1) Assuming that a diatomic molecule can be approximated by a rigid rotor with a inertia...
Rotational states of a diatomic molecule can be approximated by those of a rigid rotor. The hamiltonian of a rigid rotor is given by hrotor 12/21, where L2 is the operator for square of angular momentum and I the moment of inertia. The eigenvalues and eigenfunctions of L2 are known: Lylnu =t(1+1)ay," , where m.--1, , +1 a) Calculate the canonical partition function : of a rigid rotor. Hint: Replace summation over by integral. b) What is the probability that...
Molecular Rotations a. The wavefunction of rotations of diatomic molecules according to the rigid rotor approximation are spherical harmonics. Where have you seen spherical harmonics before? What are the quantum numbers that specify the wavefunctions for the rotational quantum states of a diatomic molecule? b. What are the gross and specific selection rules for pure rotational spectroscopy of a diatomic molecule? What region of the spectrum is used spectroscopy? What are the rotational energy levels for diatomic molecules and spherical...
Rigid rotor question Hi, I understand how to do rigid rotor questions for diatomic molecules, but I was wondering what if the molecule is linear CO2? What is the rotational first excited state energy of linear molecule CO2? Not sure if I have to just solve the energy for C=O like as a diatomic molecule, and then multiply by two...
10. In the vibrational rotational spectrum of a diatomic molecule, the second line of the P branch (J" = 2 = 1) is observed at 3100 cm and the third line of the R branch (J" = 2- )' = 3) is observed at 3160.cm! Assuming the molecule behaves as a rigid rotor and a harmonic oscillator, calculate the rotational constant (R) and the fundamental vibration wavenumber (V) for the molecule. Hint, you need two equations to solve for the...
A free-electron model for a benzene molecule can be approximated via a particle rotating in a ring (2-D rigid rotor problem). Use this model assuming the radius of benzene of 1.39 ˚A to answer the following questions: a) Find the energies of the occupied electronic levels; plot a schematic diagram of the electronic levels. b) Calculate the wavelength (in nm) of the lowest-energy electronic transition in benzene. c) In what region of the electromagnetic spectrum is this transition? How does...
SOLVE THE 3RD ONE INCLUDE ALL THE STEPS At a given temperature the rotational states of molecules are distributed according to the Boltzmann distribution. Of the hydrogen molecules in the ground state estimate the ratio of the number in the ground rotational state to the number in the first excited rotational state at 300 K. Take the interatomic distance as 1.06 Å. Estimate the wavelength of radiation emitted from adjacent vibration energy levels of NO molecule. Assume the force constant...
Solve 1st one asap At a given temperature the rotational states of molecules are distributed according to the Boltzmann distribution. Of the hydrogen molecules in the ground state estimate the ratio of the number in the ground rotational state to the number in the first excited rotational state at 300 K. Take the interatomic distance as 1.06 Å. Estimate the wavelength of radiation emitted from adjacent vibration energy levels of NO molecule. Assume the force constant k-1,550 N m In...
Solve the LAST ONE INCLUDE ALL THE STEPS The force constant for the carbon monoxide molecule is 1,908 N m At 1,000 K what is the probability that the molecule will be found in the lowest excited state? At a given temperature the rotational states of molecules are distributed according to the Boltzmann distribution. Of the hydrogen molecules in the ground state estimate the ratio of the number in the ground rotational state to the number in the first excited...
Explain (in your own chemically accurate words) why and how you can use IR spectroscopy to measure bonding parameters for a polar, diatomic molecule. You will need to address why the ro-vibrational spectrum is in the IR region of the electromagnetic spectrum (this may include a discussion of vibrational and rotational motion and the selection rules associated with them) the origin of the P, Q and R branch (including a figure to indicate the origin of each set of peaks...
(b) The rotational Raman spectrum of 1 N2 (m(N) - 14.0031u) shows a series of Stokes lines separated by 1.4567 cm, when it is exposed to monochromatic laser radiation with wavelength of 156 nm. (i) Derive the energy separation expression of the J 3 the pure rotational Raman spectrum of 1N2 1 transition in (i) Calculate the frequency of the above transition in the pure rotational Raman spectrum of 1"N2. 4 (b) The rotational Raman spectrum of 1 N2 (m(N)...