An oscillator with frequency f = 2.1×10^(12) Hz (about typical for a greenhouse gas molecule) is in equilibrium with a thermal reservoir at temperature T. The spacing between the energy levels of the oscillator is given by ε = hf, where h = 6.626×10^(-34) J*sec.
(a) For what temperature does P1/P0 = 1/2, where P1 is the probability that the oscillator has E = ε (the first excited state) and P0 is the probability that it has E = 0 (the lowest energy state)?
(b) If T is 10% of the value you calculated in part 1), what is the ratio P1/P0?
(c) At the temperature of part (b), what is the ratio P2/P1, where P2is the probability that the oscillator is in the second excited state (E = 2ε)?

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.