Author Question: Choose the true statement that compares and contrasts the Maxwell-Boltzmann (MB) distribution, the ... (Read 54 times)

stevenposner · **on:** Jul 28, 2018

Choose the true statement that compares and contrasts the Maxwell-Boltzmann (MB) distribution, the Fermi-Dirac (FD) distribution, and the Bose-Einstein (BE) distributions.
a. The MB, FD, and BE statistical factors agree only at low particle energies.
b. The MB distribution models only low-density material, while both the FD and BE distributions can model higher density material.
c. The MB statistical factor goes to infinity at low particle energies, while the FD statistical factor goes to 1/2 and the BE statistical factor goes to 1.
d. The MB and FD distributions work only for distinguishable particles while the BE distribution works for indistinguishable particles.
e. The MB distribution works for particles with integer spin, the FD distribution works for particles with half-integer spin, and the BE distribution works for particles with any value of spin.

Question 2

Imagine that you could put three electrons into isolation in a box. Initially, electrons A and B have kinetic energy E₀ and electron C has kinetic energy 2E₀. After isolation from observation for a short time, you examine the electrons again and find that one electron has energy 2E₀ and two electrons have energy E₀. Assume for this problem's sake that the electrons can transfer energy to one another but only in increments of E₀. Assume also that all electrons are exactly the same. What is the probability that the higher energy electron is electron C?

livaneabi · **Reply #1 on:** Jul 28, 2018

Answer to Question 1

b.
The MB distribution is only accurate for ideal gases and other dilute substances where the intermolecular/interatomic reactions do not have a significant impact on particle behavior. Both of the other two can model higher density material such as liquids or solids.

Answer to Question 2

c.
Since electrons are indistinguishable, identical particles and can transfer energy to one another in this problem, the higher energy electron is equally probable to be A, B, or C. The probability calculated is one-third for each electron.