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?
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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?
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- Chemistry The first excited electronic energy level of the helium atom is 3.13 ✕ 10−18 J above the ground level. Estimate the temperature at which the electronic motion will begin to make a significant contribution to the heat capacity. That is, at what temperature will 5.0% of the population be in the first excited state?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?Calculate the vibrational, rotational, and translational contributions to the constant volume heat capacity (Cv) for 14N2 at 298 K. Assume this represents the high temperature limit for rotational energy and low temperature limit for vibrational energy. Given that Cv=20.81 J/K·mol for N2, state which type or types of energy contribute most to Cv for N2 and explain why those types of energy contribute most.
- Consider the rotational temperatures of the following hetero diatomic molecules: θr(CO) = 2.1 K, θr(HF) = 30.2 K. In which case would the classical approximation be accurate? Justify your answer.b. The energy difference between consecutive vibrational states is 1.0 x 1020 J for a molecule. (i) Calculate the population ratio, n4/n¡, for this system at 298 K and discuss the significance of this ratio in terms of the distribution of molecules in the higher vibrational energy states. (ii) Estimate the vibrational partition function at 298 K. (iii) Estimate the fundamental vibration wave number for this molecule. h = 6.626 x 10-3ª J s k= 1.38 x 1023 J K' c = 2.998 x 10® m s''For two nondegenerate energy levels separated by an amount of energy ε/k=500.K, at what temperature will the population in the higher-energy state be 1/2 that of the lower-energy state? What temperature is required to make the populations equal?
- Derive an expression for the mean energy of a collection of molecules that have three energy levels at 0, ε, and 3ε with degeneracies 1, 5, and 3, respectively.Consider a molecule having three energy levels as Part A follows: What is the probability that this molecule will be in the lowest-energy state? State Energy (cm-1) Degeneracy Express your answer to three significant figures. 1 1 500. 3 ΑΣφ 3 1500. 5 Imagine a collection of N molecules all at 400. K in which one of these molecules is selected. Pi = Note: k = 0.69503476 cm¬1 . K-1. Submit Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remainingA certain atom has a doubly degenerate ground state and an upper level of four degenerate states at 450 cm−1 above the ground level. In an atomic beam study of the atoms it was observed that 30 per cent of the atoms were in the upper level, and the translational temperature of the beam was 300 K. Are the electronic states of the atoms in thermal equilibrium with the translational states? In other words, does the distribution of electronic states correspond to the same temperature as the distribution of translational states?
- This problem explores the vibrational and rotational energy levels of the hydrogen halides. Experimental data are given below. Hydrogen halides kf (kg/s²) R (pm) HF 970.0 91.7 HCI 480.0 127.5 HBr 410.0 141.4 HI 320.0 160.9 For one mole of each HF, determine the following quantities. ΔΕ1Ο 8.29 x10-20 J b. The number of vibrational energy levels occupied at 300 K j = 2 levels c. The spacing between the two lowest rotational energy levels 7.73 x10-32 ΔΕ10 J Incorrect d. The number of rotational energy levels occupied at 300 K 5 j = levels Incorrect[References) The vibrational temperature of a molecule prepared in a supersonic jet can be estimated from the observed populations of its vibrational levels, assuming a Boltzmann distribution. The vibrational frequency of CuBr is 9.44×1012 s1, and the ratio of the number of molecules in the n = 1 state to the number in the n = 0 state is 2.59x10 2. Estimate the vibrational temperature under these conditions. (Enter your answer to three significant figures.) K问题3 The 14 N160 molecule undergoes a transition between its rotational ground state and its rotational first excited state. Approximating the diatomic molecule as a rigid rotor, and given that the bond length of NO is 1.152 Angstroms, calculate the energy of the transition. As your final answer, calculate the temperature T in Kelvin, such that Eshermal = kBT equals the energy of the transition between NO's rotational ground state and first excited state.