Estimating atomic diameter from substance density

[scanwinder]

Homework Statement

Estimate the diameter of an atom of a substance whose density is 10³ kg/m³

Homework Equations

V_atom = 4 $$\pi$$ r³ /3
$$\sigma$$ = m/V

The Attempt at a Solution

I have attempted a few different things, but I always come out a variable short, and although they question says estimate, I can't see that I can estimate a variable like atomic weight as it varies too much for an estimate to be reasonable.

I have rearranged equations to get:
V = m/$$\sigma$$ = n $$\times$$ N_A $$\times$$ (4/3) $$\times$$ $$\pi$$ $$\times$$ r³

I don't even know how close together the atoms are as I don't know the sate of the substance.

 

[_coyote_]

I guess the best I can do is get the molar mass of the substance (which I don't have) and work from there, but can't see how I can estimate this without knowing the substance.