Puzzle cyclotron

Cyclotron puzzles are fiendishly difficult, but, like many problems in mathematics and science, the rules of the game are really quite simple. In fact, you can study them using just a pencil and paper. These puzzles derive their name Ifom the apparatus used for accelerating charged atomic particles as they revolve round and round in a circular orbit. 

Consider the following questions involving the cyclotron puzzle ... 

The following C code by Heiner Marxen solves the various cyclotron puzzles. 

Puzzles, such as the fiendishly difficult cyclotron puzzle, with hints to remind you there are often more ways of looking at the world than are immediately obvious. 

When this chapter was in press, Beauchamp and coworkers reopened the discussion on the relative stabilities of silaethylene (40) and methylsilylene (45)377. They found, using Fourier transform ion cyclotron resonance spectroscopy, that silaethylene (40) is by 10 3 kcalmol"1 more stable than the isomeric methylsilyene 45. The experiments were corroborated by ab initio GVB-CI calculations which found that 40 is more stable than 45 by 11.6 kcal mol-1. The discrepancy between these recent results377 and the previous high level MO calculations, which predict a 40-45 energy difference of nearly zero (see Table 19), is puzzling. Further calculations and experiments are required to resolve this problem. 

In true cyclotrons, the orbit of a particle cannot decrease in diameter. For the puzzles here, this additional constraint would imply that a particle cannot jump to a channel of smaller diameter as it travels. It could only travel in its current channel or go to an outer one. How would this alter your answers to the other questions ... 

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