Twice as far takes four times as long
- The idea
- Predict
- See it
- Why
- Check
The idea
“If a molecule has to diffuse twice as far, it takes twice as long.”
Walking twice as far takes twice as long, so it's natural to expect the same of a molecule. But a diffusing molecule wanders at random, and its progress slows the farther it goes.
The short version
The mistake: If a molecule has to diffuse twice as far, it takes twice as long.
What's actually true: Diffusion time grows with the square of the distance, so twice as far takes about four times as long.
- In diffusion, each molecule jiggles in random directions. The molecules spread outward overall, but each one keeps doubling back.
- Because of that, time grows with distance squared. Ten times as far takes a hundred times as long.
- So diffusion is fast over a few micrometers and slow over a millimeter. That's why cells stay small or flat, and big animals pump blood close to every cell.
On the exam: Diffusion time goes with distance squared, so twice as far means four times the wait.