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.
• To “see” spatial details of a size d, you need a probe (light, for example) whose wavelength satisfies λ ≲ d. What energy of photons do you need to “see” spatial details of (a) atomic size (d ~ l0−10m). (b) nuclear size (d ~ 10−14 m). (c) the distribution of “sub-elementary” constituents inside a proton (distances of order 10−17 m, say). [Your answer to part (a) may surprise you, since it suggests that energies of order keV’s are needed to probe an atom, whereas we know that we can learn about atomic energy levels with photons of a few eV. However, the latter tell us about energy levels, but not about spatial details. It remains true that to learn about spatial details one needs keV’s.]
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