Name:Partner(s):Lab #13 Particle Soup: Big Bang NucleosynthesisPurposeThe student explores how helium was made in the Big Bang.IntroductionVery little helium is made in stars. Yet the universe is roughly 1/4 helium and 3/4 hydrogenby mass. How can this be? Early in the Big Bang the Universe was hot and dense (likethe core of a star) and protons could f use together to make some helium. The fact that theUniverse is 1/4 helium is very good evidence f or the existence of the Big Bang and a hotearly Universe.Scenario 1In the very early Universe, (before 0.01 seconds), the temperature was too high for even pro-tons and neutrons t o exist. Certainly, nuclei of atoms, which require protons and neutrons,could not exist. If nuclei did form, high energy radiation (gamma rays), tore them apart.Once the Universe expanded and cooled to 100 billion degrees, neutrons and protons couldpersist. Not only that, but they could switch back and forth:neutron + neutrino → proton + electron (1)neutron + positron → proton + anti − neutrino (2)neutron → proton + neutrino + electron (3)The total number of particles stays the same but the fraction which are neutrons dependson the temperature, (and nothing else). Another way to say this is that the neutrons andprotons numbers are in thermal equilibrium. To stay in thermal equilibrium all of thereactions above need to be occurring frequently.Astronomy 101 13 – 1 Introduction to AstronomyNeutrons require more energy to make because they are heavier than protons (E = mc2).As the temperature drops, there is less energy available, and the reactions begin to favorprotons (see Ta ble 1).Temperature Equilibrium Neutron Fraction Equilibrium Reaction Speed)100,000,000,000 K50/100 Fast30,000,000,000 K 37/100 Slow10,000,000,000 K 18/100 Stopped3,000,000,000 K 1/100 Stopped1,700,000,000 K 0.01/100 Stopped1,200,000,000 K 0.0004/100 Stopped1,000,000,000 K 0.00003/100 Stopped900,000,000 K 0.000006/10 0 Stopped1. (2 pts) Here are shown 100 particles (protons or neutrons) in a box at various times.Using the Equilibrium fractions given in Table 1, indicate how many are neutrons at0.1 seconds and 1 second by marking the circles. 0.01 seconds is already marked.2. (2 pts) Use version 1 to indicate the number of neutrons at 50 seconds, 100 seconds,150 seconds and 200 seconds.Astronomy 101 13 – 2 Introduction to Astronomy3. (2 pts) In version 1, how many neutrons are left at 50 seconds or later?4. (2 pts) The Universe is too hot to make helium before 150 seconds. In version 1 , howmuch helium was made in the Big Bang (remember that helium is made of two protonsand two neutrons)?5. (2 pts) Look at the equilibrium reaction speed column in Table 1. Why might theequilibrium neutron fraction be incorrect a t 50 seconds?Scenario 2If the Equilibrium reactions have stopped then neutrons simply decay:neutron → proton + neutrino + electron (4)The decay has a half life of 600 seconds. In 600 seconds, a neutron is as likely to turninto a proton as it is to stay a neutron. This can be simulated by tossing a coin. If itlands heads up, the neutron has turned into a proton. The chance of decaying in 50seconds is much less, one in 16. The neutron will turn into a proto n if four coins landheads up.Astronomy 101 13 – 3 Introduction to Astronomy6. (2 pts) Take the neutrons present at 1 second and for version 2 of the Big Bang usefour coin flips to determine if each neutron makes it to 50 seconds and mark it in if itdoes. Take the neutrons present at 50 seconds and repeat the procedure again for 50seconds later (100 seconds). Evolve your set of neutrons to 200 seconds this way. Yo ushould have a reasonable number of neutrons left at 200 seconds.7. (2 pts) Circle groups of two neutrons and two pro t ons (helium nuclei).8. (2 pts) What fraction of helium did you get by number? ie. What is:#helium/(#helium + #deuterium + #protons)9. (2 pts) Assume each proton and neutron weigh the same. What fraction of the massis now in helium? What f raction of the mass is in deuterium?10. (2 pts) At 200 seconds the Universe is cool enough that deuterium can form, a nec-essary step in forming helium. All deuterium is converted quickly into helium. Drawcircles around groups of two neutrons and two protons at 200 seconds (version 2). Ifyou have any left over neutrons draw a circle around it and one proton. This is adeuterium nucleus. Once neutrons are inside a nucleus they stop decaying.Astronomy 101 13 – 4 Introduction to AstronomyScenario 311. (2 pts) Repeats steps in scenario 2 for version 3. This time assume deuterium is ableto form at 150 seconds so circle the helium then12. (2 pts) What fraction of helium did you get by number? i.e. what is:#helium/(#helium+#deuterium+#protons)13. (2 pts) What f raction of the mass is now in helium? What fraction of the mass is indeuterium?14. (2 pts) Did you get more or less helium when deuterium formed earlier? Why?15. (2 pts) Version 3 of the Early universe is a fairly accurate reflection of the modelsastronomers actually use. Is your mass fraction in the usual range of 20-30 percentthat theoreticians predict?Astronomy 101 13 – 5 Introduction to
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