High-Temperature Limit What happens when kBT E? † This might represent a protein

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High-Temperature Limit What happens when kBT E?

† This might represent a protein with two different conformations, an atom that is either bound to a surface or unbound, the reactants and products of a chemical reaction, the excited and ground states of a laser, and many other systems of interest. The two-level system is a versatile and useful model.

Atomic Physics The lowest energy state of a hydrogen atom (an electron in a 1s orbital) has an energy of EA = 13.6 eV. The first excited state (an electron in a 2s orbital) has an energy of EA = 3.2 eV. In a room temperature experiment in a chemistry lab, do you need to worry about excited states of hydrogen?

Solar Chemistry The temperature of the sun is about T = 5, 800 K. Is a significant fraction of hydrogen in an excited state at this temperature?

How Hot? At what temperature will a hydrogen atom be equally likely to be in the lowest energy state or the first excited state?

Explanation / Answer

Hydrogen forms diatomic molecules at room temperature and normal pressurE. At room temperatures, it is extremely difficult to form monoatmic hydrogen so it is nearly impossible to excite hydrogen to higher states at room temperature.

as per boltzmann equation, extremely high temperatures are required to excite to high state. Therefore, at 5,800 k , not very high fraction is excited

As per boltzmann equation,

T = Ej - Ei / k ln[(gj/gi) / Nj/Ni]

j - second state , i - first state , gn = 2n2 , N2 / N1 = 1 , k = 8.617e-5

we get T = 85300 K (VERY HOT)

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