Many practical devices, such as compact disks, magnetic memories, semiconductor

Question

Many practical devices, such as compact disks, magnetic memories, semiconductor chips, and optical coatings, utilize thin films of atoms deposited on solid surfaces. Atoms bind to sites on the surface; the binding energy depends on the kind of site. The equilibrium number of atoms on the various sites is determined by minimizing the free energy.

Consider a solid surface with two kinds of binding sites for a particular type of atom. There are M1 = 6 × 104 sites with binding energy 1 = 0.1 eV and M2 = 2 × 104 sites with binding energy 2 = 0.15 eV. A total of N = 900 atoms occupy these sites: N1 are on sites of type 1 and N2 are on sites of type 2.

Calculate the values of N1 and N2, and from these, their ratio for the equilibrium state at 300 K.

N1 / N2 =

Explanation / Answer

the equation for F is Fi = -Nii - kBT*ln(MiNi / (Ni!))

& the equilibrium values for N1 and N2 as -1 + kBT*ln(N1/M1) = -2 + kBT*ln(N2/M2)

N1 + N2 = 900

We get N1=272.35

Then N2= 900-272.35=627.65

So, N1/N2 =0.434

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