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?
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Hydrogen molecule bonded to a surface is acting as a quantized
harmonic oscillator with a force...
2. (10 pts) Hydrogen molecule bonded to a surface is acting as a quantized harmonic oscillator...
2. (10 pts) Hydrogen molecule bonded to a surface is acting as a quantized harmonic oscillator with a force constant of 300 Nm! What is the wavefunction of the photon whose energy matches the difference between these two energy levels? (10 pts=5 points for correct work shown, 2 points for the correct units, and 3 points for correct answer)
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...
Example Question Suppose a molecule exists as a one dimensional harmonic oscillator in a superposition state...
Example Question Suppose a molecule exists as a one dimensional harmonic oscillator in a superposition state that is given by the following wavefunction: 1 15 Y = -4 +291 Where Y. and Y, are the ground state and the first excited state wavefunctions of the harmonic oscillator. Evaluate the expectation value of the vibrational energy this molecule in such a superposition state (in cm ) given that the vibration constant for the molecule is about 1800 cm
The vibrational absorption spectrum of a diatomic molecule in the harmonic oscillator approximation consists of just...
The vibrational absorption spectrum of a diatomic molecule in the harmonic oscillator approximation consists of just one line whose frequency is given by, ν = 1 k . The bond 2π μ length of 12C14N is 117 pm and the force constant is 1630 N m-1. Predict the vibration-rotation spectrum of 12C14N within the harmonic oscillator rigid rotor approximation
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...
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?
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...
Tim Question 1 1 pts Atte OM The force constant for the bond in an HCl...
Tim Question 1 1 pts Atte OM The force constant for the bond in an HCl molecule is k = 5 16 J m2. The mass of an 1H atom is 1.008 g/mol and the mass of a 35CI atom is 34.97 g/mol. Use this information to calculate the vibrational frequency, Ve, for a molecule of 1H35CI. Report your answer in units of 1/s. Question 2 1 pts The vibrational frequency for the H2 molecule is v=1.32x 1014 s 1...
6. Consider the bond vibration of a homo-atomic diatomic molecule. In the harmonic approximation the vibrational...
6. Consider the bond vibration of a homo-atomic diatomic molecule. In the harmonic approximation the vibrational energy levels are given by, Where v = 0,1,..., and w = 6.1 x 1014 5-1. Let us assume this vibrational mode is IR active. A photon of energy E = hc/, is absorbed by the molecule and induces a fundamental vibrational transition. (a) What is the wavelength of the resulting IR absorption peak in nm? [6 marks] (b) Is it reasonable to assume...
2. (10 pts) Hydrogen molecule bonded to a surface is acting as a quantized harmonic oscillator with a force constant of 300 Nm! What is the wavefunction of the photon whose energy matches the difference between these two energy levels? (10 pts=5 points for correct work shown, 2 points for the correct units, and 3 points for correct answer)
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...
Example Question Suppose a molecule exists as a one dimensional harmonic oscillator in a superposition state that is given by the following wavefunction: 1 15 Y = -4 +291 Where Y. and Y, are the ground state and the first excited state wavefunctions of the harmonic oscillator. Evaluate the expectation value of the vibrational energy this molecule in such a superposition state (in cm ) given that the vibration constant for the molecule is about 1800 cm
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...
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?
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...
Tim Question 1 1 pts Atte OM The force constant for the bond in an HCl molecule is k = 5 16 J m2. The mass of an 1H atom is 1.008 g/mol and the mass of a 35CI atom is 34.97 g/mol. Use this information to calculate the vibrational frequency, Ve, for a molecule of 1H35CI. Report your answer in units of 1/s. Question 2 1 pts The vibrational frequency for the H2 molecule is v=1.32x 1014 s 1...
6. Consider the bond vibration of a homo-atomic diatomic molecule. In the harmonic approximation the vibrational energy levels are given by, Where v = 0,1,..., and w = 6.1 x 1014 5-1. Let us assume this vibrational mode is IR active. A photon of energy E = hc/, is absorbed by the molecule and induces a fundamental vibrational transition. (a) What is the wavelength of the resulting IR absorption peak in nm? [6 marks] (b) Is it reasonable to assume...
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