\[\langle x^2\rangle =2Dt\]
Variables
x2mean square displacement (m²)
Ddiffusion coefficient (m²/s)
tdiffusion time (s)
Description
What is this formula?
The mean square displacement equation calculates the average squared distance traveled by diffusing particles over time.
When to use it
Use this formula in diffusion theory, Brownian motion analysis, statistical mechanics, and particle transport studies to estimate random motion behavior.
Example
A particle diffuses with:
D = 3.0×10^-10 m²/s
t = 500 s
Formula:
= 2Dt
Substitution:
= 2 × 3.0×10^-10 × 500
Result:
= 3.0×10^-7 m²
The mean square displacement is 3.0×10^-7 m².
Applications
- Brownian motion
- Molecular transport
- Particle tracking
- Statistical mechanics
- Diffusion process analysis