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A problem listed for a given section requires an understanding of that section and earlier...

A problem listed for a given section requires an understanding of that section and earlier sections, but not of later sections. Within each section, 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.

•• Consider a proton confined to a region of typical nuclear dimensions, about 5 fm. (a) Use the uncertainty principle to estimate its minimum possible kinetic energy in MeV, assuming that it moves in only one dimension, (b) How would your result be modified if the proton were confined in a three-dimensional cube of side 5 fm? [See Eq. (6.40).] The actual kinetic energy of protons in nuclei is somewhat larger than this estimated minimum, being of order 10 MeV.

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