Brownian motion demonstration in class

[ddddd28]

Hello,
Einstein evaluated the size of an atom by analysing a brownian motion, assuming the size of the molecules is a a factor. In order to demonstrate this concept, I want to put some powders with different sizes of grains on a vibrator and watch how a ball moves. What is the expected result? The bigger the grains, the slower the ball moves? and why? and how is it settled with einstein's formula to find the atom's size?

 

[mfb]

The ball will move mainly from the contact to the vibrator I guess, and if you analyze its flight path then inelastic collisions will still make everything different from thermal motion. I don't see how you would get a realistic simulation of Brownian motion that way.

 

[ddddd28]

I think you didn't understand the simulation. There is no flight, I put the ball gently and watch its motion.
As you can see in that video: Random Force & Brownian Motion - Sixty Symbols

My question is what happens to the ball motion when I change the size of the grains.

 

[mfb]

That is about what I expected, and I'm not sure how much you get from a quantitative analysis. Qualitatively it is fine, of course.

My question is what happens to the ball motion when I change the size of the grains.

What do you expect?

 

[ddddd28]

I expect that the brownian motion will be shorter (the average distance the ball travels) as the grains become bigger. However, I have no good explanation. I want to show the simulation to demonstrate Einstein's motivation to think that there is a connection between the brownian motion and the size of atom(grain).

 

[mfb]

Think about the momentum the ball gets in each collision, and how frequent collisions are.

 

[Andy Resnick]

I expect that the brownian motion will be shorter (the average distance the ball travels) as the grains become bigger. However, I have no good explanation. I want to show the simulation to demonstrate Einstein's motivation to think that there is a connection between the brownian motion and the size of atom(grain).

It's not a simple question to answer- the granular bed is a very nonlinear system and only approximates Brownian motion in a limiting sense.

https://www.nature.com/articles/srep17279

If I read that article correctly, the dynamics scale as (particle diameter)^1/8.