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Is the transition A1g → E2u forbidden for electric dipole transitions in a D6h molecule?
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- Which of the following transitions are electric-dipole allowed?(i) 1Σg+ ↔ 1Σu+, (ii) 3Σg+ ↔ 3Σu+, (iii) π* ↔ n.A space probe was designed to see 13CO in the atmosphere of Saturn by looking for lines in its rotational spectrum. If the bond length of CO is 112.8 pm, at what wave number do the first three rotational transitions appear?What is the magnitude of the angular momentum of an SF6 molecule when it is rotating with its minimum energy?
- Which of the following transitions are electric-dipole allowed?(i) 2Π ↔ 2Π, (ii) 1Σ ↔ 1Σ, (iii) Σ ↔ Δ, (iv) Σ+ ↔ Σ−, (v) Σ+ ↔ Σ+.3 Calculate the frequencies and wavelengths for the rotational transition J = 0 → J = 1 and J = 4 → J = 5 for the HCl molecule. The internuclear distance is Re = 0.12745 nm. What is the frequency shift between the two isotopomers H35Cl and H37Cl for the two transitions?Calculate the energy of the J=0 to J=1 rotational transition of the O₂ molecule with a bond length of 121 pm.
- What is the magnitude the angular momentum of a SF6 molecule when it is rotating with its minimum energy. What is the degeneracy of a molecule rotating with J = 4An H2 molecule is in its vibrational and rotational ground states. It absorbs a photon of wavelength 2.211 2 μm and makes a transition to the υ = 1, J = 1 energy level. It then drops to the υ = 0, J = 2 energy level while emitting a photon of wavelength 2.405 4 mm. Calculate (a) the moment of inertia of the H2 molecule about an axis through its center of mass and perpendicular to the H–H bond, (b) the vibrational frequency of the H2 molecule, and (c) the equilibrium separation distance for this molecule.Assume that the states of the π electrons of a conjugated molecule can be approximated by the wavefunctions of a particle in a one-dimensional box, and that the magnitude of the dipole moment can be related to the displacement along this length by μ = −ex. Show that the transition probability for the transition n = 1 → n = 2 is non-zero, whereas that for n = 1 → n = 3 is zero. Hints: The following relation will be useful: sin x sin y = 1/2cos(x − y) − 1/2cos(x + y). Relevant integrals are given in the Resource section.
- Is the bond length in 1HCl the same as that in 2HCl? The wavenumbers of the J = 1 ← 0 rotational transitions for 1H35Cl and 2H35Cl are 20.8784 and 10.7840 cm–1, respectively. Accurate atomic masses are 1.007 825mu and 2.0140mu for 1H and 2H, respectively. The mass of 35Cl is 34.968 85mu. Based on this information alone, can you conclude that the bond lengths are the same or different in the two molecules?The spacing of lines in the microwave spectrum of 35Cl19F is 1.033 cm−1; calculate the moment of inertia and bond length of the molecule.The moment of inertia of an SF6 molecule is 3.07 × 10−45 kg m2. What is the minimum energy needed to start it rotating?