Consider a system of two nondegenerate energy levels separated by 3000 cm-¹. Measurement of the level populations demonstrates that there are 6 times more molecules in the ground state than in the upper state. What is the temperature of the collection?
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- 7E.3 Before solving the problem please also give a brief explanation of the concept or associated equation(s) and variables.Calculate the relative populations of two quantum statesseparated by an energy of 0.4 × 10-21 J if the temperatureis 25°C.J.G. Dojahn et al. (J. Phys. Chem. 100, 9649 (1996)) characterized the potential energy curves of the ground and electronic states of homonuclear diatomic halogen anions. These anions have a 2Σu+ ground state and 2Πg, 2Πu, and 2Σg+ excited states. To which of the excited states are electric-dipole transitions allowed from the ground state? Explain your conclusion.
- Rotational spectra are affected slightly by the fact that different isotopes have different masses. Suppose a sample of the common isotope 1H35Cl is changed to 1H37Cl. (a) By what fraction is the molecule’s rotational inertia different? (The bond length is 0.127 nm in each case.) (b) What is the change in energy of theℓ = 1 to theℓ = 0 transition if the isotope is changed?Calculate the population of the first excited level if the ground state has 1000 molecules at 29K. ( E=4.005 × 10-23J molecule-1 [4325]-201 2 )Calculate the separation between the two lowest energy levels for an N2 molecule in a one- dimensional container of length 2.0 cm. At what value of n does the energy of the molecule reach ½kT at 300 K, and what is the separation of this level from the one immediately below?
- The vibrational energy levels for XO molecule can be described by the following formula: E(n) in Joule = 1.88x10-20(n+1/2) – 2.68x10-22(n+1/2)² where n is the vibrational quantum number. What would be the equilibrium dissociation energy (De) of the XO molecule in a kJ mol-1?Calculate the ratio of the populations in the first two rotational energy levels of carbon monoxide, the lowest J=0 energy level and the higher J = 1 energy level, at 300 K if the energy difference between the levels is 3.8 cm-1and the degeneracies gJ of the two levels are g0 = 1 and g1 = 3, respectively. (You will see in Section 20.3 that there are 2J 1 1 rotational quantum states at each energy level EJ.)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 Ethermal = kBT equals the %3D energy of the transition between NO's rotational ground state and fırst excited state.
- answer under1hrYou have a vibrational degree of freedom that can be treated like a harmonic oscillator with a spacing between energy levels of 538,03 cm1, What is the probability that this degree of freedom is in state v = 1 at a temperature of 1,138.2 K. Give your answer with at least 3 significant figures.A 1.00 kg weight is traveling at a constant velocity of 10.0 ms-1, in a cubic room 3.00 m on an edge.(a). Determine the sum of the squares of its three quantum numbers.(b). What would be the ground state energy for this weight?