Hobbs in 1976 devised an experiment to test if the ISM is heating via ionization of trace elements (metals) by starlight or by cosmic-ray and X-ray ionization of hydrogen. We observed the relationship between column densities of K I and H I. Derive the proportionality (i.e. N(KI) , find x) for both cases.

Hint: Start with the ionization equilibrium equation and assume K II is the dominant for of K such that n(K II) (K) n(H), where (K) = n(K)(H) is fixed for a particular metallicity.

T NCHI) n(KII)n(e) n(KI) II ak T NCHI) n(KII)n(e) n(KI) II ak