Size Electron: Energy Increase, Size Unchanged?

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If the energy of an eletron is increased, is its size also increased? If not, how can it be that something (energy) can have the size of nothing?
 
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The electron has "infinitely long hands" to interact. It is very sticky. When they say it is "point-like", thay mean the interaction potential has a simple form like 1/r where there is a maximum at only one point.