ASTR 3730: Astrophysics 1 Problem Set #1 1) (a) Neutral hydrogen emits radio waves with a wavelength of 21cm. What is the Summary: ASTR 3730: Astrophysics 1 ­ Problem Set #1 Solutions 1) (a) Neutral hydrogen emits radio waves with a wavelength of 21cm. What is the frequency of this radiation? Use formula: c = nl. This gives n = 1.43 x 109 Hz = 1430 MHz. (b) What is the wavelength (in nm) of an X-ray photon with an energy of 6.4 keV? Use E = hn = hc / l. Photon energy is 6400 eV = 6400 x 1.6 x 10-12 erg = 1.02 x 10-8 erg. This gives l = 1.9 x 10-8 cm or 0.19 nm. 2) (a) A binary star system in the star forming region of Taurus (at a distance of 150 pc) has a separation between the two stars of 50 au. Can we resolve the binary (i.e. detect the two stars individually) using a ground-based telescope with a resolution of 1 arcsecond? No. The angular separation of the binary is q = (50 / 150) arcsec = 0.333 arcsec (note that from the definition of the parsec a binary with a separation of x au has an angular separation of 1 arcsecond when it is at a distance of x pc). (b) Improved observations show that what was previously thought to be a single Collections: Physics