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What Is the Mean Free Path?

M.J. Casey
M.J. Casey

A mean free path is the average length a particle can travel in an environment before colliding, being absorbed by, or reacting with another particle. The term is frequently used to discuss the behavior of gases but also has been applied in the fields of sound and light. One could calculate the mean free path of a player in a football game. On a relative basis, a molecule of oxygen travels much farther in air before colliding than does the football player.

Gases are a state or condition of matter in which the molecules are so loosely attracted to each other that they are free flowing and will occupy the entire volume of a container. The volume of a gas is the volume of the container. Gases are easily compressed, expanded, and mixed. Gases are often invisible due to their low concentration of matter per unit volume, or, stated differently, the long mean free path of their molecules.

Scientist with beakers
Scientist with beakers

In chemistry, calculations of the mean free path are useful in studying gas reaction behavior. The value of the path is, of necessity, the result of models, as there is no way to measure or track any one molecule. Scientists look at observable parameters such as volume, temperature, and pressure as well as the size of the molecules in the gas and the gas concentration to model gas molecule behavior and derive calculated values.

The molecules of air, at standard conditions of 1 atmosphere (14.7 pounds per square inch), 0deg;C (32°F), and a stated molecular diameter of 0.3 nanometers, nm, (1.2 x 10-8 inches ), has a calculated mean free path of 93 nm (3.6 x 10-6 inches). The average molecular separation is calculated at 3.3 nm (1.3 x10-7 inches). If football players were as nimble as atoms, their mean free path would be about 800 feet (244 meters), based on an American football field. Of course, football players are not evenly dispersed about the field as are gas molecules within an enclosure.

In sound studies, mean free path refers to the average distance a ray of sound travels before being reflected off an obstacle. This calculation is important in acoustics and depends on the volume of a room and the total surface area of the room’s walls, ceiling, and floor. Acoustic studies, while complicated, are quantifiable, since velocity of sound waves can be accurately measured under a variety of conditions.

Studies of light scattering through gases or liquids use scattering mean free path calculations. These are defined as the average distance traveled by a photon before a scattering event occurs due to collision or absorption of the photon. The calculations can be used to determine such things as water turbidity and concentrations of various solutions. Tea drinkers are observing scattering free mean path to determine if their tea has brewed sufficiently.

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      Scientist with beakers