Why is the first excited vibrational state nearly empty at room temperature?

• Vibrational gaps dwarf thermal energy
• Molecules refuse to vibrate at all
• Degeneracy is always zero for vibrations

How do the populations of two levels compare?

• The higher level always holds more
• Degeneracy ratio times an exponential falloff with the gap over temperature
• Both levels always hold equal shares

At a given temperature, each single state holds a bigger share than any state of higher energy.

Two levels have equal energy, but one has twice the degeneracy. How do populations compare?

• Equal populations
• The doubly degenerate level holds half as many molecules
• The doubly degenerate level holds twice the molecules

Why are rotational levels heavily populated at the same temperature where vibrations sit empty?

• Rotational gaps are small next to thermal energy
• Rotations ignore the Boltzmann rule
• Rotational gaps are large next to thermal energy

A sample is heated strongly. What happens to the level populations?

• The distribution sharpens and the ground state gains share
• The distribution flattens and higher levels gain share
• Populations freeze exactly where they were

Where does the Boltzmann factor itself come from?

• It is an arbitrary fitting constant
• It comes from the mass of the molecules
• Counting arrangements shows the exponential spread is the most probable one

A student expects strong infrared hot bands from excited vibrations at room temperature. What is wrong?

• Hot bands are forbidden by selection rules
• Excited vibrational states are nearly empty, so almost nothing absorbs from them
• Infrared light cannot reach excited molecules