. Suppose a system of 4 molecules has a total energy of Etot = 4(+) where the energy of each molecule can be in the range Co. Co+c, co + 2e, co + 3c, co + 4e. Find all possible configurations, calculate the weight of each, identify most probable configuration, and calculate the probability of observing the o state.
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- Consider a molecule having three energy levels as Part A follows: What is the probability that this molecule will be in the lowest-energy state? State Energy (cm-1) Degeneracy Express your answer to three significant figures. 1 1 500. 3 ΑΣφ 3 1500. 5 Imagine a collection of N molecules all at 400. K in which one of these molecules is selected. Pi = Note: k = 0.69503476 cm¬1 . K-1. Submit Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remaining3. Determine the internal energy of an HCl molecule having one quantum of vibrational excitation (v=1) and three quanta (J=3) of rotational excitation. (v = 2990.9 cm³¹ and B = 10.59 cm ¹)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…
- 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.for C2H2 1- Calculate the separation at which the minimum of the potential energy occur.2- verify that at this minimum the potential energy V = ─ .3- Choose values of r such that all characteristic points and areas are shown clearly on the graph. Let the x-axis be r in pmWe can use the classical harmonic oscillator to think about molecular bonds. The HCI molecule has a force constant k = 481 N/m. For the mass, use the reduced mass, which is defined as µ = (m₁m₂)/(m₁+m₂). a) Plot the potential energy of HCl from -1 to 1 Å. What happens to the curvature of the potential as the force constant is varied? What does this mean physically? b) Plot position as a function of time for a total energy of 6 x 10-20 J. What is the period of the motion? How does the period change as the force constant is varied? Explain why this makes sense physically.
- The Morse potential energy is very useful as a simple representation of the actual molecular potential energy. When 85Rb1H was studied, it was found that ˜ν = 936.8 cm−1 and x_eν˜ = 14.15 cm−1. Plot the potential energy curve from 50 pm to 800 pm aroundRe = 236.7 pm. Then go on to explore how the rotation of a molecule may weaken its bond by allowing for the kinetic energy of rotation of a molecule and plotting V∗ = V + hcBJ˜ (J + 1) with B˜. Plot these curves on the same diagram for J = 40, 80, and 100, and observe how the dissociation energy is affected by the rotations. Hints: Taking B˜ = 3.020 cm−1 as the equilibrium bond length will greatly simplify the calculation. The mass of 85Rb is 84.9118mu3. Hydrogen atoms (ignore spin) are first at a basic state. At the time t > 0, atoms experience the electric field Ae-bt with A> 0 and b>0, and is a unit vector in the z direction. Determine the probability of transition to the first excitation state at the time t → ∞.Estimate the value of Erot for the lowest rotational energy state of N2, which has a bond length 0.110 nm.
- 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.The 14 N160 molecule undergoes a transition between its rotational ground state and its rotational first excited state. Approximating the diatomic molecule as a rigid rotor, and given that the bond length of NO is 1.152 Angstroms, calculate the energy of the transition. As your final answer, calculate the temperature T in Kelvin, such that Ethermal = kBT equals the %3D energy of the transition between NO's rotational ground state and fırst excited state.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.