Due Date: July 17th 2013
Name: ____________________
Student #: _________________
Materials 1M03 – Assignment 3
Please show your work for all the calculation questions and keep track of your units.
1. Consider a metal that has an electrical conductivity of 33 x 107 (Ω-m)-1.
It is drawn into a wire 3 mm in diameter and 2 m long.
a) (1 mark) Compute the magnitude of the electric field (in V/m) across the ends
of the wire if the potential drop across them is 6 V.
! = ! = !
!
6!
2!
! = 3 !/!
b) (1 mark) Calculate the current density (in A/m^2) if the potential drop across
the ends of the wire is 6 V. Use scientific notation, significant figures in answer: 2
! = !"
!
! = 33 ×10 (Ω ∙ m)!! × 3 !/!
!
! = 9.9 ×10! !
!
2. (3 marks)
The intrinsic electrical conductivities of a semiconductor at 170 and 260 °C are
0.15 and 2.25 (Ω-m)-1, respectively.
The intrinsic conductivity is a function of temperature and the band gap energy as
follows:
ln ! ≅
! − !!
2!"
where k = 8.62 x 10-5 eV/atom-K.
Determine the approximate band gap energy (in eV) for this material. Use 3
significant figures in your answer.
Answer:
Use 2 equations to solve for 2 unknowns (just solve for Eg)
!
Equation 1 è ln 0.15 + !×(!.!"×!"!!!)×(!"#!!"#) ≅ !
!
Equation 2 è ln 2.25 + !×(!.!"×!"!!!)×(!"#!!"#) ≅ !
!
!
ln 0.15 + !×(!.!"×!"!!!)×(!"#!!"#) = ln 2.25 + !×(!.!"×!"!!!)×(!"#!!"#)
Due Date: July 17th 2013
Name: ____________________
Student #: _________________
ln
2.25
1
1
= !! (
−
)
0.15
0.0764 0.0919
!! = 1.23!"
3. (2 mark)
4.1 x 1023 atoms/m3 of bismuth is added to silicon. Given that the electron and
hole mobilities are 0.3 and 0.07 m2/V-s, respectively, calculate the electrical
conductivity at room temperature of the resulting semiconductor. Express your
answer in (ohm-m)^-1.
Answer:
! = ! ! !!
!!
!"#$%
! = 0.3 × 1.9×10!!" ! × (4.1×10!" )
!∙!
!!
! = 23,370 (Ω ∙ !)!!
4. (2 marks)
___________________ charge carriers will be introduced into a semiconductor
by the presence of an acceptor impurity.
___________________ charge carriers will be introduced into a semiconductor
by the presence of a donor impurity.
Answer: Hole, electron
5. a) (2 marks) Estimate the energy (in J) required to raise the temperature of 2 kg of
water from room temperature (25°C) to its boiling point (100°C).
Use scientific notation, significant figures in answer: 3
Answer:
! = !! ∙ ! ∙ !"
Q = 4187 J/kg K *2 kg * (373-298) K
Q = 6.28 * 105 J
b) (1 mark) If salt was added to the water would the energy required to raise the
temperature increase or decrease?
Answer: The cp would be lowered, because the salt would disrupt the hydrogen
bonding in water essentially lowering the energy required.
6. a) (2 marks) The evil doctor is back with a new plan to disrupt the class! This
time the plan involves using a 1m long copper rod to push a red button that will
release A LOT of balloons to come plummeting down on their classroom and all
the students inside. If the classroom is initially at 27°C and the copper rod would
Due Date: July 17th 2013
Name: ____________________
Student #: _________________
not be able to reach the red button if it were 0.05 cm shorter, how far would the
students have to turn down the temperature of the room (in Celsius), to have their
class continue uninterrupted by balloons.
The linear coefficient of thermal expansion for the copper rod is 17×10!! ℃!! .
Answer:
∆!
!!
= !! ∆!
−0.05
= 17×10!! ℃!! × (!! − !! )
100
−5×10!!
= (!! − 27)
17×10!! ℃!!
!! = −2.414 ℃
∆! = 29.414 ℃
!ℎ! !"#$%&"! !"#$% ℎ!"# !" !"#$ !ℎ! !"#$"%&!'%" !"#$ 29.414℃
b) (2 mark) Is the student solution a viable option and would it make a difference
if the rod was made of gold instead of copper?
Answer: The student solution is possible but highly unlikely to pull off. If the rod
was made of gold instead of copper the class would have to make the room even
colder due to its smaller linear coefficient of thermal expansion.
7. (2 marks) Circle all the answers that are correct
The greater the atomic bonding energy,...
a) … the larger the change in interatomic spacing with increasing temperature.
b) …the smaller the change in interatomic spacing with increasing temperature
c) … the smaller the value of αl
d) … the larger the value of αl
Answer: b, c
8. (1 Mark) True or False?
The thermal conductivity of a foamed polymer such as styrofoam increases as the
level of porosity in the foam increases.
Answer: False
Due Date: July 17th 2013
Name: ____________________
Student #: _________________
9. (1 Mark) True or False?
For most solid materials, the Debye temperature is below room temperature.
Answer: True
Mark:
/ 20