Consider a transparent cylinder filled with hydrogen at room temperature. Use the Boltzmann equation to estimate the ratio of (i) the number of atoms in the first excited state relative to the ground state, and (ii) the number of atoms in the second excited state relative to the ground state. You will need to use the fact that the statistical weight of the nth state of hydrogen is gn = 2n2. Use your findings to explain why light from a blackbody source passing through this cylinder should show only the absorption lines of the Lyman series, not those of either the Balmer or Paschen series. As part of your explanation, you should briefly define the Lyman, Balmer, and Paschen series. To what temperature would you need to heat the gas to ensure that the number of atoms in the first excited state was 1% of the atoms in the ground state? To what stellar spectral type would this temperature correspond?