1	Astr 1050 Fri. Oct. 10, 2003 Today: Finish Chapter 7, the Sun
2	Homework #4 Solutions Q1: Compared to gamma rays, radio waves travel at the same speed. Q2: Two neutral atoms of the same element but of different isotopes contain the same number of Electrons and Protons but not Neutrons. Q3: The key difference between atoms of two different chemical elements is their number of protons. Q4: According to Wien's law, an object at room temperature (approximately 300K) will radiate the most energy at a wavelength of 10 microns. λ = 3000000 nm/300 = 10000 nm = 10 microns
3	Homework #4 Solutions Q5: You identify the Balmer series absorption lines in the spectrum of a hot type O star, but notice that the lines are shifted from their laboratory wavelengths. For instance, H-beta, normally seen at 486 nm appears at 488 nm. What can you deduce about the motion of this star relative to Earth? USE THE DOPPLER EQ: v/c = (λ_obs/λ_rest) – 1; v/c = (488/486) – 1 = 0.004115 V = 0.004 x 300,000 km/s = 1200 km/s toward us
4	Homework #4 Solutions Q7-9: Stellar spectral classification: Properties Star Temp (K) Medium-strength Balmer lines, strong neutral helium lines = 20,000K Medium-strength Balmer lines, weak ionized calcium lines = 7500 K Strong TiO bands = 3000 K Weak Balmer lines, strong ionized helium lines = 40,000 K Q10 If star A has a temperature of 4000 Kelvin and star B has a temperature of twice that, or 8000 Kelvin, how much more energy does it radiate per second than star A? E goes as T to the 4^th power, so 2⁴ = 16 times.
5	Fusion in the sun 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 “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
6	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
7	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
8	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.
9	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
10	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
11	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
12	For Next time Homework #5 is up on WebCT, due Friday Friday mornings, rest of the semester: bring in an astronomy article for extra credit! (Note can earn this extra credit only once.)