H35Cl absorbs radiation at 2885.9 cm , whereas 127 absorbs at 213.2 cm . Using the Boltzmann distribution, calculate the relative populations of the ground and first excited vibrational states of these molecules at 25 C and 500 C. Give the state v = 0 a population of 1.

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Use the Boltzmann distribution to answer this question. Thevibrational energy of a bond in a molecule is given by:

E_n = hv(n + 1/2)

where n is an integer starting at zero (i.e. n = 0, 1, 2, ...),h is Planck's constant, and v is vibrational frequency. If thevibrational frequency of I₂ is 208 cm^-1, atwhat temperature will the population of the first excited state (n= 1) be half that of the ground state (n = 0)?

a) Use the Boltzmann equation (see C h. 8, equation 8 - 1: For these calculations you may assume the degeneracy, g j /g 0 = 1) to calculate the relative population of the E = 0 and E = 1 electronic state s at room temperature (25 o C) if the transition from E = 0, v = 0, J = 0 to E = 1, v = 0, J = 0 occurs at a wavelength of 454 nm. b) Repeat the calculation in (a) and determine the relative populations of the v = 0 and v = 1 vibrational state s at room temperature if the transition to the first excited vibrational state occurs at a wavelength of 4. 54 microm. c) Repeat the calculation in (a) and determine the relative population of the J = 0, J = 1, J = 2 and J = 3 rotational states at room temperature if the transitions occur at 15 microm , 7.5 microm, and 3.75 microm. d) Now consider an absorption transition from the populated states of the molecular ground state to the E = 1, v = 0, J = 0 excited state. If the wavelength separation between rotational states cannot be resolved by the absorption spectrometer what would the minimum width in nm of the absorption transition be?

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H35Cl absorbs radiation at 2885.9 cm , whereas 127 absorbs at 213.2 cm . Using the Boltzmann distribution, calculate the relative populations of the ground and first excited vibrational states of these molecules at 25 C and 500 C. Give the state v = 0 a population of 1.

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