1) You are examining the light spectrum from a hot galactic gas. From the frequencies in the spectrum, you conclude that the gas is mostly made of hydrogen. From the relative intensities of each part of the spectrum, you deduce that for every 12 hydrogen atoms in the first excited state, there are 3 in the second excited state. In order to double check your conclusions about this gas's properties, you decide to predict how many hydrogen atoms are in the third excited state, relative to the 1st excited state (which you can then subsequently compare to measured values). Looking up in a table, you find that,
a) the ground state has an energy of -13.6 eV, with a degeneracy of 1
b) the first excited state has an energy of -3.4 eV with a degeneracy of 4
c) the second excited stat has an energy of -1.5 eV with a degeneracy of 9
d) the third excited state has an energy of -0.85 eV with a degeneracy of 16