Interpretation:
Between the given diatomic molecules
Concept introduction:
The Born-Oppenheimer approximation describes the quantum state of the molecules. It stated that the motion of a nucleus and the motion of an electron in a molecule can be separated. The Schrödinger equation is solved by using the above mathematically expression for the given molecular wavefunction.
The Schrödinger equation is used to find the allowed energy levels for electronic transitions in the
Where,
•
•
•
Want to see the full answer?
Check out a sample textbook solutionChapter 12 Solutions
Physical Chemistry
- Carbon dioxide and water are important greenhouse gases. Sketch the fundamental vibrations for both molecules and indicate which you expect to be infrared active.arrow_forwardIn the context of the Born-Oppenheimer approximation, write the Hamiltonian for the molecular cation H₂⁺.arrow_forwardEnrico Fermi (1901–1954) was a famous physicist who liked to pose what are now known as Fermi problems, in which several assumptions are made in order to make a seemingly impossible estimate. Probably the most famous example is the estimate of the number of piano tuners in Chicago using the approximate population of the city and assumptions about how many households have pianos, how often pianos need tuning, and how many hours a given tuner works in a year. Another famous example of a Fermi problem is "Caesar's last breath," which estimates that you, right now, are breathing some of the molecules exhaled by Julius Caesar just before he died. The assumptions made are: 1. The gas molecules from Caesar's last breath are now evenly dispersed in the atmosphere. 2. The atmosphere is 50 km thick, has an average temperature of 15 °C, and an average pressure of 0.20 atm. 3. The radius of the Earth is about 6400 km. 4. The volume of a single human breath is roughly 500 mL. Perform the…arrow_forward
- Calculate the kinetic energy of a single 1H atom moving with an average velocity of 1220 m s−1.Calculate the kinetic energy of 1 mole of such atoms. Calculate the temperature of such a gas.arrow_forward(Q. 8) Consider a linear triatomic molecule A – B-A, where mass of the atom B is twice that of the mass of atom A. Find the normal modes of vibrations by computing relative displacements during vibration and indicate them by arrows on the atoms.arrow_forwardGIVE HANDWRITTEN ANSWERarrow_forward
- Arrange the following energies in order of increasing magnitude: a) the typical energy of a covalent single bond; b) the mean molecular translational energy for a gas at room temperature; c) the mean rotational energy of a diatomic molecule at room temperature; d) the vibrational energy for a diatomic molecule at room temperature; e) the ionization energy of H. Justify your order.arrow_forwardUsing the born-haber cycle, the delta H f of KBr is equal toarrow_forwardA). A molecule can have various types of energies (translational, rotational, vibrational, and electronic), the sum of which is the molecule's total energy. ?trans=(?^2?+?^2?+?^2?)(ℎ^2/8??^2/3) ?rot=?(?+1)ℎ^2/8?2? ?vib=(?+1/2)(ℎ?) In the equations, ??, ??, ??, ?, and ? are quantum numbers, ℎ is Planck's constant, ? is the mass of the molecule, ? is the volume of the container, ? is the moment of inertia of the molecule, and ? is the fundamental vibration frequency. For carbon monoxide, CO , the moment of inertia is ?=1.45×10−46 kg⋅m2, and the fundamental vibration frequency is ?=2130 cm−1. Let ?=12.8, and let all the quantum numbers be equal to 11 . Calculate the translational, rotational, and vibrational energies per mole of CO for these conditions. ?trans= J/mol ?rot= J/mol ?vib= J/mol B). If the electronic energy of CO is 9.14 eV per molecule, calculate the total energy of CO per mole. ?total= J/mol C). Which types of energy are…arrow_forward
- β-Carotene (1) is a linear polyene in which 10 sing le and 11 double bonds alternate along a chain of 22 carbon atoms. If the length of each CC bond is taken to be about 140 pm , then the length L of the molecular box in β-carotene is L = 2.94 nm. Estimate the wavelength of the light absorbed bythis molecule when it undergoes a t rans it ion from its ground state to the next higher excited state.arrow_forwardUse Appendix data and the approximation that AC, is independent of T to p mate AH 200 for the reaction 2C0(8) + O2(g) → 2CO2(g)arrow_forward559.7 cm¹, and a rotational constant, B = 0.244 cm ¹¹. 18. Chlorine has a vibrational constant, U = From this information, determine (a) the force constant and (b) the equilibrium bond length.arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,Principles of Modern ChemistryChemistryISBN:9781305079113Author:David W. Oxtoby, H. Pat Gillis, Laurie J. ButlerPublisher:Cengage Learning