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1000 diatomic molecules with vibrational state described by N molecules in the ground vibrational...
a) Describe and sketch the vibrational energy levels observed for diatomic molecules in the harmonic oscillator approximation, using an appropriate formula to support your answer (4 marks) b) State the selection rules for IR transitions in diatomic molecules. (2 marks) c) Briefly explain the implications of anharmonicity for vibrational spectra, with particular reference to the selection rules for diatomic molecules, and the resultant energy levels and spectra observed. (3 marks) a) Describe and sketch the vibrational energy levels observed for...
In the ro-vibrational model for spectra of diatomic molecules, the total rotational and vibrational energy for a given state is: Évj = ū(v + 3) + BJC +1) (Equation 1) where v is the vibrational quantum number and J is the rotational quantum number. Complete the following steps to create a model energy level diagram for a hypothetical diatomic molecule with ✓ = 2000 cm-1 and B = 1 cm-1. i) Draw a horizontal line to represent the ground vibrational...
1 1. Calculate the relative populations of the v1 state to the ground vibrational state for lz at 25°C. The vibrational wavenumber is 214.6 cm1. Use the equation for energy vibrational energy levels for an harmonic oscillator from FOCUS 7. 2. Repeat for the v-2 states. (v-2 state compared to to va-0 state 3. Repeat for the v#1 state at 500°C. 4. Repeat for the v-2 state at 500°c. 5. Discuss the results 1 1. Calculate the relative populations of...
The force constants for the diatomic molecules CO and HI are 1860 N/m and 320 N/m, respectively. b) (5)Calculate the frequency of motion for both molecules (does this result surprise you?). c) (5) Calculate the wave length of light needed to excite these molecules from their vibrational ground states (v=0) to their vibrational first excited states (v=1).
Calculate the ratio of HBr molecules in the first excited vibrational state compared to the ground state at 800K. Remember that finding the probability of finding a molecule in a given state, i, is related to its energy, Ei, by the following equation: P(n) e^(-En/KT) You will need the following information to calculate the energy of the vibrational states: En = hv(n+1/2) for HBr v= 7.944*10^14s^-1 K=1.3807*10^-24J/K h=6.626*10^-34J*s
A particle of charge q and mass m is bound in the ground state of a one-dimensional harmonic oscillator potential with frequency oo. At time t-0 a weak spatially uniform electric field (E) is turned on, so that the perturbation to the Hamiltonian can be described as R'(t) =-q Exe-t/t for t> 0. Using first order, time-dependent perturbation theory, calculate the following probabilities: (a) the particle is detected in the first excited state after a very long time (t »...
As a result of a sudden perturbation of the harmonic oscillator originally in the ground state, the restoring force coefficient k in its potential energy U(a) (1/2)k2 changes to k' ak, a>0. Find the proba- bility to find the new oscillator in an excited state. As a result of a sudden perturbation of the harmonic oscillator originally in the ground state, the restoring force coefficient k in its potential energy U(a) (1/2)k2 changes to k' ak, a>0. Find the proba-...
You have in your posession the first vibrational spectrum of a new diatomic molecule X_2 obtained at 1000 K. From the spectrum you determine that the fraction of molecules occupying a given vibrational energy state n is as follows: What are the vibrational energy spacings for X_2?
4. The vibrational frequency of O2 in its ground state is 1580 cm l , but the frequency is only 700 cm ı in the Σ+ excited state. Given that difference in purely electronic energy between the 1 ground and statesis 6.175 eV, predict the energy of the lowest energy transition originating from the v-0 of the ground state to the 3 state.
(a) Use the variational method to estimate the ground state energy of a particle of |mass m in a potential Vx)kx, k > 0. (b) Calculate the energy shift in the ground state and in the degenerate 1t excited state of a 2-dimensional harmonic oscillator H(P2P,2/2m m(x +y)due to the perturbation V 2Axy. (20 pts) (a) Use the variational method to estimate the ground state energy of a particle of |mass m in a potential Vx)kx, k > 0. (b)...