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 Brownian motion of the molecules? (A) The molecules all have different speeds. (B) The distance between most molecules is significantly different from the average distance between the molecules. (C) Each molecule moves in a straight line. (D) The molecules all move in the same direction.
Let’s recall that of these answer options, we’re trying to pick which one tells how the figure shown does not correctly represent Brownian motion. We can get started by recalling that Brownian motion is the apparently random motion of particles due to collisions with other particles. We would expect to see Brownian motion, for example, among the molecules that make up a gas.
We’re told that our figure shows us the molecules in a region of a larger gas. Based on the arrows indicating the velocities of these molecules, we see that they’re all moving in the same direction and at different speeds. If we imagine though having a collection of gas molecules in some container, we could expect that at any moment in time, these different molecules are moving in different directions and at different speeds. It’s in an environment like this that Brownian motion arises.
Say we were to track the motion of this particular gas particle here, highlighted in orange. This molecule would move in a straight line until it collided with another molecule. As a result of that collision, it would be redirected in some way. Later, it would collide again and be redirected then collide again and again and again and again, over and over to create a path of motion something like this. If this is Brownian motion, then we want to figure out what is it about our figure that is inconsistent with this type of motion.
Answer option (A) says that the molecules all have different speeds. This is true; we know that because the velocity vectors of these molecules have different lengths, but we expect this condition to occur for Brownian motion to happen. The fact that the molecules all have different speeds then is not a reason why the figure does not correctly show Brownian motion.
Answer choice (B) says that the distance between most molecules, that is, the molecules in this larger gas, is significantly different from the average distance between the molecules we see in our figure. This may be the case, but even if it is, that’s not a reason why the figure does not correctly show Brownian motion. At any given instant in a situation where Brownian emotion does occur, we may find varying densities of the particles involved. Answer choice (B) then is also not a reason why the figure does not correctly show Brownian motion.
Option (C) says that each molecule moves in a straight line. This is true in the sense that the molecules will move in the same direction until they’re acted on by another molecule through a collision. But it’s generally the case that an object moving in a certain direction will continue on in that direction until it’s acted on by some force. Each of the molecules in our gas here, for example, move in a straight line at any particular instant, but the directions of those straight lines of motion change over time as the molecules collide with one another. Answer choice (C) is also not a reason why the figure doesn’t show Brownian motion.
Choice (D) says that the molecules all move in the same direction. We see, first of all, that this is true of our figure and also that it’s inconsistent with a general scenario involving Brownian motion. Considering the molecules in a gas, we expect that they’re moving in all different directions at any given moment. It’s this kind of motion that helps to create the apparently random path of a given particle in that collection. So, the fact that all six of the molecules in this figure are moving in the same direction is not consistent with Brownian motion.
The way in which our figure does not correctly indicate Brownian motion is that the molecules in the figure all move in the same direction.
