Act13_sol - 12/12/05 Period 13 Solutions: Energy and Matter...

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12/12/05 1 Period 13 Solutions: Energy and Matter in the Universe 13.1 Origin of Matter in the Universe- the Big Bang 1) The Big Bang Theory and the Early Universe a) How do scientists believe that the Universe began? The big bang theory states that all of the energy now in the Universe was initially very hot and was condensed into an extremely small space. b) In what form was the energy of the early Universe? Early in the Universe, radiation, rather than matter, dominated. Energy and matter did not explode into empty space. Rather, space itself has expanded over time. Since the Big Bang, the Universe has expanded and cooled. c) How much energy was contained in the initial Universe as compared to the amount of energy and energy that has condensed into matter in the Universe today? The Law of Conservation of Energy tells us that the amount of matter and energy that exists today is the same as the amount of energy that was present at the beginning of the Universe. d) Any source of radiation is characterized by a temperature. i) What temperature characterizes radiation from the Sun? 6,000 Kelvin ii) What temperature characterizes radiation from the Earth? 300 K iii) What temperature is believed to have characterized the early Universe? 10 32 K e) In our study of gases, we saw that the average energy and temperature of gases are related by the constant k. (k = 1.38 x 10 – 23 J/Kelvin or 8.62 x 10 – 5 eV/Kelvin). Use this relationship to find the average energy per photon in the early Universe in units of joules and in electron volts. In the early Universe, where there was no matter, the average energy E of a photon was proportional to the amount of energy present. E =3 k T = 3 (1.38 x 10 – 23 J/K) x (10 32 K) = 4.14 x 10 9 J In terms of electron volts, this is E = 3 k T = 3 (8.62 x 10 – 5 eV/K) x (10 32 K) = 2.59 x 10 28 eV f) Group Discussion Question: How does the energy of an early Universe photon compare to the energy of a visible light photon from the Sun?
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12/12/05 2 2) The Expanding Universe Following the Big Bang, the Universe began expanding. We will represent the expanding Universe with an inflating balloon. a) Mark several large dots several centimeters apart on a deflated balloon. Blow up the balloon. If each dot represents a galaxy, what happens to the galaxies as the universe expands? The galaxies move farther apart. b) Consider the view of the Universe as seen by an observer on each galaxy. Do all the galaxies appear to be receding from the observer as the Universe expands? Yes c) An elastic band attached to a board can illustrate the rate of expansion of the Universe. Initially the distance between marks on the unstretched elastic band is 1 inch. Stretch the elastic band until the 1 inch mark on the band lines up with the 2 inch mark on the ruler. When the 1 inch mark on the band is stretched to 2 inches, how far has the 2
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Act13_sol - 12/12/05 Period 13 Solutions: Energy and Matter...

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