Wikipedia defines factoid as “a questionable or spurious—unverified, incorrect, or fabricated—statement presented as a fact, but with no veracity.”
Last night I was enjoying a TV documentary series, The Story of Science, when I heard a startling factoid, namely:
If the “empty space” inside the atoms that make up people were removed, the entire human population would fit inside a sugar cube.
What the? Can we improve the veracity of this factoid?
Let’s start with atoms. Assuming that atoms are spherical, with a central nucleus which is also spherical, we can calculate atomic and nuclear volumes. A Google search for average diameter of an atomic nucleus suggests that the “average” nuclear diameter is 1e-14 metres, ~ 10 000 times less than an “average” atomic diameter.
Some simple arithmetic in the R console. You remember “four-thirds PI r cubed” from high school, I hope:
avol <- 4/3 * pi * (1e-10 / 2)^3 nvol <- 4/3 * pi * (1e-14 / 2)^3 nvol / avol  1e-12
So, the average nucleus in the average atom occupies a fraction of 0.000000000001 x the atomic volume.
What’s the volume of an “average person”? A very silly question. Wikipedia states that average human density is 1010 kg m-3. Since density = mass / volume, volume = mass / density.
What’s the mass of an “average person”? A very silly question. According to Mass of an adult, it’s 70.00 kg for males and 61.14 kg for females. What about the children? 10.00, 19.50 and 32.20 kg for 1, 5 and 10 year-olds, respectively. What’s the age distribution across the global population? You know what – let’s pretend that everyone is an “average adult” and go with 65 kg. For these calculations, same order of magnitude is surely good enough.
Where were we…ah yes, average human volume:
hvol <- 65 / 1010 hvol  0.06435644
So, assuming that the volume of a person is equivalent to the volume of the atoms from which they are made, 0.000000000001 x that volume is “not the empty space” and there are ~ 7 billion and counting of us:
pvol <- nvol / avol * hvol * 7e+9 pvol  0.000450495
That’s cubic metres, which by my reckoning is ~ 450 cubic centimetres. Assuming a sugar cube with side = 1 cm, we are more like a bag of sugar than a sugar cube. However, allowing for errors, it does indeed seem conceivable that the entire human race is made up of – not very much at all.
Now you can all tell me what’s wrong with these assumptions and calculations. I’ll start: “solidity” is a macroscopic concept and has no meaning inside of atoms. I’ll disable comments when I get bored ;-)