solution_7 - ASTRONOMY 294Z: The History of the Universe...

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Unformatted text preview: ASTRONOMY 294Z: The History of the Universe Professor Barbara Ryden SOLUTIONS TO PROBLEM SET # 7 1) [20 points] The age of the universe (that is, the time since the Big Bang) is 14 billion years. The age of the Solar System is 4.56 billion years. Thus, the Solar System has existed for 32.6% of the age of the universe. For what percentage of the total age of the universe have the following things existed? a) Helium nuclei have been around since the time of primordial nucle- osynthesis, at a time t pn ≈ 7 min ≈ 420 sec after the Big Bang. The age of the universe, expressed in seconds, is t uni = 1 . 4 × 10 10 years ˆ 3 . 16 × 10 7 sec 1 year ! = 4 . 4 × 10 17 sec . (1) The fraction of the age of the universe during which helium nuclei have been around is F = t uni- t pn t uni = 1- t pn t uni = 1- 420 sec 4 . 4 × 10 17 sec = 1- 10- 15 = 0 . 999999999999999 . (2) Expressed as a percentage, this is 99.9999999999999% of the age of the universe. (There should be 13 nines after the decimal point – I hope I counted them correctly!) b) Neutral atoms have been around since the universe became transpar- ent, at a time t trans = 350 , 000 years after the Big Bang. The fraction of the age of the universe during which neutral atoms have been around is F = 1- t trans t uni = 1- 3 . 5 × 10 5 years 1 . 4 × 10 10 years = 1- . 000025 = 0...
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This note was uploaded on 07/17/2008 for the course ASTRO 294 taught by Professor Ryden during the Winter '08 term at Ohio State.

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solution_7 - ASTRONOMY 294Z: The History of the Universe...

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