Question

A. Consider a hydrogen atom with one electron and quantized energy levels. The lowest energy level (n = 1) is the ground state, with energy -13.6 eV. There are four states corresponding to the next lowest energy (n = 2), each with energy-3.4 eV. For the questions below, consider one of these four states, called one of the first excited states.

2. Assume that this hydrogen atom is present in a gas at room temperature (T ~ 300 K, kBT ~ 1/40 eV). What (approximately) is the value of the exponent -ΔE/kBT in the ratio of the Boltzmann factors for the four first excited states and ground state?

Is the probability of finding the electron in any one of the first excited states greater than, less than, or equal to the probability of finding the electron in the ground state? Explain, giving a somewhat quantitative estimate.

Based on your calculation, is it very likely that you will observe effects of the transitions from the first excited state to the ground state at room temperature? Explain.

Answer 1