Swans on Tea

Is This Answer Crazy? Maybe.

Short version: How big is a platinum atom ends up with an answer that’s pretty big. I had tweeted a response that I had once seen an answer that was “the mass of the frog is 10^24 kg”, which is a similarly egregious answer. Being able to judge answers like this is tied in with solving so-called Fermi problems — the solutions to which require reasonable estimations and approximations.

I explained the grading policy we had when I was teaching in the navy included having physically realistic answers. If you got something this far off, or a negative number for a scalar, you lost points for not grasping the concept well enough. In the navy that was a little easier to enforce, because our material was grounded in a specific application — that of running a nuclear reactor for propulsion (and other energy requirements) of a boat or ship. But even for the more basic introductory material, we used realistic numbers for whatever we could and discussed reasonableness of answers.

That’s probably a little harder in an academic setting, using a textbook written by someone else who might not adhere to some standard of reasonableness in writing up examples for each topic and dozens of questions at the end of each chapter. But it is something you could be disciplined enough to observe in class and then hold the students to some standard. Still, it’s not unreasonable to expect that students know that a human is around two meters tall and small but macroscopic objects are going to have in the vicinity of Avogadro’s number of atoms in it (give or take a few orders of magnitude), and things like that.

As for the rest of my tweet, I said that a 10^24 kg frog made of silicon that was 10^18m in diameter would probably not gravitationally form itself into a sphere. If the frog has Avogadro’s number of silicon atoms in it, that’s a hundred million atoms in each dimension, meaning the frog would be 10^26 meters in each dimension — bigger than our galaxy — yet have a mass similar to that of earth (6 x 10^24 kg). Since we’re dealing with an inverse square law, an object of equal mass but 10^19 times larger than the earth (around 10^7 meters across) will have a surface gravity 10^38 times smaller. Pretty much negligible.