Question

Show that a 3D gas of N free electrons at T = 0 K has kinetic...

Show that a 3D gas of N free electrons at T = 0 K has kinetic energy

U0 = (3/5) NEF

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
For aluminum (units of eV) at T = 0 K, calculate the Fermi Energy of electrons....
For aluminum (units of eV) at T = 0 K, calculate the Fermi Energy of electrons. Assume that each aluminum atom gives up all of its outer-shell electrons to form the electron gas. b) Find the Fermi velocity of electrons in aluminum. c) How many times larger is the Fermi velocity compared to the velocity of electrons with kinetic energy equal to thermal energy at room temperature?
The average energy per electron for the 3D electron gas at T=0 is 3*(E fermi) /...
The average energy per electron for the 3D electron gas at T=0 is 3*(E fermi) / 5, where E fermi is the Fermi energy. Now, calculate the average energy per unit volume for electron gas in 1, 2, and 3 dimensions at zero temperature. Your answer should be proportional to the Fermi energy, E fermi, and/or the electron concentration n = N / V (possibly to some power).
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...
Consider a free fermion gas of N particles in a volume V at zero temperature. The...
Consider a free fermion gas of N particles in a volume V at zero temperature. The total kinetic energy of the gas is U = (3/5)N epsilon-F with epsilon-F = (hbar^2/2m)((3(π^2)N)/V )^ 2/3 . (a) Using the thermodynamic identity show that the pressure of the gas is given by p = − (∂U/∂V )σ,N . (b) Derive an expression of the degenerated-gas pressure and express your final result in terms of U and V .
Solid State Physics Find the number of free electrons in copper at 300 K with E...
Solid State Physics Find the number of free electrons in copper at 300 K with E = 5 eV and E = 7.1 eV for a sample of volume 1 cm^3. Use the density of states g(E) and the Fermi-Dirac probability function f(E) to estimate the number of free electrons. in a metallic solid You need to multiply a small value of dE (let's say dE = 0.0001 eV) times g(E) and f(E) and the given volume of 1 cm^3....
Let {N(t), t ≥ 0} be a P P(λ). Compute P £ N(t) = k|N(t +...
Let {N(t), t ≥ 0} be a P P(λ). Compute P £ N(t) = k|N(t + s) = k + m ¤ for t ≥ 0, s ≥ 0, k ≥ 0, m ≥ 0
A beam of electrons with kinetic energy 25 eV encounter a potential barrier of height 20...
A beam of electrons with kinetic energy 25 eV encounter a potential barrier of height 20 eV. Some electrons reflect from the barrier, and some are transmitted. Find the wave number k of the transmitted electrons. You can take U = 0 for x < 0, and U = 15 eV for x > 0
Consider the Free electrons in crystals of BCC and FCC structures with the lattice constant. Plot...
Consider the Free electrons in crystals of BCC and FCC structures with the lattice constant. Plot the band structure (Energy E vs k) along the k-path: k=(0,0,0) -> (pi/a,0,0) -> (pi/a, pi/a,0) -> (pi/a,pi/a,pi/a) -> (0,0,0) for the lowest 6 bands (n=1,2,3,4,5,6) of both structures.
n = 3.50 mol of Hydrogen gas is initially at T = 309.0 K temperature and...
n = 3.50 mol of Hydrogen gas is initially at T = 309.0 K temperature and pi = 2.34×105 Pa pressure. The gas is then reversibly and isothermally compressed until its pressure reaches pf = 8.91×105 Pa. 1. What is the volume of the gas at the end of the compression process?   1.01×10-2 m^3 2. How much work did the external force perform? 3. How much heat did the gas emit? 4. How much entropy did the gas emit? 5....
n = 4.42 mol of Hydrogen gas is initially at T = 304.0 K temperature and...
n = 4.42 mol of Hydrogen gas is initially at T = 304.0 K temperature and pi = 3.23×105 Pa pressure. The gas is then reversibly and isothermally compressed until its pressure reaches pf = 8.93×105 Pa. What is the volume of the gas at the end of the compression process? Tries 0/12 How much work did the external force perform? Tries 0/12 How much heat did the gas emit? Tries 0/12 How much entropy did the gas emit? Tries...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT