ECE344, Midterm Exam 1: Solutions
October 19, 2009
1.
Problem:
The workfunction of a material is defined as the energy required to
remove an electron from the material and is usually indicated by the Greek letter
χ
(pron: ‘khi’).
The workfunction of gold is
χ
Au
= 4
.
9 eV, the workfunction of cesium is
χ
Cs
= 1
.
9
eV.
a.
Calculate the maximum wavelength (in nm) of light required to remove an
electron from Au via the photoelectric e
ff
ect.
b.
Do the same for Cs.
Solution:
Since
λ
=
c
ν
=
2
π
¯
hc
h
ν
=
2
π
¯
h
E
,
(1)
or, expressing the energy in eV:
λ
=
2
π
¯
h
eE
,
(2)
using
E
=
χ
Au
we have
λ
= 253 nm and using
E
=
χ
Cs
we get
λ
= 653 nm.
2.
Problem:
Electrons in a ‘swarm’ at thermal equilibrium have each an average
kinetic energy of (3
/
2)
k
B
T
.
a.
Calculate the value of (3
/
2)
k
B
T
in eV.
b.
Calculate the velocity (in cm/s) of an electron having a kinetic energy equal
to the average energy (3
/
2)
k
B
T
. This is the socalled ‘thermal velocity’.
c.
Calculate its average de Broglie wavevelength in cm. This is called the ‘thermal
wavelength’.
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 Spring '10
 Polizinni
 Kinetic Energy, Mass, Fundamental physics concepts, effective mass

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