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2. (10 pts) Hydrogen molecule bonded to a surface is acting as a quantized harmonic oscillator...
Hydrogen molecule bonded to a surface is acting as a quantized harmonic oscillator with a force...
Hydrogen molecule bonded to a surface is acting as a quantized harmonic oscillator with a force constant of 300 Nm^-1. a) What is the second to the lowest possible vibrational energy of this system? b) What is the wavefunction of the photon whose energy matches the difference between these two energy levels?
A hydrogen atom bonded to a surface is acting as a harmonic oscillator with a classical...
A hydrogen atom bonded to a surface is acting as a harmonic oscillator with a classical frequency of 6 x 103 1. GE=3.98x10-ROJ a. What is the energy difference in Joules between the different energy levels? b. Calculate the wavelength of light that must be absorbed in order for the hydrogen atom to go from one level to another. 2 = 5.00 *Loom C. Can you determine in what region of the electromagnetic spectrum such a wavelength belongs? IR
need # 4 or 5 o Vibrational spectroscopy of the NO molecule (with absorption at 1878 cm isotope masses of No14 and 0-16, respectively) reveals Assuming that this transition represents the energy s...
need # 4 or 5
o Vibrational spectroscopy of the NO molecule (with absorption at 1878 cm isotope masses of No14 and 0-16, respectively) reveals Assuming that this transition represents the energy spacing between vibrational energy levels, calculate the force constant of the bond Assuming that the "N"O molecule has a bond with the same force constant as in part a, predict the position (in cm) of the absorbance peak for this molecule. 1. a. b 2. Normalize the first...
One can assume a quantum mechanical harmonic oscillator model for the N-H stretching vibrations of the...
One can assume a quantum mechanical harmonic oscillator model for the N-H stretching vibrations of the peptide bonds. For the harmonic oscillator the energy levels are given by: E, = (V+})ħw where: W= /k/ u In the above express k is the force constant and u is the reduced mass. (a) Write the Schrödinger equation in terms of the reduced mass u, being sure to define all symbols. (b) Calculate the frequency of the infrared radiation absorbed by the N-H...
II. (30 pts) The diatomic molecule CO has a vibrational wavenumber of 2170 cm 'and may...
II. (30 pts) The diatomic molecule CO has a vibrational wavenumber of 2170 cm 'and may be treated as a quantized harmonic oscillator. 1. (10 pts) What is the energy of one photon of light which has the same frequency as CO (in J units)? 2. (10 pts) What is the value of the vibrational partition function of CO at 300 K? 3. (10 pts) At what temperature would approximately 5 vibrational quantum states of Co be thermally populated?
Quantum, 1D harmonic oscillator. Please answer in full. Thanks. Q3. The energy levels of the 1D harmonic oscillator are given by: En = (n +2)ha, n=0. 1, 2, 3, The CO molecule has a (reduced) mass of...
Quantum, 1D harmonic oscillator. Please answer in full.
Thanks.
Q3. The energy levels of the 1D harmonic oscillator are given by: En = (n +2)ha, n=0. 1, 2, 3, The CO molecule has a (reduced) mass of mco = 1.139 × 10-26 kg. Assuming a force constant of kco 1860 N/m, what is: a) The angular frequency, w, of the ground state CO bond vibration? b) The energy separation between the ground and first excited vibrational states? 7 marks] The...
Exercise 12.1(b) Calculate the zero-point energy of a harmonic oscillator consisting of a rigid CO molecule...
Exercise 12.1(b) Calculate the zero-point energy of a harmonic oscillator consisting of a rigid CO molecule adsorbed to a metal surface by a bond of force constant 285 N m-1.
(10 pts) The two calculations below pertain to the quantum harmonic oscillator (qho). Relevant expressions for...
(10 pts) The two calculations below pertain to the quantum harmonic oscillator (qho). Relevant expressions for the qho states and energies needed are given by: En-(n +-)ћ1_ and n-AnHn(ye- Two 1g masses are attached by a spring with a force constant k-500 kg/s2. Calculate the zero point energy of this system. How fast would this system have to move to have that much translational energy? a. b. Calculate the wavenumber and wavelength of radiation absorbed when a quantum harmonic oscillator...
thank you in advanced! Set 1: (50 pts) 1. (20 pts) The diatomic iodine anion (1:')...
thank you in advanced!
Set 1: (50 pts) 1. (20 pts) The diatomic iodine anion (1:') has a vibrational frequency of approximately 110 cm Predict the total heat capacity of I, in the gas phase at 300 K. II. (30 pts) The diatomic molecule Co has a vibrational wavenumber of 2170 cm and may be treated as a quantized harmonic oscillator. 1. (10 pts) What is the energy of one photon of light which has the same frequency as CO...
1 Vibrational states of a diatomic molecule 1. Use Taylor expansion to get a harmonic approximation...
1 Vibrational states of a diatomic molecule 1. Use Taylor expansion to get a harmonic approximation Vharmonic( 0.5k(r Ro2 of the following potential 2. Find the expressions for the equilibrium distance Ro and for the harmonic 3. Calculate the zero point energy in terms of the parameters of the given 4. Calculate the energy of a photon emitted upon a transition between ad- force constant k potential (a, ro and D jacent levels in terms of the parameters of the...
A hydrogen atom bonded to a surface is acting as a harmonic oscillator with a classical frequency of 6 x 103 1. GE=3.98x10-ROJ a. What is the energy difference in Joules between the different energy levels? b. Calculate the wavelength of light that must be absorbed in order for the hydrogen atom to go from one level to another. 2 = 5.00 *Loom C. Can you determine in what region of the electromagnetic spectrum such a wavelength belongs? IR
need # 4 or 5
o Vibrational spectroscopy of the NO molecule (with absorption at 1878 cm isotope masses of No14 and 0-16, respectively) reveals Assuming that this transition represents the energy spacing between vibrational energy levels, calculate the force constant of the bond Assuming that the "N"O molecule has a bond with the same force constant as in part a, predict the position (in cm) of the absorbance peak for this molecule. 1. a. b 2. Normalize the first...
One can assume a quantum mechanical harmonic oscillator model for the N-H stretching vibrations of the peptide bonds. For the harmonic oscillator the energy levels are given by: E, = (V+})ħw where: W= /k/ u In the above express k is the force constant and u is the reduced mass. (a) Write the Schrödinger equation in terms of the reduced mass u, being sure to define all symbols. (b) Calculate the frequency of the infrared radiation absorbed by the N-H...
II. (30 pts) The diatomic molecule CO has a vibrational wavenumber of 2170 cm 'and may be treated as a quantized harmonic oscillator. 1. (10 pts) What is the energy of one photon of light which has the same frequency as CO (in J units)? 2. (10 pts) What is the value of the vibrational partition function of CO at 300 K? 3. (10 pts) At what temperature would approximately 5 vibrational quantum states of Co be thermally populated?
Quantum, 1D harmonic oscillator. Please answer in full.
Thanks.
Q3. The energy levels of the 1D harmonic oscillator are given by: En = (n +2)ha, n=0. 1, 2, 3, The CO molecule has a (reduced) mass of mco = 1.139 × 10-26 kg. Assuming a force constant of kco 1860 N/m, what is: a) The angular frequency, w, of the ground state CO bond vibration? b) The energy separation between the ground and first excited vibrational states? 7 marks] The...
(10 pts) The two calculations below pertain to the quantum harmonic oscillator (qho). Relevant expressions for the qho states and energies needed are given by: En-(n +-)ћ1_ and n-AnHn(ye- Two 1g masses are attached by a spring with a force constant k-500 kg/s2. Calculate the zero point energy of this system. How fast would this system have to move to have that much translational energy? a. b. Calculate the wavenumber and wavelength of radiation absorbed when a quantum harmonic oscillator...
thank you in advanced!
Set 1: (50 pts) 1. (20 pts) The diatomic iodine anion (1:') has a vibrational frequency of approximately 110 cm Predict the total heat capacity of I, in the gas phase at 300 K. II. (30 pts) The diatomic molecule Co has a vibrational wavenumber of 2170 cm and may be treated as a quantized harmonic oscillator. 1. (10 pts) What is the energy of one photon of light which has the same frequency as CO...
1 Vibrational states of a diatomic molecule 1. Use Taylor expansion to get a harmonic approximation Vharmonic( 0.5k(r Ro2 of the following potential 2. Find the expressions for the equilibrium distance Ro and for the harmonic 3. Calculate the zero point energy in terms of the parameters of the given 4. Calculate the energy of a photon emitted upon a transition between ad- force constant k potential (a, ro and D jacent levels in terms of the parameters of the...
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