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 sun’s energy comes from the proton-proton cycle, which begins with the reaction (17.61):
1H + 1H → 2H + e+ + v
This reaction is exceedingly improbable, since it requires conversion of a proton to a neutron by β+ decay during the brief collision of the two protons. Estimate the probability that a proton–proton collision will lead to this reaction, as follows: Estimate the time that the first proton (with about 70 keV) is within range of the second (time to traverse about 10 fm, say). Take the mean life for a β decay of this kind to be of order 1 minute, and find the probability that the decay will occur while the protons are within range. [Hint: Recall Eq. (17.7) and the definition of r.]
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