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problem_4 - ASTRONOMY 294Z The History of the Universe...

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ASTRONOMY 294Z The History of the Universe Professor Barbara Ryden Problem Set # 4 Due Tuesday, February 5 at class time NAME (please print clearly): SCORE (instructor use only): Reminder: The midterm exam will be on Thursday, February 7, at class time.
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1) [20 points] Today, the average density of matter in the universe is ρ = 3 × 10 - 27 kg / m 3 . If the matter consisted entirely of hydrogen atoms, how many hydrogen atoms (on average) would be contained in a cubic meter of the universe? If the matter consisted entirely of regulation baseballs (of mass M = 0 . 145 kg apiece), how many baseballs (on average) would be contained in a cubic astronomical unit of the universe?
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2) [20 points] The temperature of the cosmic background light today is T 3 K. At the time the universe became transparent, the temperature of the cosmic background light was T 3000 K. This means that the universe has expanded by a factor of 1000 since it became transparent. If the density of matter today is ρ = 3 × 10 - 27 kg / m 3 , what was the density of matter when the universe became transparent? [Hint: you may assume that matter is neither created nor destroyed.]
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