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ASTR1040 Spring, 2005
Due date: Thursday, February 17
1. Let's consider what might happen when hydrogen in the Sun's core is all used up via the proton-proton chain, and the Sun is left with a pure helium core. In the following, assume that the luminosity of the Sun remains at a constant level of L = 3.83 X 10^26 J/sec (W) and that nuclear reactions take place only in the innermost 10 percent of the Sun's mass. The form of helium that remains after the p-p reaction is helium 4, aka 4He, which has two protons and two neutrons in its nucleus. The mass of this nucleus is 4.002603 u, where the u is the universal mass unit (formerly known as the atomic mass unit, or amu) and has the value 1 u = 1.67 X 10^-27 kg. Here is a brief table of isotopic masses that are relevant to this problem
1H (hydrogen: mass = 1.007825 u)
2H (deuterium: mass = 2.014102 u)
3H (tritium: mass = 3.016049 u)
3He (helium 3: mass = 3.016029 u)
4He (helium 4: mass = 4.002603 u)
6Li (lithium 6: mass = 6.015121 u)
7Li (lithium 7: mass = 7.016003 u)
7Be (beryllium 7: mass = 7.016928 u)
8Be (beryllium 8: mass = 8.005305 u)
10B (boron 10: mass = 10.012938 u)
12C (carbon12: mass = 12.000000 u)
13C (carbon 13: mass = 13.003355 u)
14C (carbon 14: mass = 14.003241 u)
14N (nitrogen 14: mass = 14.003074 u)
16O (oxygen 16: mass = 15.994915 u)
Now answer the following questions:
(a) What element is likely to be formed when two 4He nuclei merge? Specify the particular isotope (combination of mass number and atomic number) that you choose
(b) Calculate the mass difference between the ingredients (the two helium nuclei) and the product (the isotope you chose in part a). What fraction of the ingredient mass is this?
(c) Convert this mass difference (from part b) into an energy difference, in units of joules.
(d) Do you think that the reaction you chose in part a is viable? In other words, is this reaction likely to be the next source of energy for a star after its hydrogen has been converted to helium? Explain.
2. Now for some problems on a totally different topic, stellar magnitudes:
(a) Calculate the relative brightness for this star pair:
Star A has m = 4.83; star B has m = 1.97;
(b) Find the visual absolute magnitude M_v for:
A star with apparent visual magnitude m_v = +16.84 and distance d = 518 pc
(c) Find the distance to the following:
A star with m_v = +18.42 and M_v = +4.85
3. The following requires you to use what you have learned about absolute magnitudes and how they are related to luminosities (through the bolometric magnitude).
(a) What is the luminosity (in solar units) of a star whose bolometric absolute magnitude is M_bol = -6.83? (The Sun's bolometric absolute magnitude is M_bol = +4.75).
(b) If lambda_max = 1000Å, what is the diameter of the star?
(c) What is the star's angular diameter, if its parallax is π = 0.00048"? Is this angular diameter detectable with the Hubble Space Telescope? (For this last part you can refer to your notes or re-calculate the HST's diffraction limit, assuming that the observed wavelength islambda = 5500Å and the telescope diameter is 2.4 m.)
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