1	Astr 1050 Fri. Feb. 20, 2004 Today: Extra Credit Articles Finish Chapter 7, the Sun Start Chatper 8
2	The Curve of Binding Energy If you keep adding protons to a nucleus? Coulomb repulsion continues to increase new proton feels repulsion from all other protons Strong force attraction reaches limit new proton can’t feel attraction from protons on far side of a big nucleus Gain energy only up to point where Coulomb repulsion outweighs strong force attraction. Most “stable” nucleus is ⁵⁶Fe (26 protons, 30 neutrons, 56 total) Release energy by fusion of light nuclei to make heaver ones– up to ⁵⁶Fe Release energy by fission of heavy nuclei to make lighter ones – down to ⁵⁶Fe
3	The Role of the Nuclear “Weak Force” Why can’t we keep adding neutrons rather than protons? They feel strong force attraction – with no Coulomb repulsion You should be able to get lots of energy by adding neutrons Nuclear Weak Force can (slowly) convert protons to neutrons and back The reactions involve an electron or “positron” to keep charges balanced The reactions produce a new almost massless particle called a neutrino p⁺ + e^- Û n + n p⁺ is proton e^- is electron n is neutron n is neutrino p⁺ Û n + e⁺+ n e⁺ is positron = antiparticle of electron If this second reaction happens then the positron annihilates the next electron it encounters, thereby producing the equivalent of the first reaction. The weak force likes to keep ~equal protons and neutrons in a nucleus The proton repulsion tips the balance towards slightly more neutrons in big nuclei
4	The four fundamental forces Gravity Dominates on astronomical scales Electromagnetic Holds atoms together: Chemistry Strong force Holds nuclei together: Nuclear energy Weak force n Ûp⁺, e^-Radioactive decay (will also play critical role in solar fusion)
5	Fusion in the sun I. Have lots of hydrogen (p⁺ and e^-) – what can we make from it? If ²He (2 protons, 0 neutrons) were stable, fusion would be “easy” Run two protons into each other at fast enough to overcome Coulomb repulsion Once they get close enough strong force takes over, and holds them as nucleus
6	Fusion in the sun II. “Unfortunately” ²He isn’t stable To get stable He need to add one or two neutrons to: Increase Strong Force, without increasing Coulomb force Not really “unfortunate” – If ²He were stable: Sun would burn energy way too fast – and would have gone out by now Weak force converts proton to neutron–fusion will be slow In solar fusion no excess neutrons lying around Hydrogen bombs use deuterium: ²H = (p⁺n) or tritium: ³H = (p⁺n n) to provide it
7	The Proton-Proton chain The first step is slow because it relies on two rare events happening simultaneously Two protons collide with enough energy to overcome the Coulomb barrier While they are close the weak force turns one proton into a neutron The resulting combination of a proton and a neutron IS a stable nucleus ¹H + ¹H ® ²H + e⁺+ n p⁺ + p⁺ ® (p⁺ n) + e⁺ + n The next two steps go quickly because they rely only on the strong force ²H + ¹H ® ³H (p⁺ n) + p⁺ ® (p⁺ p⁺ n ) ³H + ³H ® ⁴He + ¹H + ¹H (p⁺ p⁺ n) + (p⁺ p⁺ n) ® (p⁺ p⁺ n n) + p⁺ + p⁺ The net effect is 4 ¹H ® ⁴He
8	Energy Released? Could work it out “classically” by strength of forces Classical mechanics doesn’t work at this scale – Need quantum mechanics Strength of nuclear forces not originally known Use E=mc² to do accounting Mass is a measure of the energy stored in a system Loss of mass from a system means release of energy from that system Compare mass of four ¹H to mass of one ⁴He 6.693 ´ 10^-27 kg - 6.645 ´ 10^-27kg = 0.048 ´ 10^-27 kg drop in mass E = mc² = 0.048 ´ 10^-27 kg ´ (3 ´ 10⁸ m/s)^{2 =} 0.43 ´ 10^-11 kg m²/s² = 0.43 ´ 10^-11 J (note == a Joule is just shorthand for kg m²/s²) So 4.3 ´ 10^-12 J of energy released This is huge compared to chemical energy: 2.2 ´10^-18 J to ionize hydrogen
9	How long will Sun’s fuel last? Luminosity of sun: 3.8 ´ 10²⁶ J/s H burned rate: H atoms available: Lifetime: In reality not all the atoms we start with are H, and only those near the center are available for fusion. The structure of the sun will change when about 10% of the above total have been used, so after about 10 billion years.
10	Testing solar fusion model Does lifetime of sun make sense? Oldest rocks on earth ~4 billion years old Oldest rocks in meteorites ~4.5 billion years old Other stars with higher/lower luminosity Causes for different luminosity Lifetimes of those stars Look for neutrinos from fusion Complicated story – due to neutrino properties Example of how astronomy presents “extreme” conditions
11	Neutrinos Generated by “weak” force during p⁺® n + e⁺ + n “Massless” particles which interact poorly with matter In that first respect, similar to photons Can pass through sun without being absorbed Same property makes them very hard to detect Davis experiment at Homestake Mine in Black Hills 100,000 gallon tank of C₂Cl₄ dry cleaning fluid in Cl nuclei n + n ® p⁺ + e^- so Cl (Z=17) becomes Ar (Z=18) Physically separate out the Ar, then wait for it to radioactively decay Saw only 1/3 the neutrinos predicted
12	Missing Neutrino Problem Lack of solar neutrinos confirmed by Kamiokande II detector in Japan. (Using different detection method) Possible explanation in terms of Neutrino physics 3 different types of Neutrinos: electron, muon, and tau neutrinos Sun generates and Cl detectors see only electron neutrinos Can electron neutrinos can change to another type on way here? These “neutrino oscillations” are possible if neutrino has non-zero mass Kamiokande II evidence of muon neutrinos becoming electron ones Read “Window on Science 7-2” on “scientific faith” Neutrino mass may have implications for “cosmology” Neutrinos also used to study supernova 1987A
13	For Next time Start on Chapter 8 Homework #4 is up on WebCT, due Fri.