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A molecule absorbs radiation of frequency 3.00x1014 Hz. What is the energy difference between the molecular energy states involved?
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- 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.6. The NaH molecule undergoes a rotational transition from J=0 to J=1 when it absorbs a photon of frequency 2.94×10' Hz. What is the equilibrium bond length of the molecule?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.
- The C-H bond in ethanol vibrates at a frequency of 3000 cm ¹. What frequency (s 1) of light is required to change the vibrational quantum number from v=0 to v=1, assuming that C-H acts as a harmonic oscillator.The vibrational frequency of the hydrogen chloride HCl diatomic molecule is 8.97 x 1013Hz. chloride atom is 35.5 times more massive than hydrogen atom. (mµ = 1.67 x 0-27kg,c = 3.0 x 10°m/s) a) What is the force constant of the molecular bond between the hydrogen and the chloride atoms? b) What is the energy of the emitted photon when this molecule makes a transition between adjacent vibrational energy levels? c) What is the wavelength of the emitted photon? d) The possible wavelengths of photons emitted with the HCl molecule decays from the 2nd excited state eventually to the ground state(0 state).What are the various ways in which an electronically excited molecule can lose energy?
- .Assuming reasonable bond lengths, estimate the frequency of the J=15 – 14 transition in the linear molecule N≡C-(C≡C)6-H. In which region of the electromagnetic spectrum does it lieThe vibrational frequencies of most chemical bonds are around 10^13 per second. Calculate the the corresponding wavelength and confirm that it falls within the thermal IR range of the electromagnetic spectrum.2. Molecules absorb IR radiation consistent with vibrational energy and rotational energy. Which of these is present in condensed phases (liquid, solution, solid)?
- A). 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…+ P25.2 The ground electronic state of O₂ is ³Σ, and the next two highest energy states are ¹Ag (7918 cm¯¹), and ¹Σg (13195 cm¹) where the value in parentheses is the energy of the state relative to the ground state. a. Determine the excitation wavelength required for a transition between the ground state and the first two excited states. b. Are these transitions allowed? Why or why not?4G I 5:53 2.30 O Yo 40 52% KB/s 1. The C-C stretch in allene (H,C-C=CH,) is about 1650 cm'; the C-H stretch is about 3,100 cm". Calculate the corresponding wavelengths (in nm) and energies (in kJ/mol) of these vibrations. () II