The NaH molecule undergoes a rotational transition from J=0 to J=1 when it absorbs a photon of frequency 2.94×101 Hz. What is the equilibrium bond length of the 6. molecule?
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- 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?2. Molecules absorb IR radiation consistent with vibrational energy and rotational energy. Which of these is present in condensed phases (liquid, solution, solid)?Determine the electronic configration of transition metal ion: TiO2.
- A molecule can have various types of energies (translational, rotational, vibrational, and electronic), the sum of which is the molecule's total energy. E trans = (n +n + n²) Erot = J (J + 1) h² 87²1 Evib = (U+ 1 ) h hv h² 8mV (2/3) In the equations, nx, ny, nz, J, and u are quantum numbers, h is Planck's constant, m is the mass of the molecule, V is the volume of the container, I is the moment of inertia of the molecule, and v is the fundamental vibration frequency. For carbon monoxide, CO, the moment of inertia is I = 1.45 x 10-46 kg-m², and the fundamental vibration frequency is v = 2130 cm-¹. Let V = 12.5 L, and let all the quantum numbers be equal to 1. Calculate the translational, rotational, and vibrational energies per mole of CO for these conditions.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?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.
- 7. Why is the oxygen-hydrogen absorption of CH3OH such a broad band in the infrared? a-Rotational energy levels broaden the absorption. b-Hyperconjugation resonance broadens the absorption. c-Resonance broadens the absorption. d-Hydrogen bonding broadens the absorption.1-A:-Calculate the energy and wave-length of the photon absorbed when a "Hg"Cl molecule (r. 2.23°A) makes the rotational transition J-0-J-1 and J-1->J=2. B:- In what region of the electromagnetic spectrum are these lines found? 2-Suppose that the equilibrium separation in the '11"CI molecules is the same and equal to 1.27°A. Compute for each molecule A:-The constant 13. B:- The energy of the first two excited rotationa levels. C:-The frequencies and wave length corresponding to the transition J-0-J-1 and J-1-J-2.4. The vibrational frequency of 'H³°C1 is 8.963 x 1013 Hz. What is the force X constant of the bond in this molecule?
- 3 The rotation motion of HCl molecules can be analyzed by treating each molecule as a rigid rotational constant B= 2.07x10^-22 Joules. a) what frequency of radiation will excite the transition from the J=1 energy level to the J=2 level in this case? b) what is the relative probability of observing an HCl molecule at the J=2 energy level, as compared to teh J=1 level, at 25.00 degrees C?7. Consider the Jablonski diagrams below, where So, S₁, and S2 are all singlet electronic states, and T₁ is a triplet electronic state. (So is the electronic ground state.) The horizontal lines indicate the vibrational energy levels in each electronic state. The arrow drawn on the diagram represents the absorption of a UV photon with = 250 nm, promoting the molecule to a high vibrational level in the S₁ state. (The wavelength values here and below are meant as a guide, but this is not really a quantitative question.) Two different processes are described below the diagrams. Read each one, and then draw an appropriate set of arrows on the corresponding diagram to represent the process described. E Diagram #1 - Fluorescence process S₂ S₁ So SS5 T₁ Vo V4 V3 55555 V₂ V₁ V₁ Diagram #2 - Phosphorescence process E S₂ S₁ So 55555 Vo T₁ 7.1 Diagram #1: After the absorption shown in the diagram, the molecule fluoresces, emitting a photon with = 310 nm. ラララララ 7.2 Diagram #2: After the absorption…5. The energy of one electron in H-atom is 1.36 x10-19 J. Calculate the main electronic state. a.1b.7c.4d.2