B.3 · IB Physics
Brownian motion
A large particle (red) is buffeted by hundreds of small, fast gas molecules. Change the temperature and molecular mass, follow its random path and watch its mean square displacement grow with time.
Model equations
Mean KE of a molecule: Ēk = (3/2) kBT
vrms = √(3kBT / m)
Mean square displacement (2D): ⟨r²⟩ = 4Dt
Mean KE of a molecule: Ēk = (3/2) kBT
vrms = √(3kBT / m)
Mean square displacement (2D): ⟨r²⟩ = 4Dt
On-screen speeds are scaled down; L is the side of the box. ⟨r²⟩ is averaged over all start times; gold dashed line = best fit through the origin. Changing a slider restarts the measurement.
Try this
- At 300 K and 28 u, run for about 20 s and note the MSD slope. Repeat at 1000 K: which way does the slope change?
- Keep T fixed and compare 4 u with 80 u molecules. Do lighter or heavier molecules make the large particle spread out faster?
- Hide the molecules and look at the graph at small τ: is ⟨r²⟩ proportional to τ straight away, or only after the first second or so?
Exam tip: When describing Brownian motion, say the visible particle is struck unevenly by many fast, invisible molecules, giving a random zig-zag path, and that this is evidence that molecules exist and are in constant random motion.