Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.
•• The ultimate limit of Moore’s law. In the year 2001 the line width in Pentium chips was 0.18 μm. For the past 3 decades, the line width in integrated circuits has decreased an average of 11% per year. Assume that this trend will continue, and make a graph of line width versus year. If this trend continues, in what year will the size of electronic devices decrease to the size of atoms (0.3 nm, say)? (It seems obvious that electronics cannot get smaller than single atoms, so Moore’s law must fail at that level, if not before.)
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