Dimensional formula of Mean free path

How to get the dimensional formula of mean free path

1. Start from the definition: mean free path = 1 / (number density × area).
2. volume = length³, so volume is [L]³ = [L³].
3. number density = 1 / volume, so number density is 1 / [L³] = [L^-3].
4. area = length × length, so area is [L] × [L] = [L²].
5. Put in the dimension of each part: 1 / ([L^-3] × [L²]).
6. Add the powers of each base quantity: [L].

Quantities with the dimensions [L]

• Length
• Displacement
• Radius of gyration
• Wavelength
• Amplitude
• Focal length
• Fringe width
• de Broglie wavelength
• Bohr radius

Equal dimensions do not make them the same quantity. Compare mean free path with the others in the full grid.

Three questions on mean free path

Related quantities

• Q Heat [M L² T⁻²]
• C Heat capacity [M L² T⁻² K⁻¹]
• c Specific heat capacity [L² T⁻² K⁻¹]
• C Molar heat capacity [M L² T⁻² K⁻¹ mol⁻¹]
• L Latent heat [L² T⁻²]
• K Thermal conductivity [M L T⁻³ K⁻¹]