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- 4. What is the form of the total vibrational partition function for a polyatomic molecule?What is overall molecular partition function Q, and how it is constructed using the partition functions for each energetic degree of freedom?N2O and CO2 have similar rotational constants (12.6 and 11.7 GHz, respect ively) but strikingly different rotational partition functions. Why?
- Consider a system having four energy levels. Assuming the levels have energy values of(0, 1, 4, 9, and 16) x 10-24 J, and the degeneracies of the levels are 1, 2, 3, 4 and 5 (startingfrom ground state to highest excited state respectively), calculate the value of partitionfunction at 298 K?(c) Consider the following rotational temperatures of diatomic molecules: qr(N2) = 2.9K, qr(HD) = 64.7K Assuming classical behaviour (i.e. continuum approximation): (i) Estimate the number of accessible rotational energy levels at 290 K for both moleculesThe bond length of N2 is 109.75 pm. Use the high-temperature approximation to calculate the rotational partition function of the molecule at 300 K.
- A rotating methane molecule is described by the quantum numbers J, MJ, and K. (a) For methane, how many rotational states have an energy equal to hBJ(J + 1) with J= 8? (b) Now consider chloromethane. How many rotationalstates have an energy equal to hBJ(J + 1) with J = 8?Evaluate the translational partition function of (a) N2, (b) gaseous CS2 in a flask of volume 10.0 cm3. Why is one so much larger than the other?What can we predict about fluorescence intensity as a function of temperature from Boltzmann’s distribution?
- Answer the following questions in minimum 5 sentences 3. Describe the difference between real deviations from Beer’s law and those due to instrumental orchemical factors.4. How does an electronic transition resemble a vibrational transition? How do they differ?Calculate the vibrational partition function of CCl4 at 500 K given the wavenumbers 459 cm−1 (symmetric stretch, non-degenerate), 217 cm−1 (deformation, doubly degenerate), 776 cm−1 (deformation, triply degenerate), 314 cm−1 (deformation, triply degenerate).the rotational constant for 1H35Cl is 10.6 cm-1 . What are the degeneracies, g, of the J=2, and J=3 rotational states?