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.
•• Numerous pions are created by cosmic rays in the upper atmosphere, but very few reach sea level. One reason is that most of the pions decay before they reach sea level, and another is that they are quickly absorbed by the nuclei in the atmosphere. To estimate this second effect, answer the following: (a) About how many nuclei (of nitrogen and oxygen) are contained in a column of atmosphere of area 1 m2, extending from sea level to the top of the atmosphere? (Atmospheric pressure at sea level is about 105 N/m2.) (b) About how many of these nuclei are needed to completely cover 1 m2 in a layer one nucleus thick? [Recall Eq. (16.3) for the nuclear radius.] (c) Use these two results to estimate the number of nuclei through which a pion would have to pass traveling from the upper atmosphere down to sea level.
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