seconds or kilograms times meter squared over seconds.
3
example
Heisenberg Uncertainty Principle Example 1
Video duration:
4m
Play a video:
In this example question it states, calculate the uncertainty in velocity of a neutron if the uncertainty in its position is 712 Pico Meters. Here, we're told the mass of the neutron is 1.67510 times 10 to the negative 27 kilograms. Alright. So, we're going to be utilizing the Heisenberg uncertainty principle to answer this question. Now, remember that it's going to be that the uncertainty in our position which is Delta X times the mass of our object, in this case, the neutron times the uncertainty in its velocity will be greater than or equal to Planck's constant divided by 4 times pi. All we have to do in do here is fill in the information we know. Let's see. So we know what the uncertainty in the position is at 712 picometers. But remember, we need the units of length to be in meters, not picometers. So we're gonna do a conversion here. We have 712 picometers. Remember, 1 picot is 10 to the negative 12. So this is equal to 7.1 12 times 10 to the negative 10 meters. So this will be our delta x. Next, we're going to say that m represents the mass of our neutron, which we're given as 1 point 67510 times 10 to the negative 27 kilograms and then that's going to be times our uncertainty and velocity, which we don't know. This would be greater than or equal to, Remember, Planck's constant here is 6.626 times 10 to the negative 34. Remember the units here are joules times seconds. Joules itself is equal to kilograms times meters squared over seconds squared and that's gonna be multiplying by seconds. So one of these seconds cancels out with this second. So the units here will really be kilograms times meters squared over seconds and that's gonna be divided by 4 times pi. Now, what we're gonna do here is we're going to try to simplify all of this for ourselves. We're gonna multiply these 2 together. When we multiply them together, that's gonna give me 1.19 26712 times 10 to the negative 36. Here, it's gonna be kilograms times meters. And the only reason I'm doing it in that order is because Planck's constant puts kilograms of 4 meters squared, and that's gonna be times our unknown or uncertainty in velocity, which will be greater than or equal to. So divide now Planck's constant by 4 pi. When we do that, that's going to give me 5.2728 times 10 to the negative 35 kilograms times meter squared over seconds. Finally, we want to isolate the uncertainty in our velocity. So divide both sides now by this 1.1926712 times 10 to the negative 36 kilograms times meters on both sides. So when we do that here, this cancels out and then over here, kilograms cancel out with kilograms. This meter cancels out with 1 of these meters, which at the end gives us what? Meters per seconds, which makes sense because those are the customary units for velocity. So we're going to say here, when we punch that into our calculator, the uncertainty in our velocity will be greater than or equal to 4 44 point 2 meters per second. This would be our final answer to this example question.
4
Problem
Problem
To what uncertainty (in m) can the position of a baseball traveling at 51.0 m/s be measured if the uncertainty of its speed is 0.12%? The mass of the baseball is 150 g.
A
4.2 x 10-33 m
B
5.7 x 10-33 m
C
5.9 x 10-33 m
D
4.8 x 10-33 m
5
Problem
Problem
A proton with a mass of 1.67 x 10-27 kg traveling at 4.7 x 105 m/s has an uncertainty in its velocity of 1.77 x 105 m/s. Determine its uncertainty in position.