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Unformatted text preview: MSEZSS Final Exam April 25, 2007 l8 Pages total MSE 235: Materials Physics Prof. Jun Nogami Print your name, Last name ﬁrst: Student #: This exam is out of a total of 100 points. Read through the exam in its entirety before
starting, and feel free to do the easier pans ﬁrst. For all numerical problems. assume three signiﬁcant ﬁgures for all numbers given, and give
all answers to this accuracy. Remember to write down the units for each answer. MSE 235 I 320 Final Exam December 7, 2004 IS Pages total Part 1: short answers 1 oint each 18 oints total
Fill in the bianks with a two or three word description of the four features of this Mll curve for a ferromagnetic material: Short answers: 0 Orientational polarization is analogous to what form of magnetism?
o Electromagnetic radiation of wavelength 300 nm is called 0 In a degenerate ntype semiconductor, the Femti level position is 0 Below the Curie Temperature, a ferromagnetic material is 0 In an X Ray spectrum, the L3 line corresponds to an energy transition where the electron goes from a state with n: to n:
0 The diamond structure has atoms in the unit cell. 0 The dielectric constant of water is dominated by polarization 0 Si exhibits this type of bonding: MSE 235/ 320 Final Exam December 7. 2004 18 Pages total 0 The difference between the Fermi level ofa metal and the vacuum level is called o In Gadolinium, a 4feectron has quantum numbers n: and t = 0 There are two types of magnetic materials that can make permanent magnets. One is ferromagnets. The other is
o In order for a material to be optically transparent (i.e. it does not absorb wavelengths in the visible range) its Band Gap must be greater than eV. 0 The molar heat capacity of chlorine gas (Cl2 molecules) is times the ideal gas constant. 0 For Ge doped with As. the majority charge carrier is MSE 235 I 320 Final Exam True] False DDDDDDDDDDDDa
DDDDDDDDDDDD F December 7. 2001 l8 Pages total 1 point each 10 points total The dielectric constant of Si is dominated by electronic polarization. The electron drift mobility in an n~type semiconductor decreases with increasing dopant density. The electron drift mobility in Au will decrease if it is alloyed with a small
amount of Cu. For an ntype semiconductor, the number of electrons in the conduction
band depends on the temperature in a range near room temperature. Minimizing thickness will decrease the voltage at which a capacitor will breakdown. [t is desirable for a soft magnetic material to have large coercivity.
In a transformer core, you should use a soft magnetic material A diamagnetic material has a small positive permeability. The relative permeability of a magnetic material is always greater than or equal to one. The relative permittivity ofa dielectric material is always greater than or equal to one. The index of refraction is greater than or equal to the square root of the low
frequency dielectric constant. Ge will absorb visible light. MSE 235/320 Final Exam December 7. 2004 18 Pages total la) A sample of ptype GaAs has the Fermi level at 0.2 eV above the valence band maximum at 300K. What is the doping level? [5 ptsl lb) What are the electron and hole concentrations for this sample? [5 ptsl MSE 235/320 Final Exam December 7, 2004 IS Pages total 1c) Assuming that you want to make a 1000 Ohm cylindrical resistor out of this GaAs. with a
diameter of 1 mm, what is the length of this resistor? [5 pts] MSE 235 I320 Final Exam ld) December 7, 2004 I8 Pages total Assuming that a sample of the same GaAs is put into an apparatus to measure it‘s Hall coefﬁcient. Assume dimensions as follows: L=3cm
W: 1 cm
D: l mm Assuming a ﬂux density of B = 2 x I()'3 Tesla and a longitudinal current l = 5 x104 A And given that the magnitude of the transverse r = _1_
Is: [pejw Calculate the magnitude of the transverse voltage measured across the sample. electric ﬁeld is [Sptsl MSE 235 / 320 Final Exam 2) 2a) December 7. 2004 18 Pages total
Consider a cylindrical capacitor with inner electrode radius a and outer electrode radius b,
usin a dielectric of silicone rubber
Gauss surface
Dielectric The capacitance is given by:
_ sue,er C— In I)
\aj where L is the length of the capacitor. and the electric ﬁeld is given by:
V {5(T)=m (I Properties of silicone rubber: E, (60 Hz) Dielectric strength (60 Hz) tan 5
use kwcm if the inner electrode has a diameter of 0.5 mm, and the dielectric is 0.l mm thick. what is
the capacitance per unit length? [3 ptsl MSE 235 I 320 Final Exam December 7, 2004 18 Pages total 2b) What is the minimum thickness of dielectric necessary for the capacitor [0 run at 1000\"? \ I6 PISI MSE 235 I 320 Final Exam December 7. 2004 18 Pages total 2c) What is the power dissipated per unit length if the capacitor is run at llOV at 60 Hz?
[6 plsl 10 MSE 235 I 320 Final Exam December 7. 2004 18 Pages total 3 XX is a ﬁctional ferromagnetic element, with properties given in the table below. 3a) Draw the MH and the 8:“ loops for this material, labeling all signiﬁcant points.
Assume that the MH loop is rectangular in shape. [l0 ptsl 11. MSE 235 I 320 Final Exam December 7. 2001 I8 Pages total 3b) How many Bohr magnetons are contributed to the saturation magnetization by each atom
of XX? [5 pt] 12. MSE 235 I320 Final Exam December 7, 2004 18 Pages total 3c) What is the energy required per unit volume to make one circuit of the 8H l00p? [5 pts] .13. MSE 235 / 320 Final Exam 4) 4a) December 7, 2004 l8 Pages total Consider the electron states in an inﬁnite square well potential. Suppose we want to use
these energy states in a device that will absorb light of a certain frequency. What is the energy of photons corresponding to a wavelength of A = 450 mu? [5 ptsl
Please state the answer in units of CV. 14 T—————ﬁw MSE 235/320 Final Exam December 7, 2004 18 Pages total 4b) Suppose that this photon energy corresponds to the energy spacing between the lowest
two energy states of a one dimensional inﬁnite square well. What is the width of this well? [l0 pts] December 7, 2004 MSE 235 I320 Final Exam Useful Constants and Equations:
Avogadro's number NA = 6.023 x 101‘ “(amymol h = 6.63x 10*" J ~s= 4.l3x 10‘” 0V 5
Icv=t.602x10"" J __ —ll j ' 5 V L " 1'38X '0 atom K ’8'62x [0 64mm  K m = 9. IX [031 kg one electron = .602 x IO'w Coulomb
J molK
£0 = 8.8542 x10"2 F yo = 4r: ><10’7 1%, ..v 8;
c _ 3x10 %
[3 = as = 9.2732x10'24 Am2 Planck‘s constant Electron Volt
Boltzmann’s constant Electron Mass
Electron Charge ideal gas constant R 2 {WA = 8.3145 Permittivity of vacuum m
Permeability of vacuum
speed of light Bohr magneton Equipartition of energy:
ékT per degree of freedom for a monatomic ideal gas: 18 Pages total average kinetic energy per atom (K = gkT
internal energy per mole U = % RT
molar heat capacity C“ = ﬂ = 3 R units [ J
(1T 2 mol K
Electrical properties:
 l— R  L o  r
p _ a .. pA — on; , Electromagnetic Radiation: c = 11V 0) =27rv c = 3 x lOg mfs wavenumber
Photon energy E: Irv = Ira)
Matter Waves
, It It . . .
de Broglle: A = Z = where E IS kinetic energy .16. k:— December 7. 2004 MSE 235 I 320 Final Exam 1D Inﬁnite Square Well of width 3, 0 < x < a w“ = A. sin[%:£.r) n = l, 2. 3. 4, Energies =::;,::1 = 33,2; One electron atom: En = E137: = (—13.6 ev)zz(7:?) FermiDirac Distribution F(E) = Density of States for a 30 Metal I
l 2 ’,
Fermi Energy for a metal: EF = Semiconductors: .3 104x10” 145x10‘6 0.135 0.045  6.6x 103‘ 2.4 x 10” 90
W00
83 nolype
n (5 .EF)] Zmnflﬂq
u —— N‘exp[— H. J 1 r "4 h: J
P'Upe ~11
(Er — H) 2mn' kT ‘ ‘
= N _ ' V = Q I:
P w 6‘4: kT ‘ ‘ h~
[2'
up: ",2 = N‘Nr ex5{7j::! .l']. 4 3 3'2
Z(E)dE=—fi(23—mlJFE_IIE IS Pages total T—f——_—— MSE 235/ 320 Final Exam December 7, 2004 18 Pages total Q Capacitance C = V Parallel Plate Capacitor 1 .
C = £0£,i1 dielccmc
( Permittivity of vacuum so = 3_8542x10"3 F m
Polarimbility
P=Nq£ l
e, =l+E—Na: 0 Power dissipated per unit volume
, = 2 ’ Wan
ll“, (2nj)€E £05, tan6 Al, Magnetism Permeability of vacuum “a = 4;; x10"7 1%) Bohr magneton I} = #8 = 9_2732X10—24 %
In vacuum g 2’10};
In a medium I} anon}? :14}? + [{1)=ﬂ°(1+ In”? .13. ...
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This note was uploaded on 04/28/2008 for the course MSE 235 taught by Professor Nogami during the Fall '04 term at University of Toronto.
 Fall '04
 NOGAMI

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