AppliedPhysics
I-B.Tech
ELECTRONTHEORYOFSOLIDS
FREEELECTRONTHEORY
In solids, electrons in outer most orbits of atoms determine its electrical properties.
Electron theory is applicable to all solids, both metals and non metals. In addition, it
explains the electrical, thermal and magnetic properties of solids. The structure and
properties of solids are explained employing their electronic structure by the electron
theory ofsolids.
Ithasbeendevelopedinthreemain stages:
Classicalfreeelectrontheory
QuantumFree ElectronTheory.
ZoneTheory.
Classical free electron theory: The first theory was developed by Drude & Lorentz in 1900.
According to this theory, metal contains free electrons which are responsible for the electrical
conductivity and metals obey the laws of classical mechanics.
Quantum Free Electron Theory: In 1928 Sommerfield developed the quantum free electron
theory. According to Sommerfield, the free electrons movewitha constant potential. Thistheory
obeys quantum laws.
Zone Theory: Bloch introducedthe bandtheoryin1928. According to thistheory, free electrons
move in a periodic potential provided by the lattice. This theory is also called “Band Theory of
Solids”. It gives complete informational study ofelectrons.
Classicalfreeelectrontheory:
Even though the classical free electron theory is the first theory developed to explain the electrical
conduction of metals, it has many practical applications. The advantages and disadvantages of the
classical free electron theory are as follows:
Advantages:
1.
2.
3.
4.
It explainsthe electricalconductivityand thermalconductivityofmetals.
Itverifiesohm’slaw.
It isused toexplaintheopticalpropertiesofmetals.
Metal composed of atoms in which electrons revolve around the nucleus are many
statesavailable foroccupation. Ifthe densityofstates iszero, nostatescanbe occupied at
that energy level.
5. The valence electrons are freely moving about the whole volume ofthe metals likethe
molecules of perfect gas in a container
H&SDept.
Page26
AppliedPhysics
I-B.Tech
6. The free electrons moves in random directions and collide with either positive ions or
other free electrons. Collision is independent of charges and is elastic in nature
7. Themovementsoffreeelectronsobeythelawsofclassicalkinetictheoryofgases
8. Potentialfieldremainsconstantthroughoutthelattice.
9. In metals, there are large numbers of free electrons moving freely within the metal i.e.
the free electrons or valence electrons are free to move in the metal like gaseous
molecules, because nuclei occupyonly 15% metal space and the remaining 85% space
is available for the electrons tomove.
Drawbacks:
1. Itfailstoexplaintheelectricspecificheatandthespecificheatcapacityofmetals.
2. Itfailstoexplainsuperconductingpropertiesofmetals.
3. Itfailstoexplainnewphenomena likephotoelectriceffect,Comptoneffect,black–
Bodyradiation,etc.
4.
5.
6.
7.
8.
ItfailstoexplainElectricalconductivity(perfectly)ofsemiconductorsorinsulators.
Theclassicalfreeelectronmodelpredictstheincorrecttemperaturedependenceof
Itfailstogiveacorrectmathematicalexpressionforthermalconductivity.
Ferromagnetismcouldn’tbeexplainedbythistheory.
Susceptibilityhasgreatertheoreticalvaluethantheexperimentalvalue.
Quantumfreeelectrontheory: Advantages:
1. Alltheelectronsarenotpresentinthegroundstateat0K,butthedistributionobeys
Pauli’sexclusionprinciple.At0K,thehighest energylevelfillediscalledFermi- level.
2. Thepotentialremainsconstantthroughoutthelattice.
3. Collision of electrons with positive ion cores or other free electrons is independent of
charges and is elastic in nature. Energy levels are discrete.
4. Itwassuccessfultoexplainnotonlyconductivity,butalsothermionicemission
paramagnetism, specific heat.
Drawbacks:
1.Itfailstoexplainclassificationofsolidsasconductors,semiconductorsandinsulators.
STATISTICALDISTRIBUTIONFUNCTIONS:
ThemainassumptionofMaxwell–Boltzmannstatisticsare
1. Theparticlesareidentical&distinguishable.
H&SDept.
Page27
www.android.universityupdates.in | www.universityupdates.in | https://telegram.me/jntuh
AppliedPhysics
I-B.Tech
2. The volume ofeachphase space cellchosen is extremelysmall and hence chosenvolume
has very large no of cells.
3. Sincecellsareextremelysmall,eachcellcanhaveeitheroneparticleornoparticle thoughthere is
no limit onthe number of particles which can occupya phase space cell.
4. SystemisisolatedwhichmeansbothtotalEnergyandtotalnoofparticlesremainconstant.
5. Stateofeachparticleisspecifiedeitherbyitscellnumberinphase.Spaceor instantaneous
position and momentum coordinate.
6. Energylevelsarecontinuous.
7. MaxwelldistributionfunctionFMB=A/exp(-Ei/kt)
Where Ei – ithEnergy level.
k-Boltzmannconstant
T-Absolutetemp
8. TheparticleswhichobeyM-Bstatisticssystemconsistingofmolecules.
Bose- Einsteinstatistics:
ThemainassumptionofB-Estatistics:
1) TheparticleswhichobeyB-E statisticsarecalled bosons.
2) TheBosonsofsystemareidentical&indistinguishable
3) Bosonsobeyuncertaintyprinciple.
4) Anynumberofbosonscanoccupyasinglecellinphase space.
5) BosonsdonotobeyPauli’sExclusionprinciple
6) Thenumbersofphasespacecellsiscomparablewiththenumbersofbosons.
7) wavefunctionsrepresentingtheBosonsaresymmetricieψ(2,1)=ψ(1,2)
8) Thewavefunctionsofbosondooverlapslightlyieweakinteractionexists.
9) Energystatesarediscrete
i.
E
f
BE

H&SDept.
1
E
EF
i
exp
1
 kt 
Page28
www.android.previousquestionpapers.com | www.previousquestionpapers.com | https://telegram.me/jntuh
www.android.universityupdates.in | www.universityupdates.in | https://telegram.me/jntuh
AppliedPhysics
I-B.Tech
Ei–ithenergylevel
EF- Fermi Energy
T -Absolutetemp andk-Boltzmannconst.
Theparticleswhichobeybosonarephotons.He4,πandK-mesons,phononina solids,
Bosonscan havespinofnh/2πwherenisinteger.
Fermi–DiracStatistics:
1) TheparticleswhichobeyF–Dstatisticsarecalledfermions.
2) Fermionsare identicalandindistinguishable
3) Therecannotbemorethanoneparticleinasinglecellinphasespacei.etheyobey
Pauli’sexclusionprinciple.
4) Fermionshaveintegralspin
5) Wavefunctionrepresentingfermionsareantisymmetricieφ(1,2)=-φ(2,1)
6) Weak interactionexistsbetweenparticles
7) Uncertainityprincipleisapplicable.
8) Energystatesarediscrete.
9) The Fermi Dirac distribution function f(D), is the probability that a fermions occupies a
state of energy E and is given by
f
FD
1
E
exp
 1
 kt
αisconstantandisdependentontemperatureα=-EF/kT
FermilevelandFermienergy
The distribution of energy states in a
semiconductor is explained by Fermi-Dirac
statistics since it deals withthe particles having
half integral spin like electrons. Consider that
the assembly of electrons as electron gas which
behaves like a system of Fermi particles or
fermions. The Fermions obeying Fermi–Dirac
statistics i.e., Pauli’s exclusion principle.
H&SDept.
Page29
www.android.previousquestionpapers.com | www.previousquestionpapers.com | https://telegram.me/jntuh
www.android.universityupdates.in | www.universityupdates.in | https://telegram.me/jntuh
AppliedPhysics
I-B.Tech
Fermienergy:Itistheenergyofstateatwhichthe
Probability of electron occupation is ½ at any temperature above 0K. It separates filled
energy states and unfilled energy states. The highest energy level that can be occupied
by an electron at 0 K is called Fermi energy level
Fermi level: It is a levelat whichthe electronprobabilityis ½ at anytemp above 0K(or)
always it is 1 or 0 at 0K.
Therefore,theprobabilityfunctionF(E)ofanelectronoccupyinganenergylevelEisgivenby,
f E  
1
EEF
1exp
 kT 


- ------- (1)
WhereEFknownasFermienergyand it isconstantforasystem, K is
the Boltzmann constant and T is the absolute temperature.
Case I : Probability of occupation at T= 0K,and E <
EF Therefore F(E) =1,as per above ,clearly indicates
thatatT=0K,theenergylevelbelowtheFermienergy level
EF is fully occupied by electrons leaving the upper
level vacant.
Therefore,thereis100%probabilitythat theelectronsto
occupy energy level below Fermi level.
Case II: Probabilityof occupation at T= 0K, and E > EF.i.e., all levels below EF are
completelyfilledandallevelsaboveEFarecompletelyempty. AsthetemperaturerisesF(E).
CaseIII:Probabilityof occupationatT=0K,andE =EF
Theaboveconditionstatesthat,T=0K,thereisa50%probabilityfortheelectronstooccupy Fermi energy.
TheprobabilityfunctionF(E)liesbetween0an1 Hence
there are three probabilities namely
H&SDept.
Page30
www.android.previousquestionpapers.com | www.previousquestionpapers.com | https://telegram.me/jntuh
www.android.universityupdates.in | www.universityupdates.in | https://telegram.me/jntuh
AppliedPhysics
I-B.Tech
1. F(E) =1100%probabilitytooccupytheenergylevel byelectrons.
2. F(E)=0Noprobabilitytooccupytheenergylevelsbyelectronsandhence,itisempty.
3. F(E)=0.550%probabilityoffindingtheelectronintheenergylevel.
PERIODICPOTENTIALANDBLOCHTHEOREM:
According to free electron model, a conduction electron in metal experiences constant
potential. But in real crystal, there exists a periodic arrangement of positively chargedions
through which the electrons move. As a consequence, the potential experienced by
electrons is not constant but it varies with the periodicity ofthe lattice. In zone theory, as
per Bloch, potential energy of electrons considered as varying potential with respect to
lattice‘a’.
Fig: Variationofpotentialenergyinaperiodiclattice
KRONIG-PENNEYMODEL:
According to this theory, the electrons move in a periodic potentialproduced by the positive
ion cores. The potential of electron varies periodically with periodicity of ion core and potential
energy of the electrons is zero near nucleus of the positive ion core. It is maximum when it is
lying between the adjacent nuclei which are separated by inter-atomic spacing. The variation of
potential of electrons while it is moving through ion core is shown fig.
H&SDept.
Page31
www.android.previousquestionpapers.com | www.previousquestionpapers.com | https://telegram.me/jntuh
www.android.universityupdates.in | www.universityupdates.in | https://telegram.me/jntuh
AppliedPhysics
I-B.Tech
V (x)={0,fortheregion0<x<a
{V0forthe region-b< x<a------------------------------- (1)
ApplyingthetimeindependentSchrödinger’swaveequationforabovetwo regions
d2Ψ/dx2+ 2mEΨ/ħ2= 0
and
forregion0 < x<a ------------------ (2)
d2Ψ/dx2+ 2m(E –V)Ψ/ħ2=0
Substituting
forregion-b< x<a----------------- (3)
α2=2mE/ħ2--------------------------------- (4)
β2=2m(E–V)/ħ2------------------------------- (5)
d2Ψ/dx2+ α2Ψ= 0
forregion0< x<a------------------- (6)
d2Ψ/dx2+ β2Ψ= 0
forregion
-b<x<a ---------------- (7)
Thesolutionfortheeqn.s(6) and (7)canbewrittenas
Ψ(x)=Uk(x)eikx --------------------------------------- (8)
Theabovesolutionconsistsofaplanewaveeikxmodulated bytheperiodicfunction.
Uk(x),wherethisUk(x)hastheperiodicityofthe ionsuchthat
Uk(x) = Uk(x+a) -------------------- (9)
andwherekispropagatingvectoralongx-directionandisgivenbyk=2Π/λ.Thiskis
alsoknownaswavevector.
Differentiating equation (8) twice with respect to x, and substituting in equation (6) and (7),
two independent secondorderlineardifferentialequationscanbeobtained fortheregions 0< x <
aand-b < x < 0 .
Applying the boundaryconditions to the solution ofabove equations, for linear equations in
terms of A,B,C and Dit can be obtained (where A,B,C,D are constants ) the solution for these
equations can be determined only if the determinant of the coefficients of A , B , C ,and D
vanishes, on solving the determinant.
(β2-α2/2 α β)sinhβbsin αa + coshβbcosαa = cosk(a +b) --------------------------- (10)
Theaboveequationis complicatedand Kronig andPenneycouldconcludewiththe equation.
Hence they tried to modify this equation as follows
LetVoistendingtoinfiniteandbisapproachingtozero.SuchthatVobremainsfinite.
Thereforesin hβb→ βbandcoshβb→1
β2-α2= (2m/ħ2)(Vo–E)–(2mE/ħ2)
=(2m/ħ2)(Vo–E-E)=(2m/ħ2)(Vo–2E)
H&SDept.
Page32
www.android.previousquestionpapers.com | www.previousquestionpapers.com | https://telegram.me/jntuh
www.android.universityupdates.in | www.universityupdates.in | https://telegram.me/jntuh
AppliedPhysics
I-B.Tech
=2 mVo/ħ2(sinceVo>> E)
Substitutingallthesevaluesinequation(10)itveritiesas
(2mVo/2ħ2αβ)βb.sinα a+cosα a==coska
(mVoba/ħ2)(sinα a /α a)+cosα a==coska
( P/αa)sinαa+cosαa==coska ---------------------------------------- (11)
Where
P=[mVoba /ħ2] -------------------------- (12)
andisameasureofpotentialbarrier strength.
Thelefthand side of the equation (11)isplotted as a function of α for the value of P= 3 Π /
2whichis shownin fig, theright hand sideonetakes values between -1to +1as indicatedby
thehorizontallines in fig. Thereforetheequation (11) issatisfied only forthosevaluesofka for
which left hand side between± 1.
Fromfig,thefollowingconclusionsaredrawn.
1) The energy spectrum of the electron consists of a number of allowed and forbidden
energy bands.
2) The width ofthe allowed energy band increases with increase of energy values ie
increasing the values ofαa. Thisis because the first termofequation(11) decreaseswith
increase of αa.
(P/αa)sinαa+cosαa==3Π/2
H&SDept.
Page33
www.android.previousquestionpapers.com | www.previousquestionpapers.com | https://telegram.me/jntuh
www.android.universityupdates.in | www.universityupdates.in | https://telegram.me/jntuh
AppliedPhysics
I-B.Tech
Fig.p-->infinityandp-->0
3) With increasing P, ie with increasing potential barrier, the width of an allowed band
decreases. AsP→∞,the allowed energy becomes infinitely narrowand the energy
spectrum is a line spectrumas shown in fig.
IfP→∞,thentheequation(11)hassolutionie
Sinαa=0
αa = ± n Πα
=±nΠ/a
α2=n2Π2/a2
α2 =2 m E /
But
ħ2Therefore 2mE/ħ2=n2 Π2/a2
E=[ħ2Π2/2ma2]n2
E= nh2/8ma2
(sinceħ=h/2Π)
This expression shows that the energy spectrum of the electron containsdiscrete energy levels
separated by forbidden regions.
4)
When
P→0then
Cosαa=coska
α=k,
but
α2= k2
α2=2mE/ħ2
k2=(h2/ 2 m) ( 1/ λ2)=(h2/ 2 m) (P2/ h2) E =P2 /
2m
E=1/2mv2 ------------------------- (14)
H&SDept.
Page34
www.android.previousquestionpapers.com | www.previousquestionpapers.com | https://telegram.me/jntuh
www.android.universityupdates.in | www.universityupdates.in | https://telegram.me/jntuh
AppliedPhysics
I-B.Tech
The equation (11) shows allthe electrons are completely free to move in the crystalwithout any
constraints. Hence , no energy level exists ie all the energies are allowed to the electronsand
shown in fig(5). Thiscase supports the classical free electrons theory.
[(P/αa)sinαa+cosαa],P→0
BRILLOUINZONEORE-KDIAGRAM:
The Brillouin zone are the boundaries that are marked by the values of wave vector k,in which electrons
canhaveallowed energy values. Theserepresent theallowed values of koftheelectrons in1D, 2D,&3D.
It is theenergyspectrumofanelectron moving inpresenceofa periodicpotentialfieldandis dividedinto
allowed energy regions (allowed zones) or forbidden energy gaps (forbidden zones).
Allowed energy values lie in theregion k=-π/a to =+π/a.This zone is called thefirst Brillouin zone. After a
break in the energy values, called forbidden energy band, we have another allowed zone spread fromk=π/a to -2π/a and +π/a to +2π/a. This zone is called the second Brillouin zone. Similarly, higher Brillouin
zones are formed.
CONCEPTOFEFFECTIVEMASSOFELECTRON:
When an electron in aperiodic potential of lattice is accelerated by anknown electricfield ormagnetic
field,then themassoftheelectroniscalledeffectivemassandisrepresentedbym*
Toexplain,letusconsideranelectronofcharge‘e’andmass‘m’movinginsideacrystallattice
ofelectricfieldE.
accelerationa = eE / mis not a constant in the periodic lattice of the crystal. It can be considered
that its variation is caused by the variation of electron’s mass when it moves in the crystal lattice.
ThereforeAccelerationa=eE/m*
ElectricalforceontheelectronF=m*a -------------------- (1)
H&SDept.
Page35
www.android.previousquestionpapers.com | www.previousquestionpapers.com | https://telegram.me/jntuh
www.android.universityupdates.in | www.universityupdates.in | https://telegram.me/jntuh
AppliedPhysics
I-B.Tech
Consideringthefreeelectronasawavepacket,thegroupvelocityvgcorrespondingtothe
particle’svelocitycanbewrittenas
vg= dw/dk=2Πdv/dk=(2Π/h)dE/dk -------------------------------- (2)
where the energyE= hυ
andħ= h/2Π.
Accelerationa =dvg/dt=(1/ħ)d2E/dkdt=(1/ħ)(d2E/dk2)dk/dt
Since
ħk=p
and
dp/dt=F,
dk / dt = F / ħ
Therefore
a=(1/ħ2 )(d2E/dk2) F
OrF= (ħ2/(d2E/dk2 ))a --------------------------------- (3)
Comparingeqns.(1)and(3)weget
m*=ħ2/(d2E/ dk2) ------------------------ (4)
Thiseqnindicatesthattheeffectivemassisdeterminedbyd2E/dk2
Variation of effective mass m* with k: The graphshowsvariationof m* withk. Near k=0,effective
massapproachesm.As the kvalueincreases 𝒎m* increases, reaching its maximum value known as
infinite effective mass. Above the point of inflection, m* is negative andasktendsto
,itdecreasestoasmallnegativevaluecallednegativeeffectivemass
in the lower region. The positively charged particle which can be located in the lower region
called negative
ORIGINOFENERGYBANDFORMATIONINSOLIDS:
The band theory of solids explains the formation of energy bands and determines whether a solid is a
conductor, semiconductor or insulator.
The existence of continuous bands of allowed energies can be understood starting with theatomic
scale. The electrons of a single isolated atom occupy atomic orbitals, which form a discrete set of
energy levels.
When two identical atoms are brought closer, the outermost orbits of these atoms overlap and interact.
When the wave functions of the electrons of different atoms begin to overlap considerably, the energy
levels corresponding to those wave functions split.
H&SDept.
Page36
www.android.previousquestionpapers.com | www.previousquestionpapers.com | https://telegram.me/jntuh
www.android.universityupdates.in | www.universityupdates.in | https://telegram.me/jntuh
AppliedPhysics
I-B.Tech
If moreatoms arebrought together morelevels areformed and for a solid of N atoms, each of the energy
levels of an atom splits into N energy levels. These energy levels are so close that they form an almost
continuous band. The width of the band depends upon the degree of overlap of electrons of adjacentatoms
and is largest for the outermost atomic electrons.
As a result of the finite width of the energy bands, gaps are essentially leftover between the bands called
forbidden energy gap.
The electrons first occupy the lower energy levels (and are of no importance) then the electrons
inthe higher energylevels are ofimportantto explainelectricalproperties ofsolids and these are
called valence band and conduction band.
Valenceband: Abandoccupiedbyvalenceelectronsandisresponsiblefor electrical, thermalandoptical properties of
solids and it is filled at 0K.
Conductionband: Abandcorrespondingto outer most orbit is calledconductionbandandis the highest
energy band and it is completely empty at 0K.
The forbidden energy gap between valence band conduction band is known as the energy band gap. By
this solids are classified in to conductors, semiconductors and insulators.
CLASSIFICATIONOFSOLIDSINTOCONDUCTORS,SEMICONDUCTORS&INSULAT
ORS:
Basedontheenergybanddiagrammaterialsorsolidsareclassifiedasfollows:
H&SDept.
Page37
www.android.previousquestionpapers.com | www.previousquestionpapers.com | https://telegram.me/jntuh
www.android.universityupdates.in | www.universityupdates.in | https://telegram.me/jntuh
AppliedPhysics
I-B.Tech
Conductors: In this kind of materials, there is no forbidden gap between the valence band and
conduction band. It is observed that the valence band overlaps with the conduction band inmetals
as shown in figure. There are sufficient numbers of free electrons, available for electrical
conduction and due to the overlapping of the two bands there is an easy transition of electrons
from one band to another band takes place, and there no chance for the presence of holes.
Resistivity of conductors is very small and it is very few milli ohm meters.(Ω m ).
Examples: Allmetals(Na,Mg,Al,Cu,NiCu,Ag,Li,Aretc)
Semiconductors:In semiconductors, there is a band gap exists between the valence band and
conduction band and it isveryless and it isthe order of-1to 2 eV are knownas semiconductors. It
will conduct electricity partially at normal conditions. The electrical resistivity values are 0.5to
103 ohmmeter. Duetothermal vibrations withinthe solid, someelectrons gainenoughenergy to
overcome the band gap (or barrier) and behave as conduction electrons. Conductivity exists here
due to electronics and holes.
Examples:Silicon,Germanium,GaAs.
Insulators: In insulators, the width of forbidden energy gap between the valence band and
conduction band is very large. Due to large energy gap, electrons cannot jump from V.B to
C.B.Energy gap is of the order of ~10 eV and higher than semiconductors. Resistivity values of
insulatorsare 107to 1012ohm-m. Electronsaretightlybound tothe nucleus, no valence electrons are
available.
Examples:Wood,rubber,glass.
Symmetryinsolids
A Symmetry operation is an operation that can be performed either physically or imaginatively
that results in no change in the appearance of an object.
Center of symmetry: If an imaginary straight line can be passed through a crystal from any
point on the surface of crystal such that the point of entry is similar to the point of exit, then the
crystal has a center of symmetry.
H&SDept.
Page38
www.android.previousquestionpapers.com | www.previousquestionpapers.com | https://telegram.me/jntuh
www.android.universityupdates.in | www.universityupdates.in | https://telegram.me/jntuh
AppliedPhysics
I-B.Tech
Plane of symmetry: When an imaginary plane is passed through a crystal such that the portion
ofthe crystalon one side ofthe plane is a reflection, or mirror image, ofthe portion on the other
side of the plane, the plane is a plane of symmetry (often called a mirror plane).
Axis of symmetry: When an imaginaryline can be passed through a crystalsuch that the crystal
canberotated 360oaboutthelinetofillthesamespacetwo,three,four,orsixtimes,ithas an axis of
symmetry.
H&SDept.
Page39
www.android.previousquestionpapers.com | www.previousquestionpapers.com | https://telegram.me/jntuh
www.android.universityupdates.in | www.universityupdates.in | https://telegram.me/jntuh
AppliedPhysics
I-B.Tech
Shortanswerquestions
1.
2.
3.
4.
5.
6.
7.
8.
Whatisablockbodyandexplainitsconstruction.
Explainaboutphotoelectriceffect.
DefineComptoneffectandComptonshift.
WhatarethepostulatesofPlank’shypothesis?
Distinguishbetweenwavesandparticles.
What arematterwave?Explaintheirproperties.
Stateand explain Heisenberg’suncertaintyprinciple.
ExplainPhysicalsignificanceofwavefunction.
9. Writethedrawbacksofclassicalfreeelectrontheory.
10. Discussbrieflyaboutelectroninperiodicpotential.
11. Writeshortnoteonoriginofenergybandformation insolids.
12. Whatarethepossiblesymmetriesinsolids?
Essayquestions
1. DeriveexpressionforPlank’sradiationlaw.
2. WhatisComptoneffect?DeriveComptonshiftrelation.
3. Describe experimental verification of matter waves using Davisson-Germer’s
experiment.
4. DerivetimeindependentSchrodinger’swaveequationforafreeparticle.
5. Derive an expression for energy and wave function of a particle bound to1-D
potentialbox.
6. ExplaintheKronig-Pennymodelofsolidsandshowthatitleadstoenergybandstructure.
7. Deriveanexpressionforeffectivemassofanelectronmovinginenergybandsofasolid.
8. Distinguishbetweenconductor,semiconductorsandinsulators.
H&SDept.
Page40
www.android.previousquestionpapers.com | www.previousquestionpapers.com | https://telegram.me/jntuh
www.android.universityupdates.in | www.universityupdates.in | https://telegram.me/jntuh
AppliedPhysics
I-B.Tech
Multipleanswerquestions
1.
Inthespectrumofblackbodyradiation,Wein’slawisapplicableto
[
(A) Longer wavelength region(B) shorter wavelength region
wavelength region
(D) none of wavelengths
2.
(B)∆E.∆t≤h/4π
(C)∆E.∆t≥h/2π\(D)∆E.∆t≤h/2π
Matterwavesarecalled
(A) Electromagneticwaves
[
]
[
]
(B)deBrogliewaves
(D)Planckwaves
(C)ultrasonicwaves
4.
(C)any
If ∆E and ∆t are the uncertainties in the measurement of energy and time of a system, accordingto
Heisenberg’s uncertainty principle.
[ ]
(A)∆E.∆t≥h/4π
3.
]
Thewavefunctionis
(A) Thequantityassociateswithallwaves
(B) Theprobabilityamplitudeoffindingtheparticlein space
(C) Amathematicalfunctionwithfour variables
(D) Arealfunction
5.
DavissonandGermerexperimentsupportstheconceptof..................ofmatterparticles.[
(A)Particle
6.
(C)Dualnature(D)BothBandC
ThedeBrogliewavelengthisinfinity whenthespeedofthematterparticleis.
(A) Infinity
7.
(B)Wavenature
(B)Finite
]
(c) Zero
[
]
(D)norelation
IntheDavissonandGermerexperiment,when54voltsisappliedtoelectrons,thefirstorder diffraction
spectrum is observed at the scattering angle of .....................
[ ]
(A)250
(B)500
(C)360
(D)
420
8.
Accordingto..........principle,itisnotpossibletoknowpositionandmomentumofa particle at
the same time.
[ ]
(A)de-Broglie(B)Bragg
(C)Schorindiger
(D)
Heisenberg
10.
Schorindigertimeindependentwaveequationis……….
[
]
(A)
(B)
H&SDept.
Page41
www.android.previousquestionpapers.com | www.previousquestionpapers.com | https://telegram.me/jntuh
www.android.universityupdates.in | www.universityupdates.in | https://telegram.me/jntuh
AppliedPhysics
I-B.Tech
(C)
(D)
11.
Inside the one dimensional potential box the potential energy of the particle is
(A)Infinity
12.
(B)
14.
(B)
(B)
(C)
(B)12.2cm
(B)Different
]
]
(D)
(C)1.22A0
(C)insometimesbotharesimilar
(C)Schorindiger(D)
[
]
[
]
(D)12.2m
(D)None.
Heisenberg’suncertaintyprincipleisaconsequenceof
(A)de-Broglie(B)Bragg
18.
[
(D)
Materwavesandelectromagneticwavesare
(A) Same
17.
]
(D)E= 0
Ifanelectronismovingunderpotentialfieldof100Vthewavelengthis
(A)12.2A0
16.
(C)
[
IfanelectronismovingunderafieldofVthenthede-Brogliewaveequationisgiven by[
(A)
15.
(C)
Inwhichofthefollowingde-Brigliewaveequationiswronglyinterpreted
(A)
]
(B) Depends onthesize of box(C) Depends onthesize of particle(D) Zero
Theenergyoftheparticleinonedimensionalpotential boxis
(A)
13.
[
[
]
[
]
[
]
DavissonandGermer
Acombinationofpositionspaceandmomentumspaceis called
(A)Macrostate(B)Microstate(C)Phasespace(D)Wholespace
19.
Quantumtheorysuccessfullyexplains
a.
b.
c.
d.
Interference
Polarizationandblockbodyradiation
Photoelectriceffect
All
20.
Dualnatureofmatterwasproposedby
[
]
21.
a. DeBroglie
b. Plnck
c. Newton
d. None
ThetargetmaterialinDavissonandGermer’s Experiment
[
]
a. Ni,
b. Au
H&SDept.
Page42
www.android.previousquestionpapers.com | www.previousquestionpapers.com | https://telegram.me/jntuh
www.android.universityupdates.in | www.universityupdates.in | https://telegram.me/jntuh
AppliedPhysics
22.
I-B.Tech
c. Na
d. Cl
Diffractionanglefor nickelinDavissonandGermer’s Experiment
(a).50o,
(b).60o,
(c).25o,
[
]
[
]
[
]
[
]
(d).70o
23.Comptoneffectproves
(a)lighthaveparticlenature,(b)light havewavenature,(c)a&b,(d)noneofthem
24.Davisson-Germer’sexperimentproves
(a)lighthaveparticlenature,(b)light havewavenature,(c)a&b,(d)noneofthem
25.Matterwavesarecalled
(A) Electromagneticwaves
(C)ultrasonicwaves
H&SDept.
(B)deBrogliewaves
(D)Planckwaves
Page43
www.android.previousquestionpapers.com | www.previousquestionpapers.com | https://telegram.me/jntuh