ME 141A
Intro to Nanotechnology
Due: 3/2/2009
1
Problem Set 7
Problem 6.14 in book
We can look at the band structure of an element to get an idea of how many electrons per
atom participate in conduction.
We can also determine this number based on the free
electron density, the atomic mass, and the mass density of the material.
(a)
Calculate the free electron density of lithium.
The Fermi energy is 4.72 eV.
(b)
Derive a formula for the number of atoms per unit volume.
(c)
Calculate the number of atoms per unit volume of lithium (535 kg/m
3
, 6.9 g/mol)
using the formula you derived in part (b).
(d)
Determine the number of free electrons per lithium atom.
(e) What is the electron configuration for Li?
Explain whether your answer to (d) makes
sense according to this configuration.
The free electron(s) of Li is in which sublevel?
Problem 6.27 in book
The wave function
ψ
(
x
) of an electron in a potential well of finite depth and width,
L
, is
given by:
ψ
(
x
)
= Ae
Cx
for
x
≤
0
ψ
(
x
)
= F
sin(
kx
)
+ G
cos(
kx
)
for 0
≤
x
≤
L
ψ
(
x
)
= Be
Cx
for
x
≥
L
(a)
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Winter '09
 PENNATHUR
 Atom, Electron, Fundamental physics concepts, Quantum dot, free electron

Click to edit the document details