# Brownian Motion Simulation

### Description:

In 1827 Brown reported the random motion of small pollen grains in water as viewed under a microscope. Although this behavior had been seen prior to Brown's observation, this random motion became know as Brownian motion.

In 1905 Einstein was able to explain, mathematically, the motion of pollen grains as the result of collisions with water molecules (which are too small to be seen with a microscope).

In the window on the left the large red spot simulates the motion of the pollen grains seen by Brown under the microscope and the green and blue dots simulate the water molecules which Brown could not see.

### Question 1:

The graph on the right shows the speed of a one of the smaller particles (in green) and the speed of the larger, red particle (in red). Run the speed simulation for 100 time units. What can you say about the average speed of the small particles compared to the average of the larger object?

### Question 2:

Click the 'Kinetic Energy' button below to see a graph of the kinetic energy of the green and red particles. Run the simulation for 100 time units (Note: The time graph shows total time; it does not reset to zero). What can you say about the average kinetic energy of the small particles compared to the average kinetic energy of the larger particle?

### Question 3:

Are the large particle and the smaller particles in thermal equilibrium? Explain your reasoning.

### Question 4:

In the simulation the large particle is only 40 times more massive than the smaller ones. In the real case the mass differences are quite a bit larger and there are also quite a few more water molecules. Suppose the ratio of masses between water molecules and the pollen grains used by Brown is 100 to 1. What will the ratio of speeds be on average?

### Question 5:

Helium is continually given off by radioactive decay in the earth's crust yet we find very little of it in the atmosphere. Explain this fact starting with the concepts of thermal equilibrium and escape velocity and the fact that helium is a very light atom.