Question

Solid State Physics

Consider a one-dimensional (1-D) atomic lattice with an interatomic spacing of 5 angstroms (Å). Each atomic site can be represented by a rectangular-shaped potential well of 1 eV depth and width of 1 angstrom (Å). Estimate the following parameters: The width of the 2nd lowest energy band (in eV).

Answer #1

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Solid State Physics
Consider a one-dimensional (1-D) atomic lattice with an
interatomic spacing of 5 angstroms (Å). Each atomic site can be
represented by a rectangular-shaped potential well of 1 eV depth
and width of 1 angstrom (Å). Estimate the following parameter: The
lowest energy (in eV) at which an electron starts to behave as a
hole.

Atomic interactions can be modeled using a variety of potential
energy approximations. One very common potential form is the
Lennard-Jones 6:12 potential: U(r)=4ε[(σ/r)12 − (σ/r)6]. Where ε
and σ are constants specific to a given material (note: these terms
are NOT equivalent to stress and strain, but this is the standard
notation for the L-J parameters). Here, r is the interatomic
spacing given in units of Angstroms, and U(r) is given in units of
eV/atom. A molecular dynamics simulation was...

II(20pts). Short Problems
a) The lowest energy of a particle in an infinite one-dimensional
potential well is 4.0 eV. If the width of the well is doubled, what
is its lowest energy?
b) Find the distance of closest approach of a 16.0-Mev alpha
particle incident on a gold foil.
c) The transition from the first excited state to the ground
state in potassium results in the emission of a photon with = 310
nm. If the potassium vapor is...

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