Sketch the energy level diagrams of the two different two-dimensional particle in-a-box systems given below.Include the...
Sketch the energy level diagrams of the two different two-dimensional particle in-a-box systems given below.Include the lowest-five energy levels for each system.
a.Square (i.e., a=b), degenerate energy levels
b.Rectangle (i.e., a≠b) non-degenerate energy levels
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Sketch the energy level diagrams of the two different
two-dimensional particle in-a-box systems given below.Include the...
A particle is confined to a two-dimensional box of length L and width 3L. The energy...
A particle is confined to a two-dimensional box of length L and
width 3L. The energy values are E = (Planck constant2ϝ2/2mL2)(nx2 +
ny2/9). Find the two lowest degenerate levels.
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Particle in a three-dimensional box: a. Give the equation for a particle in a three-dimensional box...
Particle in a three-dimensional box: a. Give the equation for a particle in a three-dimensional box b. How does the density of states (i.e., number of states per unit of energy) change with increasing energy? Explain the answer.
(ii) The quantised energies of a particle in a two-dimensional square box are given by: where a i...
(ii) The quantised energies of a particle in a two-dimensional square box are given by: where a is the length of the box in each dimension. Obtain expressions for the particle's energy for nı = 1 and n-= 3, and for nı = 3 and n-=1. Comnnment on the results. 121
(ii) The quantised energies of a particle in a two-dimensional square box are given by: where a is the length of the box in each dimension. Obtain expressions for...
nh 61. The energy for one-dimensional particle-in-a-box is E=" 1. For a particle in a 0...
nh 61. The energy for one-dimensional particle-in-a-box is E=" 1. For a particle in a 0 three-dimensional cubic box (Lx=Ly=L2), if an energy level has twice the energy of the ground state, what is the degeneracy of this energy level? (B) 1 (C)2 (D) 3 (E) 4 (A) 0
3. You have a gas of 10 particles confined in a rigid 1D box of length L-1nm-10 °m. a) Sketch an ...
3. You have a gas of 10 particles confined in a rigid 1D box of length L-1nm-10 °m. a) Sketch an energy level diagram for the lowest five energies (including a quantitative calculation of the energy levels) if these are electrons and they are in their lowest lying state. How many electrons are in each level and what is their state? b) Sketch an energy level diagram for the lowest five levels (including a quantitative calculation of the energy levels)...
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)...
Consider a particle confined in two-dimensional box with infinite walls at x 0, L;y 0, L. the dou...
quantum mechanics
Consider a particle confined in two-dimensional box with infinite walls at x 0, L;y 0, L. the doubly degenerate eigenstates are: Ιψη, p (x,y))-2sinnLx sinpry for 0 < x, y < L elsewhere and their eigenenergies are: n + p, n, p where n, p-1,2, 3,.... Calculate the energy of the first excited state up to the first order in perturbation theory due to the addition of: 2 2
Consider a particle confined in two-dimensional box with infinite...
The eigenfunctions for a particle in a one-dimensional box of length L, and the corresponding energy...
The eigenfunctions for a particle in a one-dimensional box of length L, and the corresponding energy eigenvalues are given below. What is the variance of measurements for the linear momentum, i.e., Op = v<p? > - <p>2? Øn (x) = ( )" sin nga, n= 1, 2,.. En = n2h2 8m12 Note the Hamiltonian operator to give the energy is H = = - 42 8n72 dx2 nh 2L oo O nềh2 412 Uncertain since x is known. Following Question...
4. A (one dimensional) particle in a box of length 2a (i.e., zero potential energy) is...
4. A (one dimensional) particle in a box of length 2a (i.e., zero potential energy) is represented by the wavefunction v(x) 0, otherwise a. Sketch the wavefunction. Write down the (time independent) Schrodinger equation. Show whether or not the wavefunction is a solution to the equation. b. What does it mean physically if the wavefunction of the particle is NOT a solution to the Schrodinger equation? Explain. c. Determine the normalization constant A. 5. Same system. Find the average or...
(ii) The quantised energies of a particle in a two-dimensional square box are given by: where a is the length of the box in each dimension. Obtain expressions for the particle's energy for nı = 1 and n-= 3, and for nı = 3 and n-=1. Comnnment on the results. 121
(ii) The quantised energies of a particle in a two-dimensional square box are given by: where a is the length of the box in each dimension. Obtain expressions for...
nh 61. The energy for one-dimensional particle-in-a-box is E=" 1. For a particle in a 0 three-dimensional cubic box (Lx=Ly=L2), if an energy level has twice the energy of the ground state, what is the degeneracy of this energy level? (B) 1 (C)2 (D) 3 (E) 4 (A) 0
3. You have a gas of 10 particles confined in a rigid 1D box of length L-1nm-10 °m. a) Sketch an energy level diagram for the lowest five energies (including a quantitative calculation of the energy levels) if these are electrons and they are in their lowest lying state. How many electrons are in each level and what is their state? b) Sketch an energy level diagram for the lowest five levels (including a quantitative calculation of the energy levels)...
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)...
quantum mechanics
Consider a particle confined in two-dimensional box with infinite walls at x 0, L;y 0, L. the doubly degenerate eigenstates are: Ιψη, p (x,y))-2sinnLx sinpry for 0 < x, y < L elsewhere and their eigenenergies are: n + p, n, p where n, p-1,2, 3,.... Calculate the energy of the first excited state up to the first order in perturbation theory due to the addition of: 2 2
Consider a particle confined in two-dimensional box with infinite...
The eigenfunctions for a particle in a one-dimensional box of length L, and the corresponding energy eigenvalues are given below. What is the variance of measurements for the linear momentum, i.e., Op = v<p? > - <p>2? Øn (x) = ( )" sin nga, n= 1, 2,.. En = n2h2 8m12 Note the Hamiltonian operator to give the energy is H = = - 42 8n72 dx2 nh 2L oo O nềh2 412 Uncertain since x is known. Following Question...
4. A (one dimensional) particle in a box of length 2a (i.e., zero potential energy) is represented by the wavefunction v(x) 0, otherwise a. Sketch the wavefunction. Write down the (time independent) Schrodinger equation. Show whether or not the wavefunction is a solution to the equation. b. What does it mean physically if the wavefunction of the particle is NOT a solution to the Schrodinger equation? Explain. c. Determine the normalization constant A. 5. Same system. Find the average or...
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