# Question Video: Identifying Properties of Brownian Motion Physics

A gas consists of a very large number of particles that are in Brownian motion. Which of the following most correctly relates the most likely speed of a particle in a gas to the direction of its motion? [A] The more particles in the gas moving in the same direction as the particle, the greater its speed is likely to be. [B] The more particles in the gas moving in the same direction as the particle, the smaller its speed is likely to be. [C] The more particles in the gas moving in the opposite direction to the particle, the greater its speed is likely to be. [D] The more particles in the gas moving in the opposite direction to the particle, the smaller its speed is likely to be. [E] The speed of a particle is independent of the direction of its motion.

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### Video Transcript

A gas consists of a very large number of particles that are in Brownian motion. Which of the following most correctly relates the most likely speed of a particle in a gas to the direction of its motion? (A) The more particles in the gas moving in the same direction as the particle, the greater its speed is likely to be. (B) The more particles in the gas moving in the same direction as the particle, the smaller its speed is likely to be. (C) The more particles in the gas moving in the opposite direction to the particle, the greater its speed is likely to be. (D) The more particles in the gas moving in the opposite direction to the particle, the smaller its speed is likely to be. (E) The speed of a particle is independent of the direction of its motion.

To begin, let’s recall that Brownian motion describes the seemingly random movement of many identical fluid particles. To help us think about this, we can make some room on screen and draw a diagram. A particle experiencing Brownian motion changes direction rapidly due to repeated collisions with other particles. Since the many particles in a system are colliding with each other over and over again, their motion seems random. And over time, any given particle tends to have a net zero displacement since it’s equally likely to be redirected in any direction at any time.

Now, let’s think about the question at hand. We want to relate the speed of a particle in a gas to the direction of its motion. Answer options (A) and (B) talk about many particles in the gas moving in the same direction, so let’s picture this scenario. Imagine that somehow we have a group of particles with most of them moving in the same direction. Let’s focus on the motion of one single particle. To help us keep track, we can color this one particle magenta, but note that all the particles are identical in every other way.

At first, with lots of particles moving along nicely together, the magenta particle will likely carry on without as many collisions as usual. But all it takes is one straight particle to start a chain reaction of collisions in different directions. And we should note that the identical particles collide elastically. So the bulk of the particles won’t experience an overall change in momentum. The magenta particle would likely still experience several changes to its own momentum. So as time passes and the particles interact, it’s not reasonable to predict that generally the magenta particle would either be moving faster or slower. So answer options (A) and (B) aren’t looking great.

Next, let’s think about options (C) and (D), which talk about many particles moving in the opposite direction to one particle of interest. Again, let’s sketch out this scenario and color one particle magenta to help us think about its motion.

Say we have lots of particles moving to the right and the magenta particle is initially moving left. At first, this one particle is still not likely to experience as many collisions as it would if all the particles had random motion in all sorts of directions. But it would eventually collide with another particle. And in that case, the two particles’ incoming speeds will determine the magenta particle’s speed after the collision. Likely, though, it would simply be accelerated to the right. And then, it would be moving in the same direction as the bulk of the particles, like we saw before in answer options (A) and (B).

So none of these four options are particularly convincing. Considering what we know about the chaotic nature of fluid particle motion, it would be naive to think that we could predict a single particle’s speed by noting the direction it moves at a certain moment. And the thing is, Brownian motion doesn’t work like this. Options (A) through (D) don’t even describe Brownian motion, which is what this question is supposed to be about.

In real life, we’re not going to find a very large number of particles all synchronized and moving together. Even if a smaller group of particles were somehow sent in the same direction, this configuration wouldn’t be stable as collisions would likely soon decay any sense of order into the randomness of Brownian motion. Realistically, the motion of each gas particle is independent of the others. And the speed of a particle is independent of its direction of motion, which is why the motion seems so random.

Thus, we know that option (E) is the best answer. The speed of a particle is independent of the direction of its motion.