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Problem 3.png

Problem 3.png

There are N carbon monoxide molecules adsorbed In a uniform material surface at Iemperature
T, with one molecule occupying exactly one adsorption site. Assume that there is no interaction
between adsorbed molecules, only interactions between each adsorbed molecule and the surface.
We denote the plane parallel to the metal surface as the ply-plane; An adsorbed molecule can either lie flat on the surface, being aligned to x or y direction in No
distinct states with energy ER“, or it can stand up along the z direction with energy Eur. The
energy difference between a molecule standing up and lying flat is dE, i.e. Eflat — Earn = AE.
Assume that the state in which the molecule stands up is more stable than the states in which it
lies flat. a) Draw a simple energy diagram for the states that are available to a single adsorbed
molecule (hint: there are a total of 3 states}. Label the energies of the states and indicate
the degeneracy of the energy levels. in) Given that there is a total ofN molecules. derive an expression for the number of
molecules that are standing up as a function ofT and dE. [Hint account for an
appropriate nonnalization Factor for the Boltzmann probability] c] For a given energy gap dE, deaennine the temperature at which it is equally likely to find
a given molecule lying flat as it is to find it standing up.

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