You have a vibrational degree of freedom that can be treated like a harmonic oscillator with a spacing between energy levels of 538.03 cm1, What is the probability that this degree of freedom is in state v= 1 at a temperature of 1,138.2 K. Give your answer with at least 3 significant figures.
Q: 2. The following is the relative number of molecules in the vibrational states of the 1CI molecule…
A: The above question can be solved using the Maxwell- Boltzmann distribution law The Maxwell–Boltzmann…
Q: What is the temperature of a two-level system of energy separation equivalent to 300 cm−1 when the…
A:
Q: Why does the vibrational state of a diatomic molecule affect its rotational constant? Is there an…
A: Each vibrational level consists of several rotational levels. So the vibrational transition will…
Q: Evaluate, by explicit summation, the mean vibrational energy of CI4 and plot its value as a function…
A:
Q: A certain molecule has a doubly degenerate excited state lying at 360 cm−1 above the non-degenerate…
A: Percentage of the molecules in upper state (a) = 15% Percentage of the molecules in lower state (b)…
Q: Calculate the relative populations of the J = 2 and J = 1 rotational levels of HCI at 25 oC. For HCI…
A: Relative population gives the ratio of population in the higher energy levels to the number of…
Q: Calculate the relative populations of a spherical rotor at 298 K in the levels with J = 0 and J = 5,…
A:
Q: Estimate the ratio of the number of molecules in the firstexcited vibrational state of the molecule…
A: The energy delivered can be determined as follows:
Q: A diatomic Hydrogen (H2) molecule with a potential between its two Hydrogen atoms can be modelled…
A: The Morse potential equation has been given as: V(x) = V0 e−αx (e−αx - 2) The H2 molecule has…
Q: The vibrational temperature of a molecule prepared in a supersonic jet can be estimated from the…
A: The ratio of populations in the two levels is given by following Boltzmann equation. The above…
Q: Evaluate the rotational partition function at 298 K of (a) 1H35Cl. for which the rotational constant…
A: The rotational partition function expression is shown below,
Q: Calculate the relative population of the first two rotational levels for HCI at 300 K given that the…
A: The population of different rotational energy states depend on the energy difference between the two…
Q: Calculate the vibrational partition function of CS2 at 500 K given the wavenumbers 658 cm−1…
A: The vibration partition function can be expressed as follows:
Q: The 14 N160 molecule undergoes a transition between its rotational ground state and its rotational…
A: Bond length of molecule = 1.152 Angstroms We need to find temperature such that, Energy of…
Q: Consider a rotating molecule of ®Li'H. At T = 300 K, the rotational kinetic energy in the eighth…
A: A rotating molecule has energy in the form of kinetic energy and is given by the formula written in…
Q: Arrange the following energies in order of increasing magnitude: a) the typical energy of a…
A: The bond energy of a covalent single bond, the mean molecular translational energy for a gas at…
Q: A certain molecule has a non-degenerate excited state lying at 540 cm−1 above the non-degenerate…
A: GIVEN: Molecule has a non-degenerate excited state lying at 540 cm−1 To Solve: Temperature at which…
Q: Calculate the value of Cp at 298K and 1 atm pressure predicted for CH4(g) and C2H4(g) by the…
A:
Q: 14.44) The lowest triplet state in naphthalene (C10H8) is about 11,000 cm-1 below then lowest…
A: The ratio of population of the two states is given by Boltzmann equation. The expression for…
Q: Consider an ideal diatomic gas in a piston, at T = 22.7°C and atmospheric pressure (1.01 x 105 Pa)…
A:
Q: The hydrogen halides have the following fundamental vibrational wavenumbers: 4141.3 cm−1 (1H19F);…
A: Force constant: Hook's law defines the force constant as spring constant . Basically it is a…
Q: Estimate the values of γ = Cp,m/CV,m for gaseous ammonia and methane. Do this calculation with and…
A:
Q: For each state with J = 0 andJ = 1, use the function form of the Y spherical harmonics and the…
A:
Q: 4. What is the form of the total vibrational partition function for a polyatomic molecule
A: For an isolated molecule of n atoms, the number of vibrational modes (i.e. values of j) is 3n − 5…
Q: Calculate the contribution of each normal mode to the molar vibrational heat capacity of H_2O (g) at…
A: According to equipartition theorem, each transitional and rotational degree of freedom contributes ½…
Q: [References] The vibrational temperature of a molecule prepared in a supersonic jet can be estimated…
A:
Q: What molar constant-volume heat capacities would you expect under classical conditions for the…
A: According to equipartition theorem, the contribution of degree of freedom to the heat capacity is ½…
Q: Outline the principles behind the derivation of the Boltzmann distribution.
A: To find: The principle behind the derivation of the Boltzmann distribution
Q: The ground configuration of carbon gives rise to a triplet with the three levels 3P0, 3P1, and 3P2…
A: a) The electronic partition function of carbon at (i) 10 K, (ii) 298 K has to be given,
Q: For two nondegenerate energy levels separated by an amount of energy ε/k=500.K, at what temperature…
A: Given: Energy level separation ,=e/k = 500K Boltzmann distribution, N2/N1 = 1/2
Q: Plot the molar heat capacity of a collection of harmonic oscillators as a function of T/θV, and…
A: (a) At T = 298K qv= 1/1-ehcv/KT mode 1 2 3 4 5 v/cm 612 729…
Q: . For carbon monoxide at 298K, determine the fraction of molecules in the rotational levels for…
A:
Q: Calculate the relative populations of a linear rotor at 298 K in the levels with J = 0 and J = 5,…
A: The population of a linear rotor of the Jth level is given by: NJ = gJ e-EJkT Here, N is the…
Q: Suppose that 1.0 mol of perfect gas molecules all occupy the lowest energy level of a cubic box. (a)…
A: a.
Q: What is the temperature of a two-level system of energy separation equivalent to 400 cm−1 when the…
A: According to Boltzmann distribution, the equation for the probability distribution is given by,…
Q: Calculate the ratio of the populations in the first two rotational energy levels of carbon monoxide,…
A: The population ratio between two levels is given by: ninj=ωiωje-∆EKBT…
Q: Calculate the wavelength and frequency at which the intensity of the radiation is a maximum for a…
A:
Q: The vibrational wavenumber of Br2 is 323.2 cm−1. Evaluate the vibrational partition function…
A: Vibrational partition function refers to component of canonical partition function results from…
Q: 3) For the two level system with the energy indicated in the figure below, calculate (a) the…
A:
Q: Calculate the relative numbers of Cl2 molecules ( ᷉v = 559.7 cm−1) in the ground and first excited…
A: In this problem, we have to calculate the relative number of molecules of the given compound at two…
Q: Calculate the vibrational partition function of HCN at 900 K given the wavenumbers 3311 cm−1…
A: The vibrational partition function of HCN at 900 K given the wavenumbers, 3311 cm-1, 712 cm-1, 2097…
Q: For a specific molecule the ground state is nondegenerate while the first excited state is doubly…
A:
Q: Considering that the HCI molecule behaves like a harmonic oscillator, calculate: a) The reduced mass…
A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…
Q: A rotating methane molecule is described by the quantum numbers J, MJ, and K. (a) For methane, how…
A: (a)
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 2 images
- Determine the number of total degrees of freedom and the number of vibrational degrees of freedom for the following species. a Hydrogen sulfide, H2S b Carbonyl sulfide, OCS c The sulfate ion, SO42 d Phosgene, COCl2 e Elemental chlorine, Cl2 f A linear molecule having 20 atoms g A nonlinear molecule having 20 atomsThe rotational constant of 12C16O is 57.65 GHz. Calculate the value of J for the most populated level at (a) 300 K and (b) 1000 K.As noted in lecture, the rigid rotor model can be improved by recognizing that in a realistic anharmonic potential, the bond length increases with the vibrational quantum number v. Thus, the rotational constant depends on v, and it can be shown that By = Be – ae(v +). For 'H®Br, B = 8.473 cm1 and a = 0.226 cm². Use this information to calculate the bond length for HBr a) as a rigid rotor, and b) as a nonrigid rotor in the ground vibrational state. Find a literature value for this bond length (cite your source) and compare your answers. Under what conditions would you expect the nonrigid rotor to be a significantly better model?
- Calculate the ratio of the populations in the first two rotational energy levels of carbon monoxide, the lowest J=0 energy level and the higher J = 1 energy level, at 300 K if the energy difference between the levels is 3.8 cm-1and the degeneracies gJ of the two levels are g0 = 1 and g1 = 3, respectively. (You will see in Section 20.3 that there are 2J 1 1 rotational quantum states at each energy level EJ.)A diatomic molecule has a rotational constant of 8.0 cm-1, and vibrational frequency of 1200 cm 1. What is the energy of the state with v = 1 and j = 6 relative to the lowest energy state, E = E(v=0,j=0)? 0J.G. Dojahn et al. (J. Phys. Chem. 100, 9649 (1996)) characterized the potential energy curves of the ground and electronic states of homonuclear diatomic halogen anions. These anions have a 2Σu+ ground state and 2Πg, 2Πu, and 2Σg+ excited states. To which of the excited states are electric-dipole transitions allowed from the ground state? Explain your conclusion.
- Assuming the vibrations of a ¹4N2 molecule are equivalent to those of a harmonic oscillator with a force constant kr = 2293.8 N/m, what is the zero-point energy of vibration of this molecule? Use m(14N) = 14.0031 mu.Consider the diatomic molecule AB modeled as a rigid rotor (two masses separated by a fixed distance equal to the bond length of the molecule). The rotational constant of the diatomic AB is 25.5263 cm-1. (a) What is the difference in energy, expressed in wavenumbers, between the energy levels of AB with J = 10 and J = 6? (b) Consider now a diatomic A'B', for which the atomic masses are ma 0.85 mA and mB' 0.85 mB and for its bond length ra'B' = 0.913 rAB. What is the difference in energy, expressed in wavenumbers, between the energy levels of the A'B' molecule with J = 9 and J = 7?What can we predict about fluorescence intensity as a function of temperature from Boltzmann’s distribution?
- Develop an expression for the value of J corresponding to the most highly populated rotational energy level of a diatomic rotor at a temperature T remembering that the degeneracy of each level is 2J + 1. Evaluate the expression for ICl (for which ᷉ B = 0.1142 cm−1) at 25 °C. Repeat the problem for the most highly populated level of a spherical rotor, taking note of the fact that each level is (2J + 1)2-fold degenerate. Evaluate the expression for CH4 (for which ᷉ B = 5.24 cm−1) at 25 °C. Hint: To develop the expression, recall that the first derivative of a function is zero when the function reaches either a maximum or minimum value.The first five vibrational energy levels of ¹H¹27 I are at 1144.83, 3374.90, 5525.51, 7596.66, and 9588.35 cm¹. Treating the molecule as an anharmonic oscillator, estimate the dissociation energy of the molecule in units of reciprocal centimetres (cm-¹). [Note: m(¹H) = 1.0078 u, m(¹271) = 126.9045 u; assume the second order anharmonicity constant, Ye, to be zero.] [Note: Use graph paper in your answer.]7 The fundamental vibrational wavenumber ( ṽ) for 1H 127I molecule is 23096 cm-1 A. Determine the force constant (k) of 1H 127I B. Calculate the value of for 2H 127I. Show all calculations and the units. Explain the reasoning