Question

Problem 7-5. Find the Fermi energy and Fermi velocity of the induction electrons in a sodium metal.

Answer #1

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?

a)Determine the Fermi factor at T = -25.0 ∘C for electrons with
energy ΔE = 0.16 eV above the Fermi energy. The material under
consideration is gold with a Fermi energy of Ef = 5.53
eV.
b)Determine the probability that the space below 0.16 eV below
the Fermi energy is occupied at -25.0 ∘C
c)Determine the probability that the state below 0.16 eV below
the Fermi energy is unoccupied.

Compute the Fermi energy and the average energy per particle for
electrons in copper (you may look up the electron density for
copper)

3. Sketch the energy band diagrams along with the positions of
the Fermi energy or the chemical potential, shade the regions
occupied by electrons to show the difference between
metal/conductor, insulator, and semiconductor
a. at 0 Kelvin
b. at a room temperature.

(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...

What is the maximum kinetic energy in eV of electrons ejected
from sodium metal by 2.3 x 102-nm EM radiation, given
that the binding energy is 2.28 eV? Your answer should be a number
with two decimal places, do not include unit.

It requires a photon with a minimum energy of 4.41 ✕ 10-19 J to
emit electrons from sodium metal. c) If sodium is irradiated with
light of 389 nm, what is the maximum possible kinetic energy of the
emitted electrons?(answer in J) (d) What is the maximum number of
electrons that can be freed by a burst of light (λ = 389 nm) whose
total energy is 1.20 µJ? (answer in electrons)

Problem 5
: Electrons on the surface of a metal can be ejected by shining
light on them. However,
a very bright red light source will not eject electrons, while
even a very dim violet light source will
eject electrons from the metal immediately. Why is this?

Electrons are ejected from sodium metal by any light that has a
wavelength shorter than 544 nm. What is the kinetic energy of an
electron (in J) that is ejected from sodium by light with a
wavelength of 385 nm?

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....

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