Consider a system composed of four harmonic oscillators. The energy of the ground state is E0/2....

Consider a system composed of four harmonic oscillators. The energy of the ground state is E0/2. The distribution of oscillators in each system is described by the set following distributions {Ni} 

Distribution I: N0=2, N1=1 N2=1, N3=0 

Distribution II: N0=1, N1=3 N2=N3=0 

Distribution III: N0=3 N1=N2=0 N3=1

For each distribution, calculate.

1. The energy of each system and the average energy

2. The number of equivalent particle arrangements W that yield equivalent distributions (assume the particles are distinguishable), or degeneracy, of each distribution

3. The absolute entropy S of each distribution; which distribution is the most likely to occur?

4. Do any of these distributions correspond to thermodynamic equilibrium? If not, state the condition for thermodynamic equilibrium

Expert Solution

genius_generous answered 2 years ago

Consider the ground state energy of the hydrogen atom E0. Enter the expression you use to...

Consider the ground state energy of the hydrogen atom E0. Enter the expression you use to verify that the ground state energy is 13.6 eV? Use fundamental constants e, me, k and h. E0 = ?

Consider the asymmetric 1/2 harmonic oscillator. use the Variational Principle to estimate the ground state energy...

Consider the asymmetric 1/2 harmonic oscillator. use the Variational Principle to estimate the ground state energy of this potential. Use as your trial function Axe^bx^2

Consider a two-state system as shown: E1 = 0.05 eV E0 = 0 eV The system...

Consider a two-state system as shown: E1 = 0.05 eV E0 = 0 eV The system is in a thermal reservoir at temperature T. a) [4 points] What is the entropy of the system at a temperature of T = 0 K? Explain your reasoning. b) [4 points] Find the approximate entropy of the system at a temperature of ? = 1010 K. Explain your reasoning. c) [6 points] Find the temperature T at which the system is 4 times...

Explain these concepts (a)Marcostate and microstate: Give an example using a system of 3 harmonic oscillators....

Explain these concepts (a)Marcostate and microstate: Give an example using a system of 3 harmonic oscillators. (b) Boltzmann factor: You have to explain how this expression is derived. (c)Microcanonical ensemble (d)Canonical ensemble

Consider a hydrogen atom in the ground state. What is the energy of its electron? E=...

Consider a hydrogen atom in the ground state. What is the energy of its electron? E= J Consider a hydrogen atom in an excited state of 2s^1. What is the energy of its electron? E= J

For the ground state of the Harmonic Oscillator and 2D Rigid Rotor A. Give the time...

For the ground state of the Harmonic Oscillator and 2D Rigid Rotor A. Give the time dependent wave function B. Determine <x> and <p> for both the Harmonic Oscillator and 2D Rigid Rotor

A harmonic oscillator is in the ground state when the parameter k DOUBLES without changing the...

A harmonic oscillator is in the ground state when the parameter k DOUBLES without changing the wavefunction. What's the probability that the oscillator is found in the new ground state?

The ground state energy of an oscillating electron is 1.24 eV

The ground state energy of an oscillating electron is 1.24 eV. How much energy must be added to the electron to move it to the second excited state? The fourth excited state?

An electron is in the ground state of an infinite square well. The energy of the...

An electron is in the ground state of an infinite square well. The energy of the ground state is E1 = 1.35 eV. (a) What wavelength of electromagnetic radiation would be needed to excite the electron to the n = 4 state? nm (b) What is the width of the square well? nm

An electron at ground state, absorbs the energy of a photon that has a frequency of...

An electron at ground state, absorbs the energy of a photon that has a frequency of 3.1573 x 1015/s, and jumps to the higher level. The same electron makes two more consecutive jumps. First, the electron jumps to another energy level by emitting a photon with a wavelength of 434.1 nm. This electron jumps immediately to the third energy level. Find the energy and the frequency of the photon which are the result of the third jump

Question