Mean Free Path Calculator
Utilize the handy tool Mean Free Path Calculator to compute the mean free path of a particle having specific diameter. Simply enter the inputs and hit the calculate button to avail the result in a short span of time.
Mean Free Path Calculator: Get the help to solve the mean free path of a particle in ideal gas on this page. An ideal gas has a large number of particles or atoms or molecules that are in constant rapid motion and can collide with each other. You can check the details about the mean free path and its formula here. Take the help of our calculator to find the average distance between atoms. Find the manual steps & solved examples on mean free path.
Step by Step Process to Find Mean Free Path
Go through the following steps to compute the mean free path of an atom. You will get the solution easily by following the mentioned guidelines.
- Get the particle diameter, pressure and temperature.
- Multiply the square of diameter with the pressure.
- Multiply the result by √2π.
- Find the product of temperature and boltzmann constant.
- Divide the obtained product by result from step III to check mean free path value.
What is Mean Free Path?
The mean free path is the average distance that molecule travels between collisions. It is determined by the criterion that there is one molecule within the collision tube.
The mean free path of particles of a gas equation is mentioned-below:
λ = k * T / (√2 * π * d² * p)
Where,
╬╗ is the mean free path
k is the Boltzmann constant i.e k = 1.380649 x 10-23 J/K
T is the temperature of the gas
d is the diameter of the particle
p is the pressure of the gas
The mean free path formula requires atomic diameter to perform proper calculations. The raddi and diameters of the atomes of some gases are mentioned below:
| Element | Atomic radius (pm) | Atomic diameter (pm) |
|---|---|---|
| Hydrogen [H] | 120 | 240 |
| Helium [He] | 140 | 280 |
| Nitrogen [N] | 155 | 310 |
| Oxygen [O] | 152 | 304 |
| Fluorine [F] | 147 | 294 |
| Neon [Ne] | 154 | 308 |
| Chlorine [Cl] | 175 | 350 |
| Argon [Ar] | 188 | 376 |
| Krypton [Kr] | 202 | 404 |
| Xenon [Xe] | 216 | 432 |
| Radon [Rn] | 220 | 440 |
Example
Question: Calculate the mean free path of nitrogren molecule at 27┬░C when pressure is 1.5 atm. If the diameter of the nitrogen molecule is 1.5 A, the average speed of the nitrogen molecule is 675m/s. Find the time taken by the molecule between two successive collisions?
Solution:
Given that
Temperature T = 27┬░C = 27 + 273 = 300 K
Pressure p = 1.5 atm = 1.515 x 105 N/m┬▓
Nitrogen diameter d = 1.5 A = 1.5 x 10-10 m
Boltzmann constant k = 1.380649 x 10-23 J/K
Mean free path λ = k * T / (√2 * π * d² * p)
= (1.380649 x 10-23 x 300)/(√2 x π x (1.5 x 10-10)² x 1.515 x 105)
= 27.35 x 10-7 m
The time interval between two successive collisions t = distance/speed
= ╬╗/v
= 27.35 x 10-7/675
= 0.6 x 10-9 s
Therefore, the mean free path of nitrogen is 27.35 x 10-7 m
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Frequently Asked Questions on Mean Free Path Calculator
1. How is mean free path calculated?
The mean free path is the average distance between two consecutive collisions. The equation to calculate the mean free path is λ = kT/(√2πd²p). Substitute the values in the values and calculate to get the mean free path of a molecule.
2. What are the factors affecting mean free path?
The factors affecting the mean free path are density of the molecule, number of molecules, diameter of the molecule, pressur, temperature and other physical factors.
3. How temperature affect the mean free path?
As per the kinetic theory of gases, increasing the temperature, molecules run faster. The distance or mean free path remains constant and mean time of collision decreases. So, mean free path is independent of the temperature.
4. What are the applications of mean free path?
The mean free path is used in electronics to describe the electrical mobility, radiography to find the thickness of material, nuclear physics, astronomy, optics and many more.
