A water molecule can vibrate in various ways, but the easiest
type of vibration to excite is the "flexing' mode in which the hydrogen atoms move
toward and away from each other but the HO bonds do not stretch. The oscillations
of this mode are approximately harmonic, with a frequency of 4.8 x 1013Hz. As
for any quantum harmonic oscillator, the energy levels are , and so
on. None of these levels are degenerate.
(a)
state and in each of the first two excited states, assuming that it is in equilibrium with a reservoir (say the atmosphere) at 300 K. (Hint: Calculate 2
by adding up the first few Boltzmann factors, until the rest are negligible.)
Calculate the probability of a water molecule being in its flexing ground
(b) Repeat the calculation for a water molecule in equilibrium with a reservoir
at 700 K (perhaps in a steam turbine).