# Harvard Astronomy 201b

In your bathroom, if you clean it—$NH_3$ is actually just ammonia!  Ammonia is common in regions near the galactic center (Kaifu et al. 1975). And CO  becomes optically thick before ammonia—and optically thick is optically useless when you want to find densities!  Ammonia allows study of denser regions—exactly what is needed to probe star formation.
Making simple assumptions, we can estimate the energy of the inversion.  Assuming the distance to the base’s center for each H’s electron is (a+l), a the Bohr radius and l the ammonia bond length, 1 angstrom, and that the N’s electrons are (a+l) above this center, we calculate the potential where the 7 protons in N are.  Converting to energy and thence frequency, we obtain $\nu\sim 1 \;\rm{GHz}$. Incidentally, to go further one could use the WKB approximation to estimate the tunneling probability.  Given a minimum flux per beam width to which the telescope is sensitive (14 mJy here is the noise), one could even then place a lower bound on the column density observable with this transition by a particular instrument, and assuming isotropy, one could get a density from the column density.