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9

Experimental approach Here are 100 marbles in a polyethylene bag: If a marble touches the bag, it is counted as being on the surface. I did not count, and the bag was not perfectly round. A balloon might be better. Theoretical approach This works for large $N,$ and the result is as Ivan predicted (from scaling arguments in 2D and 3D, I would imagine). We ...

6

Here I used a numerical approach roughly equivalent to the analytic approach in Poutnik's answer. The procedure is to generate the smallest enclosing sphere containing within its radius 100 hexagonally close-packed beads, and then determine the number of beads in a second smaller concentric enclosing sphere. If r=1 is the radius of a bead, R=5.074 is the ...

7

Note that the classical idea of an atomic nucleus as a set of nucleon balls is very wrong, similarly as another classical idea of an atom as a planetary system of orbiting and spinning electron balls. I suppose you have had bad luck until now as this task is in opinion of my non-math brain resistant to both general theoretical ( geometry, topology ) and ...

0

Your termination of BCC is incorrect about the $\ce{NaCl}$ crystal structure upon pressurization. It is actually simple cubic (SC as $\ce{CsCl}$) where eight $\ce{Cl-}$ ions ate the corners of unit cell and one $\ce{Na+}$ in the center or vise versa. Although either $\ce{Na+}$ or $\ce{Cl-}$ in the center, it is not BCC because ion possessing the center of ...

0

According to the Wikipedia article Potassium alum, the dodecahydrate melts at 92 to 95 °C. So if I wanted a large lump, I'd put the salt in a test tube (or some other container), dunk the container in boiling water to melt the salt, then pour the melted salt into some type of a mold to cool and solidify.

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