Video Transcript
The following figure shows a region in a gas containing some of the molecules of the gas. The velocities of the molecules are shown by the arrows. In what way does the figure not correctly show the Brownian motion of the molecules? (A) Each molecule moves in a straight line. (B) The molecules all have the same speed. (C) The molecules all move in different directions. (D) The distance between most molecules is significantly different from the average distance between the molecules.
Let’s recall that we want to pick which of these explanations tells why the figure does not correctly show Brownian motion. We can define Brownian motion this way: it’s the apparently random motion of a particle due to collisions with other particles. So, say we had a collection of particles that were all moving in different directions and at different speeds. Over time, these particles would collide with one another. That would mean that if we follow the path of one of these particles, say, this one right here, then the path over time might look like this, where each of these small straight-line segments is the path of the particle in between collisions.
We see then how this motion is apparently random. It seems to go in any direction, but these directions are guided by collisions. So, if that’s what Brownian motion looks like, how do the molecules in our figure not display this motion? We see that these six molecules are moving in all different directions. That is a characteristic though of Brownian motion. So, it’s not a reason why the figure does not show this motion.
As claimed by answer option (A), it’s true that each molecule in the figure moves in a straight line. This though is always true of Brownian motion in between collisions with other particles. So long as a given particle is not experiencing a collision, it will move in a straight line. Answer choice (B) says that the molecules all have the same speed. We can tell this is so by comparing the lengths of these velocity vectors. All the lengths are the same, meaning that these molecules do all move with the same speed. In a real cloud of molecules though or another set of particles that demonstrate Brownian motion, the speeds of the objects involved do vary. Some particles move faster; some move slower. And this is characteristic of particles undergoing Brownian motion.
It looks then that option (B) will be our choice for a way that the figure does not correctly show Brownian motion. The molecules in the figure do all have the same speed, but this is not consistent with Brownian motion. To make sure that this is the best answer though, let’s look at option (D). This reads that the distance between most molecules is significantly different from the average distance between the molecules, that is, those in the figure. Recall that these six molecules occupy one region in a larger collection of molecules making up a gas.
Answer choice (D) is saying that the spacing, the distance between these molecules, is very different from the spacing between most of the molecules that make up the larger gas. However, because we don’t see the rest of the gas, we don’t know whether this is true or not. But even if it was true, that would not be a reason why the motion shown here does not demonstrate Brownian motion. Even among a collection of particles that do demonstrate Brownian motion, at a given point in time, the density of particles across the region of that collection may vary. That doesn’t mean that the motion experienced by the particles is not Brownian. Therefore, we won’t choose answer choice (D) either.
This confirms choice (B) as the best answer. The fact that all the molecules in our figure have the same speed shows us that this figure does not correctly show Brownian motion.
