The π-electrons of naphthalene(C10H8) can be considered to be confined to a rectangular box of dimension...
The π-electrons of naphthalene(C10H8) can be considered to be confined to a rectangular box of dimension 4 A by 7 A (particle-in-a-box)
1) set up and solve the Schrodinger equation to find the energy levels.
2) Add the electrons to the energy-level diagram
3) which levels correspond to HOMO and LUMO? at what wavelength will the lowest energy transition occur?
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The π-electrons of naphthalene(C10H8) can be considered to be
confined to a rectangular box of dimension...
. The π-electrons of naphthalene(C10H8) can be considered to be confined to a rectangular box of dimension 4 A by 7 A (particle-in-a-box) 1) set up and solve the Schrodinger equation to find the energ...
. The π-electrons of naphthalene(C10H8) can be considered to be confined to a rectangular box of dimension 4 A by 7 A (particle-in-a-box) 1) set up and solve the Schrodinger equation to find the energy levels. 2) Add the electrons to the energy-level diagram 3) which levels correspond to HOMO and LUMO? at what wavelength will the lowest energy transition occur?
The electrons within the confined 1,3-diene, C4Hs. observed in the uv region of the spectrum at...
The electrons within the confined 1,3-diene, C4Hs. observed in the uv region of the spectrum at a wavelength of 210 nm. Estimate the effective π system of conjugated hydrocarbons may be treated a s particles Within a one-dimensional box. The lowest energy transition in the spectrum of buta- ene, CaH6, corresponds to excitation of an electron from the HOMO to LUMO and is chain length of buta-1,3-diene in Angstrom.
Problem 1 Assume r-electrons in benzene can be modelled according to a 2D particle in box model. ...
Problem 1 Assume r-electrons in benzene can be modelled according to a 2D particle in box model. The box can be assumed square with the side of 5 Angstrom. Assume each C atom contributes only 1 electron. a) Sketch qualitatively the energy levels diagram for the up to 5 energy states (count degenerate states as one). b) Compute the HOMO-LUMO gap [in eV. c) How much do the conclusions above would change if we assume a non-zero thickness (e.g. 0.5...
Problem 1 Assume m-electrons in benzene can be modelled according to a 2D particle in box model. ...
Problem 1 Assume m-electrons in benzene can be modelled according to a 2D particle in box model. The box can be assumed square with the side of 5 Angstrom. Assume each C atom contributes only 1 electron a) Sketch qualitatively the energy levels diagram for the up to 5 energy states (count degenerate states as one). b) Compute the HOMO-LUMO gap [in eV] c) How much do the conclusions above would change if we assume a non-zero thickness (e.g.0.5 Angstrom)...
1. Use the model of the particle in the ring (rotation in two dimensions) of quantum...
1. Use the model of the particle in the ring (rotation in two dimensions) of quantum mechanics to describe the movement of electrons in the conjugate system of the benzene molecule. Presume that the circumference of the ring is equal to 8.40A. a. ((3 pts) Make a diagram of the energy levels of the electrons Pi in the benzene molecule, clearly identifying the HOMO and the LUMO. b. (3 pts) Calculate the energy of the HOMO and LUMO C. (3...
7. π electron is an electron which resides in the pi bond(s) of a double bond or a triple bond, o...
7. π electron is an electron which resides in the pi bond(s) of a double bond or a triple bond, or in a conjugated p orbital. The 1,3,5-hexatriene molecule is a conjugated molecule with 6 t electrons. Consider the Tt electrons free to move back and forth along the molecule through the delocalized pi system. Using the particle in a box approximation, treat the carbon chain as a linear one-dimensional "box". Allow each energy level in the box to hold...
Question # 1: Find the unit of energy in the energy expression of a free particle...
Question # 1: Find the unit of energy in the energy expression of a free particle in 1-D box: Question # 2: A proton in a box is in a state n = 5 falls to a state n = 4 and loose energy with a wavelength of 2000 nm, what is the length of the box? (answer: 4 x 10 m) Question # 3: a. Consider an electron confined to move in an atom in one dimension over a...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can'...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can't n take the value of 0, briefly explain C) For n-3 determine the values of x (in terms of L) that correspond to a maximum or a minimum in the wave function D) For n-3 determine the values of x (in...
The electrons within the confined 1,3-diene, C4Hs. observed in the uv region of the spectrum at a wavelength of 210 nm. Estimate the effective π system of conjugated hydrocarbons may be treated a s particles Within a one-dimensional box. The lowest energy transition in the spectrum of buta- ene, CaH6, corresponds to excitation of an electron from the HOMO to LUMO and is chain length of buta-1,3-diene in Angstrom.
Problem 1 Assume r-electrons in benzene can be modelled according to a 2D particle in box model. The box can be assumed square with the side of 5 Angstrom. Assume each C atom contributes only 1 electron. a) Sketch qualitatively the energy levels diagram for the up to 5 energy states (count degenerate states as one). b) Compute the HOMO-LUMO gap [in eV. c) How much do the conclusions above would change if we assume a non-zero thickness (e.g. 0.5...
Problem 1 Assume m-electrons in benzene can be modelled according to a 2D particle in box model. The box can be assumed square with the side of 5 Angstrom. Assume each C atom contributes only 1 electron a) Sketch qualitatively the energy levels diagram for the up to 5 energy states (count degenerate states as one). b) Compute the HOMO-LUMO gap [in eV] c) How much do the conclusions above would change if we assume a non-zero thickness (e.g.0.5 Angstrom)...
1. Use the model of the particle in the ring (rotation in two dimensions) of quantum mechanics to describe the movement of electrons in the conjugate system of the benzene molecule. Presume that the circumference of the ring is equal to 8.40A. a. ((3 pts) Make a diagram of the energy levels of the electrons Pi in the benzene molecule, clearly identifying the HOMO and the LUMO. b. (3 pts) Calculate the energy of the HOMO and LUMO C. (3...
7. π electron is an electron which resides in the pi bond(s) of a double bond or a triple bond, or in a conjugated p orbital. The 1,3,5-hexatriene molecule is a conjugated molecule with 6 t electrons. Consider the Tt electrons free to move back and forth along the molecule through the delocalized pi system. Using the particle in a box approximation, treat the carbon chain as a linear one-dimensional "box". Allow each energy level in the box to hold...
Question # 1: Find the unit of energy in the energy expression of a free particle in 1-D box: Question # 2: A proton in a box is in a state n = 5 falls to a state n = 4 and loose energy with a wavelength of 2000 nm, what is the length of the box? (answer: 4 x 10 m) Question # 3: a. Consider an electron confined to move in an atom in one dimension over a...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can't n take the value of 0, briefly explain C) For n-3 determine the values of x (in terms of L) that correspond to a maximum or a minimum in the wave function D) For n-3 determine the values of x (in...
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