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Unformatted text preview: Astro 346, Spring Semester 2004 Second intermediate exam, solutions Problem 1: Nuclear fusion Helium burning is impeded by a stronger Coulomb repulsion of the nuclei (by Z 2 = 4 ), and thus requires a much higher temperature. The energy yield is much smaller on account of the small binding energy per nucleon of carbon compared with helium. Energy loss by fusion of elements beyond iron, energy loss by photodisintegration of iron, and loss of electron Fermi pressure by neutron formation. Problem 2: Red giants The relative energy yield of hydrogen burning is η = Δ m m p c 2 = 0 . 0075 c 2 , using the helium mass m He = 3 . 97 m p . The total energy is calculated from the total mass of burned material. E tot = M tot η ' 4 · 10 51 erg The time can be estimated as the total energy divided by the power output. τ ' E tot 20 L ' 5 · 10 16 sec ' 1 . 6 billion years This life-time is 1/6 of the main-sequence life-time of the star. If the Galaxy is sufficiently old, the number ratio would also be 1:6. Noting that each red giant has twenty times theold, the number ratio would also be 1:6....
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