In a diatomic molecule, two atoms combine. Atomic quantum numbers can couple with each other in various ways, giving rise to different molecular electronic states/terms which are named as 2S+1LJ. Is it correct to put 2S+1LJ?.
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In a diatomic molecule, two atoms combine.
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- 2. Molecules absorb IR radiation consistent with vibrational energy and rotational energy. Which of these is present in condensed phases (liquid, solution, solid)?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.Consider the molecules: CH2=CH-CH=CH-CH=CH-CH=CH-CH=CH2. Let’s assume that the 10 electrons that make up the double bonds can exist everywhere along the carbon chains. The electrons can then be considered as particles in a box; the ends of the molecule correspond to the boundaries of the box with a finite or zero potential energy inside. In this “molecular box”, 2 electrons can occupy an energy level. What are quantum states that the electrons from this molecule can occupy in the ground state? Note that the length of a C-C bond is about 1.54A and the length of a C=C bond is 1.34A to allow you to estimate the length of the “molecular box”
- The potential energy function for either one of the two atoms in a diatomic molecule is often approximated by U(x) a b = x22 x11 where x is the distance between the atoms. a. At what distance of separation does the potential energy have a local minimum (not at x = Express your answer algebraically. xmin b. What is the force on an atom at this separation? F(x = 2min)= N ∞)?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.A microwave using 18.99cm IR radiation is used to heat 18.2g water from 18.8C to 71.2C. Find the number of MOLES of photons required to accomplish this task.
- 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.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…For the different electronic states of a diatomic molecule, it can be stated about the energy that: a) it is expressed in a general way as G(v) = v(v + 1/2) - VêX(V + 1/2)² b) it is expressed in a general way as F(J) = BJ(J + 1) - DJ²(J + 1)² c) the electronic energy is not quantized d) there is no general expression that can be applied to obtain the energy of the different electronic states of the type mentioned above.
- 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?When β-carotene is oxidized in vivo, it breaks in half and forms two molecules of retinal (vitamin A), which is a precursor to the pigment in the retina responsible for vision. The conjugated system of retinal consists of 11 C atoms and 1 O atom. In the ground state of retinal, each level up to n = 6 is occupied by two electrons. Assuming an average internuclear distance of 140 pm, calculate (a) the separation in energy between the ground and first exciteted state in which one electron occupies the state with n = 7, and (b) the frequency of radiation required to produce a transition between these two states. From your results, correct the following sentence (from the options in brackets). The absorption spectrum of a linear polyene shifts to (higher/lower) frequency as the number of conjugated atoms (increases/decreases).It takes 463./kJmol to break an oxygen-hydrogen single bond. Calculate the maximum wavelength of light for which an oxygen-hydrogen single bond could be broken by absorbing a single photon. Be sure your answer has the correct number of significant digits.