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Consider N non-interacting oxygen molecules, each with spin 1 and three quantum states
Consider a two-dimensional non-interacting and non-relativistic gas of N spin-1/2 fermions at T 0 in a box of area A. (a) Find the Fermi energy εF. (b) Show that the total energy is given by E- NE. 2
(a)Write down the classical and the quantum partition functions for two non-interacting diatomic molecules in a volume V, where each molecule is treated as a simple harmonic oscillator. (b)Obtain the internal energy of the system and the entropy by using the partition functions
Question 1 A system of N identical non-interacting magnetic ions of spin Y%, has energy u tHo for each spin. μο is the magnetic moment in a crystal at absolute temperature T in a magnetic field B. For this system calculate: a) The partition function, Z. b) Free energy, F. c) The entropy. S d) The average energy, U e) The average magnetic moment, M
the nuclear spin quantum number for deuterium, 2H is I=1. The number of nuclear spin states is ____?
Problem 1. Consider a system of three identical particles. Each particle has 5 quantum states with energies 0, ε, 2E, 3E, 4E. For distinguishable particles, calculate the number of quantum states where (1) three particles are in the same single-particle state, (2) only two particles are in the same single-particle state, and (3) no two particles are in the same single-particle state. Problem 2. For fermions, (1) calculate the total number of quantum states, and (2) the number of states...
6. Consider a quantum system of N particles with only three possible states to oc cupy for each particle. The energy values of these states are equal to 0, E and 3, respectively. (a) (10 points) You observe that the probability to sample eash state is p=0.9, P2 = 0.09 and p = 0.01 at T = 300 K. What are the energies ez and ez? Recall that the probability to occupy 4th state is proportional to e«/T where k...
6. Consider a quantum system of N particles with only three possible states to oc- cupy for each particle. The energy values of these states are equal to 0, €and €3, respectively. (a) [10 points) You observe that the probability to sample eash state is P = 0.9. P2 = 0.09 and p = 0.01 at T = 300 K. What are the energies and c? Recall that the probability to occupy state is proportional to where k= 1.38 x...
To first approximation, a neutron star may be treated as a non-interacting gas of neutrons (spin-1/2 fermions). ( a) Find an expression for the degeneracy (zero point) energy of the star as a function its mass M and radius R. (Don’t worry that our calculation for degenerate Fermi systems was done for particles in a cubical box, the same results apply to a sphere of the same volume.) (b) Write down an expression for the gravitational potential energy of the...
(a)Write down the classical and the quantum partition functions for two non-interacting atoms confined to in their motion along a line of length L. (b)Obtain the internal energy of the system and the entropy by using the partition functions
Consider N non-interacting electrons confined to a two-dimensional square well of dimensions a × a. Derive an expression for the Fermi energy of this system in terms of the areal density σ = N/a2 and calculate the corresponding density of states. Show all steps.