29:62 General Astronomy

Third Homework Set...Due February 17, 1999

Show calculations and give reasons for your answers. Don't go around confused and despondent; if you do not know how to get started, ask us for help.

1. An electron moving in a gas has a kinetic energy equal to the mean energy for particles at the gas temperature of K. It collides with an ion, coming to a complete stop. In the process it radiates a photon. What is the wavelength of this photon? This process is an important one in astrophysics, and is referred to as bremstrahlung, German for ``braking radiation''.
2. In the discussion on blackbody radiation it was emphasized that the Planck function, which gives the numbers of Watts/m per wavelength interval radiated by a blackbody, depends only on the wavelength of observation and the temperature of the blackbody. Thus the total number of Watts/m radiated over all wavelengths is the same for two blackbodies at the same temperature, irrespective of their sizes. Given this, what would you say is the ratio of the radius of a red supergiant like Betelgeuse to that of a red dwarf?
3. Using the same principles as in the previous problem, what is your estimate of the radius (in meters!) of the star Capella (the pretty bright yellow star straight overhead these evenings)?
4. An important nuclear reaction which occurs in red giant stars is the following;

   

   What is the energy released in each such reaction? To obtain the answer, you will need to find the precise values for the masses of the nuclei involved. They will be given in atomic mass units (amu). By definition, an amu is 1/12 the mass of a Carbon nucleus. For the precision of this problem, you may take it to be equal to the mass of a proton. Need DATA? Try Table of Nuclides
   

5. Assume the following model for the energy source of the Sun. The innermost 10 % of the mass of the Sun can undergo a process (of unspecified nature) in which Joules/kg are released. If this energy is released gradually, how long could it provide the energy requirements of the Sun?

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