Answered: (a) Show that the partition function of… | bartleby

Related questions

Question

Bhwa),` where a is
(a) Show that the partition function of a photon gas is Z = Πα
for the vibration modes of the electromagnetic field.
(b) Show that the free energy of an electromagnetic radiation is F(V,T) = = -aVT4,
1-e-Bħwa,
where a is a constant. The density of states of an electromagnetic radiation is given by
V
g(w) = 723 w².

Expert Solution

Step by step

Solved in 6 steps with 21 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

A one-dimensional square well of infinite depth and 1 Å width contains 3 electrons. The potential well is described by V = 0 for 0 1 Å. For a temperature of T = 0 K, the average energy of the 3 electrons is E = 12.4 cV in the approxination that one neglects the Coulomb interaction between clectrons. In the same approximation and for T = 0 K, what is the average cuergy for 4 electrons in this potential well?
(1) A single particla quantum mechanical oscillator has energy levels (n + 1/2) hw, where n = 0, 1, 2, .. and w is the natural frequency of the oscillator. This oscillator is in thermal equi- librium with a reservoir at temperature T. (a) Find the ratio of probability of the oscillator being in the first excited state (n = 1) to the probability of being in the ground state. (b) Assuming that only the two states in Part la are occupied, find the average energy as a function of T. (c) Calculate the heat capacity at a constant volume. Does it depend on temperature?
6QM Please answer question throughly and detailed.
classical physics
For a quantum particle in a scattering state as it interacts a certain potential, the general expressions for the transmission and reflection coefficients are given by T = Jtrans Jinc R = | Jref Jinc (1) where Jinc, Jref, Jtrans are probability currents corresponding to the incident, reflected, and transmitted plane waves, respectively. (a). potential For the particle incident from the left to the symmetric finite square well -Vo; a < x < a, V(x) = 0 ; elsewhere, show that B Ꭲ ; R = A A
Consider a particle moving in a one-dimensional box with walls at x = -L/2 and L/2. (a) Write the wavefunction and probability density for the state n=1. (b) If the particle has a potential barrier at x =0 to x = L/4 (where L = 10 angstroms) with a height of 10.0 eV, what would be the transmission probability of the electrons at the n = 1 state? (c) Compare the energy of the particle at the n= 1 state to the energy of the oscillator at its first excited state.
An arbitrary quantm mechanical system is initially in the ground state |0). At t = 0, a perturbation of the form H' (t) = Hoc:/T is applied. Show that at large times the probability that. tlhe system is in state |1) is given by |(0}Ho|1}|2 (A) A + (Ac)? where As is the difference in cnergy of states |0) and |1). Be specific about what assumption, if any, were inade arriving at your conclusion.
A deuterium molecule (D2₂) at 30°K is known to be in the state, 1 /26 12/₂) = = |3|1, 1) + 4 |7, 3) + |7, 1) where , m) are eigenstates of the angular momentum operator. (a) If one were to measure L₂, what posible values one would get and what would be their associated probabilities? (b) Repeat (a) but for L². (c) What is the expectation value of the energy (E) of the molecule in this state, assuming purely rotational states. Take c= 30.4 cm-¹, where I=moment of inertia of D₂ and c=speed of light. Express your answer in eV. -
pls answer d and e
(a) A quantum dot can be modelled as an electron trapped in a cubic three-dimensional infinite square well. Calculate the wavelength of the electromagnetic radiation emitted when an electron makes a transition from the third lowest energy level, E3, to the lowest energy level, E₁, in such a well. Take the sides of the cubic box to be of length L = 3.2 x 10-8 m and the electron mass to be me = 9.11 x 10-³¹ kg. for each of the E₁ and E3 energy (b) Specify the degree of degeneracy levels, explaining your reasoning.
Consider a state of a 2-electron diatomic molecule AB described by the electronic normalized wave function Þ(1, 2) = y(1,2) [a(1) B(2) – a(2) B(1)] where p(1, 2) is the spatial part of the electronic wave function. (a) What must be the value of the integral (p(1, 2)|4(1,2)) so that the complete (spatial and spin) function (1, 2) is normalized?. (b) Is the spatial function p(1, 2) symmetric or antisymmetric with respect to the exchange of the space coordinates of electron 1 and 2?
A particle is in a three-dimensional box. The y length of the box is twice the x length, and the z length is one-third of the y length. (a) What is the energy difference between the first excited level and the ground level? (b) Is the first excited level degenerate? (c) In terms of the x length, where is the probability distribution the greatest in the lowest-energy level?

SEE MORE QUESTIONS