Question Video: Identifying Properties of Brownian Motion Physics • Second Year of Secondary School

Video Transcript

Fill in the blanks. Particles that move randomly will have fewer collisions with other particles where there are blank other particles, and so when they move in this direction, they are less likely to be accelerated in blank direction by collisions. (A) Fewer, this. (B) More, the opposite. (C) Fewer, the opposite. Or (D) more, this.

In this question, we’re trying to relate two concepts concerning Brownian motion, or the seemingly random movement of fluid particles. To fill in the first blank, we need to recognize the conditions that allow for fewer particle collisions in a region. Then once we have that, it’ll be easier to fill in the second blank. So, let’s begin by thinking about this first blank.

Here it says: particles that move randomly will have fewer collisions with other particles where there are either more or fewer other particles. Suppose we have two separate chambers containing gas particles. The chamber on the left contains only a few particles and the other chamber, on the right, contains many particles. To make things simpler, let’s think specifically about the motion of just one particle per chamber. And to help us keep track, we can color this one particle magenta, but note that all the particles are the same in every other way.

Now, the particles move essentially randomly, experiencing Brownian motion. Comparing the two magenta particles, it’s reasonable to presume that the one in the chamber on the left will experience fewer collisions with other particles because there are fewer other particles in its path to collide with. The magenta particle in the chamber on the right, however, will likely not be able to travel very far in any direction without soon colliding with another particle. There are more particles here, so more opportunities for collisions.

Now, let’s think about the first blank in the question. If we want to have fewer particle collisions, we will want fewer particles in a given space. This way, each particle has more room to move freely, meaning collisions happen less often. So, we know that the first blank should be filled with the word “fewer” to make the statement correct. Let’s eliminate options (B) and (D).

Now, we have to figure out which option fits in the second blank to make the entire statement correct. It says: particles that move randomly will have fewer collisions with other particles where there are fewer other particles, and so when they move in this direction, they are less likely to be accelerated in either this same direction or the opposite direction by collisions.

We know that collisions cause particles to accelerate in different directions. We can see this happening in the process of diffusion, in which particles spread out evenly over a volume. To visualize this, suppose now that we have one chamber and that gas particles are introduced into it from the left-hand side.

At first, the particles are all concentrated at one end of the container, and the other end is mostly empty. And as time goes on, we know that there will be lots of collisions over here where there are lots of particles. Because of this, the particles will tend to move towards the right end of the container, where there are fewer particles and thus where there will be fewer collisions. Eventually, the particles will be evenly spread out.

Returning back to the question at hand, we know that particles will diffuse and move to where there are fewer collisions. When they move this way, they become less likely to collide and therefore less likely to accelerate back in the opposite direction, towards where there are more particles.

We can think about it like this. If we introduce particles to a chamber from the left end and follow the path of one magenta-colored particle, we expect to see it diffuse towards the right, towards where there are fewer particles. We would not expect to see the magenta particle accelerate back to the left, towards where there are more particles. Thus, during diffusion, the particle is less likely to accelerate in the opposite direction due to collisions.

So, we choose to fill in the second blank with the opposite direction, rather than this same direction. Thus, we know option (C) must be correct. We’ve now filled in both of the blanks. So, the correct statement reads “Particles that move randomly will have fewer collisions with other particles where there are fewer other particles, and so when they move in this direction, they are less likely to be accelerated in the opposite direction by collisions.”