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Assume a quantum system with two energy levels that are separated by E1-Ep= 1.66 x 10-1°...
3. Consider a canonical system with uniformly spaced energy levels (spacing = €). The populations of...
3. Consider a canonical system with uniformly spaced energy levels (spacing = €). The populations of the energy levels are given by the Bolzmann distribution. (a) What fraction of particles is in the ground state at T = 300 K when the energy spacing is € = 3.0 x 10-20 J? You can set the ground state energy to be zero. (b) The e value mentioned in part (a) is the typical energy spacing in the vibrational energy levels of...
3. Consider a canonical system with uniformly spaced energy levels (spacing = e). The populations of...
3. Consider a canonical system with uniformly spaced energy levels (spacing = e). The populations of the energy levels are given by the Bolzmann distribution (a) What fraction of particles is in the ground state at T 300 K when the energy spacing is e 3.0 x 10-20 J? You can set the ground state energy to be zero. (b) The e value mentioned in part (a) is the typical energy spacing in the vibrational energy levels of a molecule....
Question 3 a) Consider the hypothetical case of two degenerate quantum levels of energy E1, E2...
Question 3 a) Consider the hypothetical case of two degenerate quantum levels of energy E1, E2 (E. < Ez) and statistical weights g1 = 4, 92 = 2. These levels have respective populations N1 = 3 and N2 = 1 particles. What are the possible microstates if the particles are (1) bosons (6 marks) or (ii) fermions (6 marks)? AP3, PHA3, PBM3 PS302 Semester One 2011 Repeat page 2 of 5 b) Show how the number of microstates would be...
A quantum mechanical transition between two rotational energy levels is measured between E0 = 3.6x10-23 J...
A quantum mechanical transition between two rotational energy levels is measured between E0 = 3.6x10-23 J and E1 = 2.4x10-23 J. What is the wavelength of light that will excite this transition? What region of the electromagnetic spectrum does this light fall into?
5. 10 points Two energy levels Ej and E2, with A = E2 - E1, are...
5. 10 points Two energy levels Ej and E2, with A = E2 - E1, are populated by N distinguishable non-interactive particles at temperature T. a) Find the average energy of the system. (3 pts) b) Consider the limits T – 0 and T - and find the average energy per particle in these two limits to the lowest order in A. (2 pts) c) Calculate the specific heat C for this system. (3 pts) d) Consider the limits T...
A system has 11 energy levels with an equidistant spacing of delta E = 1 kJ...
A system has 11 energy levels with an equidistant spacing of delta E = 1 kJ mol-1. (a) In a single Excel graph, plot the population probabilities pi of all levels for the temperatures T = 3 K, 300 K, and 6000 K. (energy on the x-axis, probability on the y-axis) Note that: 3 K temperature of deep space 300 K “room temperature” 6000 K surface temperature of the sun. (b) Determine the value of the partition function...
Fermions in a two-level or three-level system with degeneracy Consider a have only two energy levels,...
Fermions in a two-level or three-level system with degeneracy Consider a have only two energy levels, with energy eo = degeneracies no and n1, which are integers. Hint: Note that system of N independent fermions. Assume that single-particle Hamiltonian 0 and e1 = €. However, the two levels have 1 1 (4) e 1 e- 1 a) For the case of N = 1 = no = n1. Find the chemical potential, u, as a function of temperature. Find the...
Consider a molecule that has two energy levels separated by e, where the ground state has...
Consider a molecule that has two energy levels separated by e, where the ground state has a degeneracy of 2 and the excited state has a degeneracy of 3. (a) What is the expression for the partition function at temperature T? (b) What are the fractional populations of the two states at temperature T? (c) What is the internal energy per particle at temperature T?
Item 5 An particle in a 1-D box of length L=2A∘ has allowed energy levels that...
Item 5 An particle in a 1-D box of length L=2A∘ has allowed energy levels that include 84.82 eV and 150.79 eV; however, the quantum numbers for these two states are unknown. Part A - What is the ground-state energy of the system? E1=9.42eV E1=37.7eV E1=5.30 eV E1=16.75 eV E1=28.3eV E1=21.2 eV Part B - What is the de Broglie wavelength for the n=2 state? 2.5A∘ 0.5A∘ 1.5A∘ 3.0 A∘ 1.0 A∘ 2.0 A∘
A system consists of N weakly interacting subsystems. Each subsystem possesses only two energy levels E1...
A system consists of N weakly interacting subsystems. Each subsystem possesses only two energy levels E1 and E2 each of them non-degenerate. (i) Draw rough sketches (i.e. from common sense, not from exact mathematics) of the temperature dependence of the mean energy and of the heat capacity of the system. (ii) Obtain an exact expression for the heat capacity of the system. Very Detailed Explanation please.
3. Consider a canonical system with uniformly spaced energy levels (spacing = €). The populations of the energy levels are given by the Bolzmann distribution. (a) What fraction of particles is in the ground state at T = 300 K when the energy spacing is € = 3.0 x 10-20 J? You can set the ground state energy to be zero. (b) The e value mentioned in part (a) is the typical energy spacing in the vibrational energy levels of...
3. Consider a canonical system with uniformly spaced energy levels (spacing = e). The populations of the energy levels are given by the Bolzmann distribution (a) What fraction of particles is in the ground state at T 300 K when the energy spacing is e 3.0 x 10-20 J? You can set the ground state energy to be zero. (b) The e value mentioned in part (a) is the typical energy spacing in the vibrational energy levels of a molecule....
Question 3 a) Consider the hypothetical case of two degenerate quantum levels of energy E1, E2 (E. < Ez) and statistical weights g1 = 4, 92 = 2. These levels have respective populations N1 = 3 and N2 = 1 particles. What are the possible microstates if the particles are (1) bosons (6 marks) or (ii) fermions (6 marks)? AP3, PHA3, PBM3 PS302 Semester One 2011 Repeat page 2 of 5 b) Show how the number of microstates would be...
5. 10 points Two energy levels Ej and E2, with A = E2 - E1, are populated by N distinguishable non-interactive particles at temperature T. a) Find the average energy of the system. (3 pts) b) Consider the limits T – 0 and T - and find the average energy per particle in these two limits to the lowest order in A. (2 pts) c) Calculate the specific heat C for this system. (3 pts) d) Consider the limits T...
Fermions in a two-level or three-level system with degeneracy Consider a have only two energy levels, with energy eo = degeneracies no and n1, which are integers. Hint: Note that system of N independent fermions. Assume that single-particle Hamiltonian 0 and e1 = €. However, the two levels have 1 1 (4) e 1 e- 1 a) For the case of N = 1 = no = n1. Find the chemical potential, u, as a function of temperature. Find the...
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