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Consider a system of 1000 particles that can only have two energies, E1 and E2, with...
Consider a system of 1000 particles that can only have two energies, E1 and E2 with...
Consider a system of 1000 particles that can only have two energies, E1 and E2 with E2>E1. The difference in the energy between these two values is delta E= E2-E1. Asume g1=g2=1. a) graph the number of paricle n1, n2 in states of E1 E2 as a function of kbT/deltaE, where kb is Boltzmann constant. Explain the result b) at what value kbT/deltaE do 750 of the particles have the energy E1
Consider a system with 1000 particles that can only have two energies, &, and &, with...
Consider a system with 1000 particles that can only have two energies, &, and &, with &z > &. The difference between these two values is Aε = &z - & . Assume that gi=g2 = 1. Using the equation for the Boltzmann distribution graph the number of particles, ni and n2, in states & and Ez as a function of temperature for a Aε = 1x10-21 J and for a temperature range from 2 to 300 K. n; -...
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...
Question 9 Consider a quantum system comprising two indistinguishable particles which can occupy only three individual-particle...
Question 9 Consider a quantum system comprising two indistinguishable particles which can occupy only three individual-particle energy levels, with energies 81 0, 82 2 and E3 38.The system is in thermal equilibrium at temperature T. (a) Suppose the particles which can occupy an energy level. are spinless, and there is no limit to the number of particles (i) How many states do you expect this system to have? Justify your answer (ii) Make a table showing, for each state of...
need help with thermodynamics A system consists of N weakly interacting particles, each of which can...
need help with thermodynamics
A system consists of N weakly interacting particles, each of which can be in either of two states with respective energies e and 2. where e1 2 1. Without explicit calculation, make a qualitative plot of the mean energy U the entropy S of the system as a function of its temperature T. What is in the limit of very low and very high temperatures? What is S in the limit of very low and very...
1. Consider a quantum system comprising three indistinguishable particles which can occupy only three individual-partic...
1. Consider a quantum system comprising three indistinguishable particles which can occupy only three individual-particle energy levels, with energies ε,-0, ε,-2e and ε,-3. The system is in thermal equilibrium at temperature T. Suppose the particles are bosons with integer spin. i) How many states do you expect this system to have? Justify your answer [2 marks] (ii) Make a table showing, for each state of this system, the energy of the state, the number of particles (M, M,, N) with...
Artificial rubies have an atomic system consisting of three main energy levels and can be used to...
Artificial rubies have an atomic system consisting of three main energy levels and can be used to produce short pulses of laser light. The energies of these levels are Eo, E1 and E2, in increasing order of energy (a) Write down an expression giving the relative population of the energy levels Eo and E1 at thermal equilibrium. b) Explain what is meant by the term population inversion. Described how this is achieved in a three-level laser system Photons of wavelength...
Suppose two plane waves of light with electric field amplitudes E1 and E2 arrive at a...
Suppose two plane waves of light with electric field amplitudes E1 and E2 arrive at a detector at time t having travelled different distances z1 and z2. Assume the field vectors have the same polarization direction P. The fields of the two plane waves at the detector individually are Epcos(ω-ka) and E2pcos(ot-kz2) . Here the wavenumber is k = 2πα and the angular frequency is ck 2nclv, where A is the wavelength, c is the speed, and is the frequency...
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 system with 1000 particles that can only have two energies, &, and &, with &z > &. The difference between these two values is Aε = &z - & . Assume that gi=g2 = 1. Using the equation for the Boltzmann distribution graph the number of particles, ni and n2, in states & and Ez as a function of temperature for a Aε = 1x10-21 J and for a temperature range from 2 to 300 K. n; -...
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...
Question 9 Consider a quantum system comprising two indistinguishable particles which can occupy only three individual-particle energy levels, with energies 81 0, 82 2 and E3 38.The system is in thermal equilibrium at temperature T. (a) Suppose the particles which can occupy an energy level. are spinless, and there is no limit to the number of particles (i) How many states do you expect this system to have? Justify your answer (ii) Make a table showing, for each state of...
need help with thermodynamics
A system consists of N weakly interacting particles, each of which can be in either of two states with respective energies e and 2. where e1 2 1. Without explicit calculation, make a qualitative plot of the mean energy U the entropy S of the system as a function of its temperature T. What is in the limit of very low and very high temperatures? What is S in the limit of very low and very...
1. Consider a quantum system comprising three indistinguishable particles which can occupy only three individual-particle energy levels, with energies ε,-0, ε,-2e and ε,-3. The system is in thermal equilibrium at temperature T. Suppose the particles are bosons with integer spin. i) How many states do you expect this system to have? Justify your answer [2 marks] (ii) Make a table showing, for each state of this system, the energy of the state, the number of particles (M, M,, N) with...
Artificial rubies have an atomic system consisting of three main energy levels and can be used to produce short pulses of laser light. The energies of these levels are Eo, E1 and E2, in increasing order of energy (a) Write down an expression giving the relative population of the energy levels Eo and E1 at thermal equilibrium. b) Explain what is meant by the term population inversion. Described how this is achieved in a three-level laser system Photons of wavelength...
Suppose two plane waves of light with electric field amplitudes E1 and E2 arrive at a detector at time t having travelled different distances z1 and z2. Assume the field vectors have the same polarization direction P. The fields of the two plane waves at the detector individually are Epcos(ω-ka) and E2pcos(ot-kz2) . Here the wavenumber is k = 2πα and the angular frequency is ck 2nclv, where A is the wavelength, c is the speed, and is the frequency...
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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