An oscillator with frequency f = 2.1×1012 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. 1)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)?

(a) assume the equation x = at^3 + bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. determine the dimensions of the constants a and b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.) (b) determine the dimensions of the derivative dx/dt = 3at^2 + b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.)