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Draw a typical Morse potential energy surface for a diatomic molecule. Label the following i) The...
In the ro-vibrational model for spectra of diatomic molecules, the total rotational and vibrational energy 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...
2.2) The Morse interatomic potential for a diatomic molecule is given by VM(r) D[1-e-a-1 r-ro where...
2.2) The Morse interatomic potential for a diatomic molecule is given by VM(r) D[1-e-a-1 r-ro where r is the interatomic distance. a) Sketch the potential, and indicate its attractive and repulsive region. [4 marks] b) Show that the equilibrium bond length is given by r ro. [4 marks] c) Determine the dissociation energy of the diatomic molecule. [4 marks]
5. (10 points) A simple function that looks like the potential well of a diatomic molecule...
5. (10 points) A simple function that looks like the potential well of a diatomic molecule is the Morse potential given by: U(x) = D. (1-e-Bx) (1) where, x is the displacement of the bond from its equilibrium position, and D. is the value of U(x) at large separations. D. is called the classical dissociation energy and is characterized by the depth of the potential well. We can expand U(x) in a Taylor series about x = 0 to obtain...
Don’t have to give exact answer, I just need to know one n equals in terms...
Don’t have to give exact answer, I just need to know one n
equals in terms of variables
d. The solution of the Schrödinger equation for the Morse potential yields the following expression for the vibrational energy levels (in units of cm 1) of a diatomic molecule: where n is the vibrational quantum number, V is the fundamental vibrational frequency (in cm1) that you calculated in part a), and is the anharmonicity constant given by: En n1/2) 1/2)2 = hc9/4D....
Place the following five diatomic molecules in the first column of the table. For each molecule,...
Place the following five diatomic molecules in the first column of the table. For each molecule, write down its bond order. Li2, H2, C2, O2, N2, Be2 Molecule Bond order Bond length (Å) Dissociation energy (kJ/mol) 0.74 457 1.09 1.21 599 1.21 105 2.72 10.0 942 494 2.67 Number of electrons: H(1), He(2), Li(3), Be(4), C(6), N(7), O(8). Based on the table, draw (on the same plot) the ground state potential energy function of N2, Liz and Be2. Annotate axes....
(ii) Draw an energy level diagram for an electronic transition from an electronic ground state to...
(ii) Draw an energy level diagram for an electronic transition from an electronic ground state to an excited state that has an increase in bond length. Include vibrational energy levels in your diagram. (iii) Sketch the electronic absorption spectrum corresponding to the energy level diagram of part (ii) showing the vibrational components.
Consider the Morse energy potential curve above. Please draw two more curves, one with a weaker...
Consider the Morse energy potential curve above. Please draw two
more curves, one with a weaker chemical bond and one with a longer
chemical bond. Please clearly label all three curves.
Energy
I know how to do A but not sure how to do B, C and D....
I know how to do A but not sure how to do B, C and D.
Thank you so much!
5. Vibration of diatomic molecule (20 points total) The adjacent figure shows the experimentally detemined potential energy curve of the electronic ground state of Br2 with a few of the vibrational levels. The vibrational transitions are reasonably well described by a harmonic-oscillator model but much more accurately by including a small anharmonic correction term: En/hc = e(n +1/2) - exe(n...
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...
4. Anharmonic potential (15 points) The adjacent figure shows the experimentally determined potential energy curve of the electronic ground state of"Br2, with a few of the vibrational levels. The...
4. Anharmonic potential (15 points) The adjacent figure shows the experimentally determined potential energy curve of the electronic ground state of"Br2, with a few of the vibrational levels. The vibrational transitions are reasonably well described by a harmonic oscillator model, but much more accurately by including a small anharmonic correction term: En/hcVe(n 1/2) - vexe(n + 1/2)2. From fits to experimental data, the values of the constants are 325.32 cm and exe 1.08 cm .5 10 15 (a) Calculate the...
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...
2.2) The Morse interatomic potential for a diatomic molecule is given by VM(r) D[1-e-a-1 r-ro where r is the interatomic distance. a) Sketch the potential, and indicate its attractive and repulsive region. [4 marks] b) Show that the equilibrium bond length is given by r ro. [4 marks] c) Determine the dissociation energy of the diatomic molecule. [4 marks]
5. (10 points) A simple function that looks like the potential well of a diatomic molecule is the Morse potential given by: U(x) = D. (1-e-Bx) (1) where, x is the displacement of the bond from its equilibrium position, and D. is the value of U(x) at large separations. D. is called the classical dissociation energy and is characterized by the depth of the potential well. We can expand U(x) in a Taylor series about x = 0 to obtain...
Don’t have to give exact answer, I just need to know one n
equals in terms of variables
d. The solution of the Schrödinger equation for the Morse potential yields the following expression for the vibrational energy levels (in units of cm 1) of a diatomic molecule: where n is the vibrational quantum number, V is the fundamental vibrational frequency (in cm1) that you calculated in part a), and is the anharmonicity constant given by: En n1/2) 1/2)2 = hc9/4D....
Place the following five diatomic molecules in the first column of the table. For each molecule, write down its bond order. Li2, H2, C2, O2, N2, Be2 Molecule Bond order Bond length (Å) Dissociation energy (kJ/mol) 0.74 457 1.09 1.21 599 1.21 105 2.72 10.0 942 494 2.67 Number of electrons: H(1), He(2), Li(3), Be(4), C(6), N(7), O(8). Based on the table, draw (on the same plot) the ground state potential energy function of N2, Liz and Be2. Annotate axes....
(ii) Draw an energy level diagram for an electronic transition from an electronic ground state to an excited state that has an increase in bond length. Include vibrational energy levels in your diagram. (iii) Sketch the electronic absorption spectrum corresponding to the energy level diagram of part (ii) showing the vibrational components.
Consider the Morse energy potential curve above. Please draw two
more curves, one with a weaker chemical bond and one with a longer
chemical bond. Please clearly label all three curves.
Energy
I know how to do A but not sure how to do B, C and D.
Thank you so much!
5. Vibration of diatomic molecule (20 points total) The adjacent figure shows the experimentally detemined potential energy curve of the electronic ground state of Br2 with a few of the vibrational levels. The vibrational transitions are reasonably well described by a harmonic-oscillator model but much more accurately by including a small anharmonic correction term: En/hc = e(n +1/2) - exe(n...
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...
4. Anharmonic potential (15 points) The adjacent figure shows the experimentally determined potential energy curve of the electronic ground state of"Br2, with a few of the vibrational levels. The vibrational transitions are reasonably well described by a harmonic oscillator model, but much more accurately by including a small anharmonic correction term: En/hcVe(n 1/2) - vexe(n + 1/2)2. From fits to experimental data, the values of the constants are 325.32 cm and exe 1.08 cm .5 10 15 (a) Calculate the...
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