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# Find the average distance between atoms in a uniform gas that has a density of N atoms per unit volume.?

Please help I’m so confused, this is a HW problem for my physics class and this is all the information we were given

### 1 Answer

- Steve4PhysicsLv 71 year agoFavorite Answer
There is a whole article about this here: https://en.wikipedia.org/wiki/Mean_inter-particle_... However, I’m guessing this is just a basic school-level question and a simple answer will do.

Call the unit length L. E.g. L=1m. Imagine a cube of unit volume (L x L x L= 1m x 1m x 1m = 1m³).

Suppose the average distance between atoms is d unit lengths (e.g. d metres).

We have to imagine the atoms spaced evenly. To make the calculation simpler we have the atoms arranged in rows with each row a distance d from its neighbouring row. Like the arrangement in the diagram (link below).

(Note we are ignoring the effects of distance measured diagonally between atoms. So answer is approximate.)

Each row contains n = L/d atoms. For example if d = 0.01 m there are 1m/0.01m = 100 atoms per row. n = 100.

(Actually we should use n-1 = 99 if counting correctly. But as n will be huge when considering actual atoms, using n or n-1 makes no real difference.)

The total number of atoms in a unit cube is n x n x n = n³ = (L/d)³. For example with 100 atoms per row the cube contains 100 x 100 x 100 = 10⁶ atoms.

With L = 1 (the unit length) and d measured in these units, then (L/d)³ can be written as (1/d)³ which is 1/d³.

As there are N atoms per unit volume, N = 1/d³

d³ = 1/N

d = 1/∛N

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