Question

The density for spin-1/2 fermions in a box is ?(?) = ?/ 2?^2( 2?/ℏ^2)^3/2 √? will...

The density for spin-1/2 fermions in a box is

?(?) = ?/ 2?^2( 2?/ℏ^2)^3/2 √?

will the Fermi energy increase, decrease, or stay the same if

1) we increase the number of fermions?

2) we increase the mass of the fermions?

3) we increase the spin of the fermions (say from 1/2 to 3/2)?

4) Make a rough sketch of the original density-of-states and compare to 1-3

Science   Advanced-Physics   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A system with a spin of 1/2 has a probability of 1/4 to gain Sz with...
A system with a spin of 1/2 has a probability of 1/4 to gain Sz with a value of -ℏ/2 and 3/4 probability to gain Sx with value of ℏ/2. Determine the spin state.
(d) Using the fact that there is one electron per energy state up to the Fermi...
(d) Using the fact that there is one electron per energy state up to the Fermi energy, Ef, and that the total number of electrons in the volume V of the metal, is given by ? = ∫ ?(?)?? (boundaries ?f top, 0 bottom of integral) show that ?f = (ℏ^2/2?)* (( 3?^2 ?)/ ?)^ 2/3 Estimate the value of the Fermi energy at T = 0 K for aluminium, assuming the density, p = 2.7 g/cm^3,the atomic mass is...
1. In a H2 molecule there are two protons, and these have spin 1/2 ħ, that...
1. In a H2 molecule there are two protons, and these have spin 1/2 ħ, that is, they are fermions. If we just look at the two protons, would you expect their spins to be parallel or anti parallel in the ground state of the H2 molecule? 2. Is there a type of viscosity that acts on holes in a semiconductor and gives them a terminal velocity in an electric field, or do holes just accelerate under the influence of...
2. Free Electron Gas a. Consider a free electron gas of valence 4s-electrons in potassium (atomic...
2. Free Electron Gas a. Consider a free electron gas of valence 4s-electrons in potassium (atomic mass M=39.1 and density 856 kg/m3). What is the energy (in electron volts, eV) of the highest filled level in the ground state (i.e., the Fermi energy at zero temperature)? b. Calculate the corresponding electron velocities. c. Calculate the density of states at the Fermi energy. How large is the number of electrons in so- called “soft zone” or “Fermi window” of about 4kBT...
Suppose electrons had a spin of 3/2 instead of 1/2. What would be Z for the...
Suppose electrons had a spin of 3/2 instead of 1/2. What would be Z for the first noble gas? What if electrons instead had spin 1? Explain your reasoning. --------- I think the answer for 3/2 is Z=4 since there will be 4 spacial states, but there are conflicting answers from previous cheggs. A clear explanation would be very apprecaited!
  1. You have three boxes labelled Box #1, Box #2, and Box #3.   Initially each box contains...
  1. You have three boxes labelled Box #1, Box #2, and Box #3.   Initially each box contains 4 red balls and 4 green balls.  One ball is randomly selected from Box #1 and placed in Box #2 Then one ball is randomly selected from Box #2 and placed in Box #3. Then one ball is randomly selected from Box #3 and placed in Box #1.  At the conclusion of this process, what is the probability that that each box has the same  number of...
An atomic nucleus can be crudely modeled as a gas of nucleons with a number density...
An atomic nucleus can be crudely modeled as a gas of nucleons with a number density of 0.18 fm-3 (where 1 fm = 10-15 m). Because nucleons come in two different types (protons and neutrons), each with spin 1/2, each spatial wavefunction can hold four nucleons. (a) [10 pts] Calculate the Fermi energy εF of this system, in MeV. Also calculate the Fermi temperature TF. Is it reasonable to treat the nucleus as a degenerate Fermi gas at room temperature?...
1) Free electron model: (a) Show that the mean kinetic energy of one electron in the...
1) Free electron model: (a) Show that the mean kinetic energy of one electron in the quantum mechanical free electron model is 3/5 E F at T = 0 K. (b) Calculate the Fermi energy and the mean kinetic energy for potassium in electron volts. Use that K has a relative atomic mass of M = 39.1 u and a density of 856 kg m^−3 . (c) Calculate the corresponding electron velocities. (d) Calculate the density of states at the...
1. PDD is measured with SSD setup? True or False ? 2. TPR is measured with...
1. PDD is measured with SSD setup? True or False ? 2. TPR is measured with SSD setup? True or False ? 3. For each of the following, indicate if increasing them causes the PDD to increase, decrease, of stay the same. -Energy (Increase, Decrease or stays the same?) -Field size (Increase, Decrease or stays the same?) -SSD (Increase, Decrease or stays the same?) -Beam intensity (Increase, Decrease or stays the same?)
1. For a clean sand, if the relative density of the sand is increased, the friction...
1. For a clean sand, if the relative density of the sand is increased, the friction angle, φ, will a. decrease b. increase c. stay the same 2. In general, a well graded gravel will have a friction angle, φ, that is __________ the friction angle of a poorly graded gravel of the same relative density a. less than b. greater than c.equal to 3. Loose sands sometime liquefy during earthquakes, but dense sands never do. Why?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT