We are told that the noble gases, with their atomic numbers, are: helium 2, neon 10, argon 18, krypton 36, xenon 54, radon 86, and ununoctium 118.

Thus, the sizes (number of elements) of the rings of electrons around the nucleus are the differences between the atomic numbers: 2, 8, 8, 18, 18, 32, 32.

Does anybody know the theory, i.e. the math, of why these particular numbers are correct? Normally, I hate these what's-the-next-number-in-this-sequence puzzles, because they often have multiple reasonable answers. For example, what is the next number in the sequence 2, 4, 6, 8 ... ? One reasonable answer is 9, because those are the numbers that have the letter E in the spelling of their names.

Anyway, I noticed (of course) that these numbers come in pairs, except for the first one. I also eventually noticed that the numbers are each 2*(n^2):

2*(1^2) =2

2*(2^2) =8

2*(2^2) =8

2*(3^2) =18

2*(3^2) =18

2*(4^2) =32

2*(4^2) =32

Is there any theory behind this? Would the next ring size be

2*(5^2) =50

which would make the next noble gas have an atomic number of 118+50, which is 168? Should we call this element diunoctium, maybe?

Bill Smythe