Greetings!
It is easy to understand that for a free electron, we can easily define the energy state density, and by doing the integration of the State density* Fermi-Dirac distribution we will be able to figure out the chemical potential at zero kelvin, which is the Fermi-Energy. Hence, we can...
Homework Statement
Calculate the velocity of the fastest neutron in a 96Mo nucleus and, based on this, explain whether or not we are safe to consider such nucleons in a non-relativistic way. Hint: first
calculate the Fermi energy.
Homework Equations
Fermi energy from Fermi gas model...
Homework Statement
Homework Equations
The Attempt at a Solution
The probability of getting a state with energy ## E_v## is ## \frac { N_v } { N_v +N_c } = \frac1{ e^{-(E_v – E_f)/k_BT} +1} ## ………….(1)
Since, ## E_v < E_f, e^{-(E_v – E_f)/k_BT}>>1 ## as ## E_f – E_v>> k_BT ##……….(2)...
\bf{Setup}
Hi! I am trying to derive the wavefunctions of the zero energy solutions of the Schrodinger equation in a 1D p-wave superconductor (Kitaev model). I am starting with the Hamiltonian
$$
\begin{equation}
H =
\left[\begin{array}{cc}
\epsilon_k & \Delta^{\ast}_k\\
\Delta_k & -\epsilon_k...
Homework Statement
Let's consider conduction electrons (at T=0K) that are put in a magnetic field. The electrons can have spin that is parallel or antiparallel to the magnetic field. Below is the density of occupied states for such a system (horizontally) as a function of energy (vertically)...
Homework Statement
The conduction band of a hypothetical crystal of one-dimensional Cesium reticular with step a=300 pm (1 atom per cell) is characterized by the ε dispersion law
##\epsilon (k) = V_0 + \frac{\hbar^2}{m_e}(\frac{1}{2}k^2 - \frac{a}{3\pi}|k|^3##
where ##V_0 = -4 eV##, is set so...
A free electron gas would have zero magnetoresistance; it takes two carrier types to get ordinary magnetoresistance, which is always positive in sign.
Beal-Monod and Weiner explain the negative magnetoresistance found in very dilute magnetic alloys, in terms of the spin-flip scattering of...
I'm practicing for the Physics GRE, and came across a question that has me stumped.
"In elementary nuclear physics, we learn about the Fermi gas model of the nucleus. The Fermi energy for normal nuclear density (ρ0) is 38.4 MeV. Suppose that the nucleus is compressed, for example in a heavy ion...
Hi people,
I dont understand why when we apply the electric field to the metal Ef remains the same. Ef as translation energy of electrons remains the same but we accelerate the electrons with applied electric field so the translation energy increases too? In other hand according the formula...
I have some qualitative questions about the relation between band structure, density of states, and Fermi energy (or Fermi level).
1) Say you have a given electronic band structure (energy as a function of k) obtained by any method. How do you relate this to the Fermi energy (or Fermi level) ...
Homework Statement
[/B]
Five free electrons exist in a three-dimensional infinite potential well with all three widths equal to a 12 angstroms. Determine the Fermi energy level at T 0 K.
Homework Equations
E = [(h_bar*pi)2/(2*m*a2)]*(nx2 + ny2 + nz2)
The Attempt at a Solution
Tried using EF...
Homework Statement
Consider a monovalent 2D crystal with a rectangular lattice constants ##a## and ##b##. Find expressions for the fermi energy and fermi wavevector in 2D. Show that the fermi surface extends beyond first zone if ## 2a > b\pi##. If the crystal is now divalent, estimate the...
I get that in a single particle of a metal, Fermi energy is defined at T = 0 as the maximum energy that electrons can reach.
I get that, but my book defines this concept called Fermi Temperature.
Is Fermi Temperature the temperature where electrons can reach the next empty energy band in...
Hi there,
I am new to electron theory, and have a question regarding fermi energy. The book I am reading plots the Fermi energy distribuiton function vs Energy for T=0 ( upper right graph in pcture) and for T not equal to zero. The book says that, when T does not equal zero, the decrease in the...
Homework Statement
Calculate the Fermi energy, EF at 0K for potassium (atomic weight = 39, density = 860 kgm3).
Homework Equations
KF3 = 3π2n
Fermi Momentum ρ = h(bar)KF
The Attempt at a Solution :[/B]
For the first part:
Using: E = ρ2/ 2m
Can substitute Fermi momentum into that to get:
EF...
A structure with free electron density around 10^26 m^-3 is considered as a highly doped semiconductor or a metal?
Or in other words, what is the lowest possible free electron concentration for a metal and what is the highest possible free electron concentration for a doped semiconductor?