Problems are listed in approximate order of difficulty. A single dot (•) indicates straigh...

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 gets its energy from a sequence of nuclear reactions called the proton-proton cycle. These reactions take place near the sun’s center and have the net effect

the particles involved being (in order) protons, helium nuclei, positrons, neutrinos, and high-energy photons (called γ-rays). About 95% of the energy released in this composite reaction goes to the γ-ray photons, whose average wavelength is about 250 fm (1 fm = 10−15 m). (a) What is the total energy released in the above reaction? The mass of the v is so small you can take it to be zero. (b) Over the course of a few million years, these γ-rays diffuse toward the surface and are slowly converted into visible photons. About how many visible photons are generated from one of the original γ’s?