Mean Free Path Calculator
Calculate the average distance traveled by gas molecules between collisions using kinetic theory
Calculate Mean Free Path
Select a gas molecule or choose custom to enter your own kinetic diameter
Gas temperature affects molecular motion
Gas pressure affects molecular density
Mean Free Path Results
Formula used: λ = kᵦT / (√2 × π × d² × p)
Where: kᵦ = 1.381e-23 J/K (Boltzmann constant)
Gas: Nitrogen (N₂), d = 364 pm
Conditions: T = 0.0 K, p = 0.000e+0 Pa
Physical Insights
Example Calculation
Air at Room Conditions
Given: Nitrogen gas (main component of air)
Temperature: 298 K (25°C)
Pressure: 101,325 Pa (1 atm)
Kinetic diameter: 364 pm
Solution:
λ = (1.381×10⁻²³ × 298) / (√2 × π × (364×10⁻¹²)² × 101,325)
λ ≈ 68 nm
High Vacuum Example
Helium at high vacuum: p = 10⁻⁵ Pa, T = 298 K
Kinetic diameter: 260 pm
Result: λ ≈ 1 km (molecules travel very far without collision)
Applications
Vacuum Technology
Quality assessment of vacuum systems
Electronics
Electrical mobility and drift velocity
Particle Physics
Radiation length measurements
Transport Phenomena
Diffusion and heat transfer
Key Facts
Inversely proportional to pressure and molecular cross-section
Directly proportional to temperature
Air at STP: ~68 nm between collisions
High vacuum (10⁻⁵ Pa): ~1 km for small molecules
Foundation for kinetic theory of gases
Understanding Mean Free Path
What is Mean Free Path?
The mean free path is the average distance traveled by a moving particle (atom or molecule) between successive collisions with other particles in a gas or other medium. It's a fundamental concept in kinetic theory and statistical mechanics.
Physical Significance
- •Characterizes the scale of molecular interactions
- •Determines transport properties (viscosity, diffusion)
- •Critical for vacuum technology and surface science
- •Essential for understanding gas behavior
Formula and Variables
λ = kᵦT / (√2 × π × d² × p)
- λ: Mean free path (m)
- kᵦ: Boltzmann constant (1.381×10⁻²³ J/K)
- T: Absolute temperature (K)
- d: Kinetic diameter of molecule (m)
- p: Gas pressure (Pa)
Note: This formula assumes an ideal gas with spherical molecules and elastic collisions.
Pressure Regimes and Applications
Atmospheric Pressure
~10⁵ Pa: Mean free path ~68 nm for air. Molecules collide frequently, enabling continuum mechanics description of fluid flow.
High Vacuum
~10⁻³-10⁻⁶ Pa: Mean free path ~cm to m range. Transition regime where both molecular and continuum effects are important.
Ultra-High Vacuum
<10⁻⁶ Pa: Mean free path >1 km. Molecular flow regime where gas behavior is governed by wall collisions rather than intermolecular collisions.