Atom Or Universe?

Is a person proportionally closer in size to an atom or the universe?

This is a good question for using Fermi Estimation.

A person is about one meter across. At atom is about a hundred picometers across and the universe is about 100 sextillion kilometers across. If we convert these values to scientific notation, an atom is
10^-10 meters across, a person is 10⁰ meters across, and the universe is 10²⁶ meters across. Thus, the universe is 36 orders of magnitude larger than an atom, so an object that is in between the two in size would be 18 orders of magnitude larger than an atom and 36 orders of magnitude smaller than the universe. 26-18 (and for that matter -10+18) is 8, so an in-between object would have a diameter of 100,000,000 meters 100,000 kilometers. This is smaller than Jupiter and Saturn, but larger than the other two gas giants (Uranus and Neptune) and much larger than Earth.[1] It's also probably larger than you are unless you happen to be a gas giant or star (as far as I'm aware, there aren't any reading my blog).

Oh. Right. Sorry. Anyway, I'll bring some real numbers into the equation and see if that changes anything. The atomic radius of hydrogen (the most common atom in the
universe) is 53 picometers[2] so the diameter would be 106 picometers. The average height of an American male over 20 is 69.3 inches[3], or 1.76022 meters. The obeservable universe is 92 billion light years across.[4]

There are 9.4605284 quadrillion meters in a light year, so the observable universe is 8.703686128*10²⁶ meters across. So far, it seems that my Fermi Estimation was
pretty close to the actual sizes (within an order of magnitude or so, which is pretty close considering the roughness of the estimates). Let's plug in these new values.

A hydrogen atom is 1.06*10^-12 meters across, a human is 1.76022*10⁰ meters acorss, and the observable universe is 8.703686128*10²⁶ meters across. Thus, the observable universe is 9.225907296*10³⁸ times the size of a hydrogen atom. Some plugging in of numbers on my calculator shows that an in-between object is 3.037417867*10^19 times the size of a hydrogen atom.
This comes out to 28,654,885.53 meters. It's a bit closer to the size of a human than the result I got with Fermi Estimation. It's twice the size of the largest terrestrial planets and half the size of the smallest gas giants.[5]

Does this make you feel small and insignificant? (You are small and insignificant) Well...

I was counting by diameter in the previous examples. But since humans are full of mass and the universe is rather diffuse, maybe counting by mass will bring a more satisfactory result. A typical human weighs 62 kilograms[6], but weights of individuals can vary wildly.^{[citation needed]}. A hydrogen atom weighs 1.673534*10^-27 kilograms.[7] The mass of a hydrogen atom tends not to vary so much. The typical obsevable universe has a mass of 10^53 kilograms (the average of all known observable universes).[8] This figure isn't known to differ from individual to individual.

So the mass of the universe is 5.98*10^79 times heavier than the mass of a hydrogen atom. Thus, an object with a mass in between that of a hydrogen atom and that of the universe would be very roughly 10^40 times heavier than a hydrogen atom, or 1.673534*10^13 kilograms. This result is the best of all. It's far, far smaller than any planet (though obviously nowhere near as small as a person). This Wikipedia article tells me that such a mass would be about as heavy as a fairly large mountain.

I guess that still makes you feel small and insignificant. Oh well.