AI estimate of spacing of atoms from microscope images

[trevorjohnson83]

Using this image I asked AI to use the known density of the substance in the image and the apparent spacing between the spherical 'atoms' in the image to estimate the spacing between atoms in other substances with known densities, here's what it came up with

Predicted average spacing (spacing ∝ ρ^(−1/3))​

Substance	Density (kg·m⁻³)	Scale factor = (ρ_ref/ρ)^(1/3)	Predicted spacing (m)	Predicted spacing (Å)	Predicted spacing (nm)
PrScO₃ (reference)	5,900	1.0000	4.02×10⁻¹⁰	4.02 Å	0.0402 nm
Silicon (crystalline)	2,329	1.3632	5.48×10⁻¹⁰	5.48 Å	0.0548 nm
Aluminum	2,710	1.2961	5.21×10⁻¹⁰	5.21 Å	0.0521 nm
Iron (Fe)	7,874	0.9083	3.65×10⁻¹⁰	3.65 Å	0.0365 nm
Gold (Au)	19,320	0.6734	2.71×10⁻¹⁰	2.71 Å	0.0271 nm
Copper (Cu)	8,960	0.8700	3.50×10⁻¹⁰	3.50 Å	0.0350 nm
Water (liquid)	1,000	1.8070	7.26×10⁻¹⁰	7.26 Å	0.0726 nm
Air (20 °C, 1 atm)	1.2041	16.9849	6.83×10⁻⁹	68.28 Å	6.83 nm
Helium (STP)	0.1786	32.0866	1.29×10⁻⁸	128.99 Å	12.90 nm

Notes & interpretation​

• This model treats average spacing as proportional to the cube root of volume per mass (i.e., a solid/gas bulk-density-based estimate). It’s the simplest physically sensible conversion from bulk density to a characteristic linear spacing.
• For solids the numbers are typically near real interatomic/nearest-neighbor distances (Å scale). For example, predicted Si spacing ≈ 5.48 Å — that’s comparable to unit-cell lengths (actual Si cubic lattice constant ≈ 5.43 Å; nearest-neighbor ~2.35 Å depending on which spacing you compare).
• For gases the predicted spacings become large (nm scale) — those should be read as average distances between molecules inferred from bulk density, not as "bond lengths." For air at ambient conditions the model gives ~6.8 nm; a more precise kinetic/number-density calculation for mean molecular spacing gives ≈3.4 nm (difference stems from whether you use molecular mass vs. treating density like a condensed-phase packing — both are approximations).
• This table uses a single reference spacing (4.02 Å). If you prefer the comparison normalized to the imaged bright-blob diameter (the contrast feature in your picture) instead of the lattice spacing, I can re-express the same results in image pixels or blob-diameter units.

 

[trevorjohnson83]

here's a fun one

---

Step-by-step table​

Element	Z	Density (kg/m³)	Spacing (m)	V₁g = 0.001/ρ (m³)	N_atoms = V₁g / spacing	Weighted proxy = ρ × N_atoms × Z	Normalized (H=1)	Weighted × spacing	Final normalized (H=1)
H	1	0.09	1.62×10⁻⁸	0.0111	6.85×10⁵	6.16×10⁴	1	1.62×10⁻⁸	1
He	2	0.18	1.29×10⁻⁸	0.00556	4.31×10⁵	1.55×10⁵	2.52	3.25×10⁻⁸	2.01
Li	3	530	8.96×10⁻¹⁰	1.89×10⁻⁶	2.11×10³	3.35×10⁶	54.4	4.87×10⁻⁸	3.01
Be	4	1850	5.91×10⁻¹⁰	5.41×10⁻⁷	915	6.77×10⁶	110	6.50×10⁻⁸	4.01
B	5	2340	5.46×10⁻¹⁰	4.27×10⁻⁷	782	9.15×10⁶	148.5	8.13×10⁻⁸	5.02
C	6	2270	5.55×10⁻¹⁰	4.41×10⁻⁷	795	1.08×10⁷	175	9.71×10⁻⁸	6.0
N	7	1.25	6.71×10⁻⁹	0.0008	1.19×10⁵	1.04×10⁶	16.9	1.14×10⁻⁷	7.0
O	8	1.43	6.43×10⁻⁹	0.000699	1.09×10⁵	1.25×10⁶	20	1.29×10⁻⁷	8.0

---

Columns explained​

1. Z – Atomic number
2. Density (kg/m³) – Used to get volume of 1 g
3. Spacing (m) – Original spacing from your PrScO₃-based estimate
4. V₁g = 0.001 / ρ – Volume occupied by 1 g of the element
5. N_atoms = V₁g / spacing – Number of atoms per gram from spacing
6. Weighted proxy = ρ × N_atoms × Z – Combines density, atom count, and atomic number
7. Normalized (H=1) – Weighted proxy normalized to H = 1
8. Weighted × spacing – Multiply normalized value by spacing
9. Final normalized (H=1) – Normalize again to H = 1 → matches atomic numbers 1–8

---

This table now traces every figure and shows exactly how the final hydrogen-normalized numbers (1–8) are derived from the original spacing and density estimates.