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solution_6 - ASTRONOMY 294Z The History of the Universe...

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ASTRONOMY 294Z: The History of the Universe Professor Barbara Ryden SOLUTIONS TO PROBLEM SET # 6 1) [20 points] Potassium-40 is an unstable atomic nucleus; it decays to argon- 40 with a half-life of 1.3 billion years. Suppose that a rock contains 1,000,000 potassium-40 atoms at the time it forms. How many potassium-40 atoms will be left after 1.3 billion years? How many will be left after 2.6 billion years? How many will be left after 3.9 billion years? After one half-life (1.3 billion years), there will be 500,000 potassium-40 atoms left. After two half-lives (2.6 billion years), there will be 250,000 potassium-40 atoms left. After three half-lives (3.9 billion years), there will be 125,000 potassium- 40 atoms left.
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2) [20 points] The “lifespan” of the Sun is 10 billion years; that is, at the time it formed, it contained enough hydrogen to power nuclear fusion for 10 billion years. The star Altair, like the Sun, is powered by the fusion of hydrogen to helium. The mass of Altair is M altair = 1 . 7 M sun . The luminosity of Altair is L altair = 10 . 7 L sun . Is the lifespan of Altair shorter or longer than that of the Sun? What is the approximate lifespan of Altair, in billions of years? The lifespan of a star is directly proportional to its mass; the mass of a star represents its fuel supply, so doubling the mass, all other things being equal, will double its lifespan. In addition, the lifespan of a star is
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