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 principal source of energy in stars like the sun is the proton-proton cycle, the net effect of which is to fuse four protons into 4He (plus two positrons and two neutrinos). In hotter stars the same effect is produced by a different cycle, called the carbon, or CNO, cycle. This cycle involves six reactions, parts of which are as follows:
1. 1H + 12C → _____+ γ
2. _____ → 13C + e+ + v
3. 1H + 13C→ _____ + γ
4. 1H + _____ → 15O + γ
5. 15O → _____ + e+ + v
6. 1H + _____ → 12C + 4He
(a) Fill in the blanks in these reactions, (b) Verify that the net effect of one complete cycle is to replace four protons by a 4He nucleus plus two positrons, two neutrinos, and some photons, (c) Obviously, the possibility of the cycle depends on the star’s having some 12C to act as a “catalyst.” In addition, it requires higher temperatures than are needed for the proton-proton cycle. Explain why. Very roughly, how much higher would you expect the required temperature to be? (Remember that the high temperatures are needed to overcome the Coulomb repulsion.)
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