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Problem 1 Assume m-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. ...
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...
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...
. 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?
Q 1: For particle in a box problem, answer the following questions, a) Why n=0 is...
Q 1: For particle in a box problem, answer the following questions, a) Why n=0 is not an allowed quantum number? b) En = 0 is not allowed for particle in a box, why? c) Ground state wavefunction is orthogonal to the first excited state wavefunction, what does it mean? Q 2: An electronic system that is treated as particle in 3-D box with dimensions of 3Å x 3Å x 4Å. Calculate the wavelength corresponding to the lowest energy transition...
4. Estimate the transition frequency for the poryphyrin molecule from m-11 to m 12, assuming that the pi electrons can be modeled as a particle in a ring of radius 440 picometers. (C 7. The...
4. Estimate the transition frequency for the poryphyrin molecule from m-11 to m 12, assuming that the pi electrons can be modeled as a particle in a ring of radius 440 picometers. (C 7. The most probable distance of the electron from the nucleus in a 1ls state hydrogen atom (with wavefunction V1) can be determined by 21. A (A) solving the eigenvalue equation: Rvw rV., finding the maximum in the 1s radial distribution function by differentiation. (C) substituting vi,...
EENG 245 Physical electronics HW 1 1) The NaCl crystal is cubic, and can be described...
EENG 245 Physical electronics HW 1 1) The NaCl crystal is cubic, and can be described as follows. Na atoms sit at the corners and faces of a cube, and Cl atoms sit in between two Na atoms. This means that a Clatom is found half-way along each of the cube edges, and there is a Cl in the center of the cube. (We could also have described the lattice by interchanging Na and Cl in the description above.) Another...
TSD.1 In this problem, we will see (in outline) how we can calculate the multiplicity of a monatomic ideal gas This derivation involves concepts presented in chapter 17 Note that the task is to...
TSD.1 In this problem, we will see (in outline) how we can calculate the multiplicity of a monatomic ideal gas This derivation involves concepts presented in chapter 17 Note that the task is to count the number of microstates that are compatible with a given gas macrostate, which we describe by specifying the gas's total energy u (within a tiny range of width dlu), the gas's volume V and the num- ber of molecules N in the gas. We will...
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...
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...
4. Estimate the transition frequency for the poryphyrin molecule from m-11 to m 12, assuming that the pi electrons can be modeled as a particle in a ring of radius 440 picometers. (C 7. The most probable distance of the electron from the nucleus in a 1ls state hydrogen atom (with wavefunction V1) can be determined by 21. A (A) solving the eigenvalue equation: Rvw rV., finding the maximum in the 1s radial distribution function by differentiation. (C) substituting vi,...
EENG 245 Physical electronics HW 1 1) The NaCl crystal is cubic, and can be described as follows. Na atoms sit at the corners and faces of a cube, and Cl atoms sit in between two Na atoms. This means that a Clatom is found half-way along each of the cube edges, and there is a Cl in the center of the cube. (We could also have described the lattice by interchanging Na and Cl in the description above.) Another...
TSD.1 In this problem, we will see (in outline) how we can calculate the multiplicity of a monatomic ideal gas This derivation involves concepts presented in chapter 17 Note that the task is to count the number of microstates that are compatible with a given gas macrostate, which we describe by specifying the gas's total energy u (within a tiny range of width dlu), the gas's volume V and the num- ber of molecules N in the gas. We will...
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