Consider the H 35 Cl molecule. For HCl the value of B e = 10.59 cm -1 . a. Consi

Question

Consider the H35Cl molecule. For HCl the value of Be = 10.59 cm-1.

a. Consider the H35Cl molecule. For HCl the value of B3 = 10.59 cm-1.a. Calculate the energy for the first 5 levels and the degeneracy for those levels. Collect this information in a simple table. (The first 5 levels will be for J = 0, 1, 2, 3, and 4.) Also calculate the degeneracy value for each of these 5 levels. Make a table with all of these numbers in it! Column 1, J, column 2, EJ, column 3 gJ.

b. For a system of H35Cl molecules at 298.15 K, calculate the ratio of populations: .n1/n0

c. Calculate the ratio of populations: n4/n0

Explanation / Answer

a. for HCl,

Be = 10.59 cm-1

So,

hcBe = 6.626 x 10^-34 x 3 x 10^8 x 1059

         = 2.10 x 10^-22 J

So,

energy levels

E = hcBeJ(J+1)

with,

J = 0,                 E = 0 J                                                       

J = 1,                 E = 2.10 x 10^-22 x 1(2) = 4.20 x 10^-22 J

J = 2,                 E = 2.10 x 10^-22 x 2(3) = 1.26 x 10^-21 J

J = 3,                 E = 2.10 x 10^-22 x 3(4) = 2.52 x 10^-21 J

J = 4,                 E = 2.10 x 10^-22 x 4(5) = 4.20 x 10^-21 J

Degeneracy level = 2J+1

For J = 0,             Degeneracy level = 1

For J = 1,             Degeneracy level = 3

For J = 2,             Degeneracy level = 5

For J = 3,             Degeneracy level = 7

For J = 4,             Degeneracy level = 9

b. Population by Maxwell Bolzmann equation,

n1/n0 = e^(-dE/KbT)

with,

Kb = Boltzmann constant

T = 298.15 K

we get,

n1/no = e^(-6.626 x 10^-34 x 2 x 3 x 10^8 x 1059/1.38 x 10^-23 x 298.15)

          = 0.86

c. ratio of population,

n4/n0 = e^(-6.626 x 10^-34 x 2 x 3 x 10^8 x 1059 x 4/1.38 x 10^-23 x 298.15)

          = 0.66

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