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Solution_Set_06 - SOLUTION SET 6 Physics 2022 1 L = 1000...

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SOLUTION SET 6 Physics 2022 1. L * = 1000 L sun T * = 1000 K T sun = 5800 K L * / L sun = (R * / R sun ) 2 (T * / T sun ) 4 1000 = (R * / R sun ) 2 (1000 / 5800) 4 R * = 1064 R sun = 7.4 x 10 8 km = 4.9 AU 2. L sun = 3.85 x 10 26 J/s 1 reaction of H to He releases 26.7 MeV Number of reactions = (3.85 x 10 26 J/s) / (26.7 x 10 6 x 1.6 x 10 -19 J/eV) = 9.0 x 10 37 reactions per second Mass = (4 hydrogen atoms) (number of reactions) = 4 (1.67 x 10 -27 kg) (9.0 x 10 37 reactions/second) = 6.0 x 10 11 kg/s 3a. In one reaction of H burning, 4.031280 u release 26.71 MeV [(4.03128 u)(1.66054 x 10 -27 kg/u)] / [(26.7 x 10 6 eV)(1.6 x 10 -19 J/eV)] = 1.57 x 10 -15 kg/J In one second, the Luminosity (energy) is 3.83 x 10 26 J/s, so H burned in one second = (1.57 x 10 -15 kg/J)(3.83 x 10 26 J/s) = 6.0 x 10 11 kg/s The main sequence lifetime of the Sun is 1.2 x 10 10 years, so the total H burned is Total H burned = (6.0 x 10 11 kg/s) (1.2 x 10 10 )(365.25)(24)(3600 s) = 2.27 x 10 29 kg 3b. M sun = 1.99 x 10 30 kg The composition of the Sun is 74% Hydrogen. M H = (0.74) (1.99 x 10 30 kg) = 1.47 x 10 30 kg Ratio = (2.27 x 10 29 kg) / (1.47 x 10 30 kg) = 0.154
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4a. E = Δ m c 2 = (2 x 10 -26 kg) (3 x 10 8 m/s) 2 = 1.8 x 10 -9 J 4b. E = Δ m c 2 = (1 kg) (3 x 10 8 m/s) 2 = 9.0 x 10 16 J 4c. E = Δ m c 2 = (6 x 10 +24 kg) (3 x 10 8 m/s) 2 = 5.4 x 10 41 J 5a. τ = E / L sun = (1.8 x 10 -9 J) / (3.9 x 10 26 J/s) = 4.6 x 10
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