No. The characteristic length for an atom is an angstrom ~10^-10 meters. A toothpick has a thickness of roughly a millimeter, or 10^-3 meters. The earth, at the equator, is roughly 10^7 meters "thick / wide". So a toothpick is around 10^7 times thicker than an atom while the earth is around 10^10 times thicker than a toothpick.
The atom in that pic has 3 reds, 4 blues and 3 electrons (assuming nothing's hidden behind the nucleus). It could be Lithium with a mass of 6.942 g/mol . A single atom of Lithium has a mass of 6.942 g divided by 6.02214076 × 1023 . Earth has a mass of 5.972 x 1027 grams. To calculate how much bigger the Earth is, use the formula
(5.972g x 1027 ) / (6.942g x 10-23 )
=5.972g / 6.942g x 1050
=5.972 / 6.942 x 1050
The Earth has 5.972 / 6.942 x 1050 times more mass than the atom. Something logarithmically between the two would have a mass of the root of this number. That is
2V[5.972/6.942] x 2V[1050 ]
=2V[5.972/6.942] x 1025
times the mass of the atom. If we're not just interested in ratios and want to know the real world mass, that's
6.941765353712grams / 6.02214076 × 10-23 x 2V[5.972/6.942] x 1025
=6.941765353712grams / 6.02214076 x 2V[5.972/6.942] x 102
≈1.069grams x 100
So 106.9 grams is the logarithmic middle between that Lithium atom and the Earth. An orange weighs about this much.
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u/chessgremlin 2d ago
No. The characteristic length for an atom is an angstrom ~10^-10 meters. A toothpick has a thickness of roughly a millimeter, or 10^-3 meters. The earth, at the equator, is roughly 10^7 meters "thick / wide". So a toothpick is around 10^7 times thicker than an atom while the earth is around 10^10 times thicker than a toothpick.