b) A hydrogen atom in the 2P state is placed in a cavity. Find the temperature of the cavity at which the transition probabilities for stimulated and spontaneous emissions are equal.
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- What can we predict about fluorescence intensity as a function of temperature from Boltzmann’s distribution?4. What is the form of the total vibrational partition function for a polyatomic molecule?A certain molecule has a doubly degenerate excited state lying at 360 cm−1 above the non-degenerate ground state. At what temperature will 15 per cent of the molecules be in the upper state?
- 5. For carbon monoxide at 298K, determine the fraction of molecules in the rotational levels for J=0, 5, 10, 15, and 20. The rotational constant (B) is 3.83x10^-23 Joules.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?Calculate realtive population of the two rotational level for HCl at 300K
- The ground configuration of carbon gives rise to a triplet with the three levels 3P0, 3P1, and 3P2 at wavenumbers 0, 16.4, and 43.5 cm-1, respectively. (a) Eva luate the electronic partition function of carbon at (i) 10 K, (ii) 298 K, (b) Hence derive an expression for the electronic contribution to the molarinternal energy and plot it as a function of temperature. (c) Evaluate the expression at 25 °C.Calculate, by explicit summation, the vibrational partition function of I2 molecules at (a) 100 K, (b) 298 K given that its vibrational energy levels lie at the following wavenumbers above the zero-point energy level: 0, 215.30, 425.39, 636.27, 845.93 cm−1. What proportion of I2 molecules are in the ground and first two excited levels at the two temperatures?A certain molecule has a non-degenerate excited state lying at 540 cm−1 above the non-degenerate ground state. At what temperature will 10 per cent of the molecules be in the upper state?
- Evaluate the rotational partition function of pyridine, C5H5N, at 25 °C given that ᷉ A = 0.2014 cm−1, ᷉ B = 0.1936 cm−1, ᷉ C = 0.0987 cm−1. Take the symmetry number into account.For 16O2, Δ ᷉ G values for the transitions v = 1 ← 0, 2 ← 0, and 3 ← 0 are, respectively, 1556.22, 3088.28, and 4596.21 cm−1. Calculate ᷉v and xe. Assume ye to be zero.Calculate the vibrational partition function of CI4 at 500 K given the wavenumbers 178 cm−1 (symmetric stretch, non-degenerate), 90 cm−1 (deformation, doubly degenerate), 555 cm−1 (deformation, triply degenerate), 125 cm−1 (deformation, triply degenerate).