## Homework Handout #8

8.01:  An A0 V star has an apparent visual magnitude of 12.5 and an apparent blue magnitude of 13.3.
(a) What is the color excess for this star?
(b) What is the visual absorption in front of this star?
(c) Calculate the distance to the star, in pc.
(d) What error would have been introduced if you had neglected interstellar absorption?

8.02:  Somewhere in our galaxy resides a cloud of neutral hydrogen gas with a radius of 10 pc.  The gas density is 10 atoms/cm3.
(a) How many 21-cm photons does the cloud emit every second?
(b) If the cloud is 100 pc from the Sun, what is the energy flux of this radiation (in erg/s/cm2) at the Sun?

8.03: Using Bohr's formula for the wavelengths of hydrogen lines, calculate the wavelength and frequency of the radio recombination line with upper level 93 and lower level 92.  What part of the electromagnetic spectrum does this correspond to?

8.04: (This is problem 12.2 of the text) Estimate the temperature of a dust grain that is located 100 AU from a newly formed F0 main-sequence star.  [Hint: Assume that the dust grain is in thermal equilibrium--meaning that the amount of energy absorbed by the grain in a given time interval must equal the amount of energy radiated away during the same interval of time.  Assume also that the dust grain is spherically symmetric and emits and absorbs radiation as a perfect blackbody.  You may want to refer to Appendix E for the luminosity of an F0 main-sequence star.]