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Question, — Derive energy and devuily of) Ale
: \ conditions, (i8)
Geplon the ides of fetiove beurdony
oR
whed ane the —leruily Aleta of fy ib in Abree dimenstend
b ne esily ef akete { be deen ges in @)
Answer =
Seept.
pk The fie — fevtice Schyoadinge equation in dhaer ditrersiom 14
a)
~#/ FY +2 ) Yet = Se Hes
am ( wy tie
hoe @ = enegy of He op bitel,
SEB fentedic beondany conto
Gi) Tn 3- dimension, the wave vecta bk con he deles mined by ihe condition
expf iChat byt DT = ogp) Ef be Cou + hy Ged Cw]
ay this bs only forsibte uchen
kertye tg = 8% ta, eM pose
w) There fone fen the voave fnclena te be pevedic in Hye wilh poied L,
se Bho pave
Y (ath y ade Plryed
els yi z= Png)
L. ¥ ( % yr at) = § (aye!
Sheps. ’
ep aed A en waauefnshen acting, theft perfil Schaced ps vm
ad the awe pesedldly anblonS fav of dawuclny fare ese Ut
Yyad= exp (1-4) pee
b
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er Peoth Ly eben ik a peurtve oa pegalive eae
re
ep fide, nyt seep L eden Cr dT
= ep fama] ef ttn)
: exp Céanax/LT
> orp (4)
Therefore tetiey Pfs ep , Reve vind vey he ad subshboting
iy ep .O, we gd
at (Hath) Yo > Sod
ae
” 4 Cita yt by) > &
Re
>t oe —__ @
me
oe cpostry eth van wramentims aberebor ov eps. @, ot gd
Pyne th edu i by fe te
-iK(E K ptm)
> RE YR
=) Plone wae Yn & abso an edgenfinchon ef the Linen mmentew
the etgaale Ak,
Lhe Ite feats velocity in aphid 15 given by > fe [et]
woh
Steps:
far a ayplem of 1 free alechons, which ig Aepraertel or ar plese,
The = ewer sat fhe suafoce ch 15 the fermi eney hich 14
gien by equ: © eath firm unbeer wove yen Fp
a
> pis tk
, ze 8
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TS Neel allsed somrevecln K fon the valine clomast
k shes is ame
Tnerefere fps uit volume Clement roe itlues of ke = a
2 fon the voluure of Aphow
the no of, allowed albowed yale of Ie ‘4
Ly3 3
2) Tefal novo oni = 26,) Snr
bere Lachag ig Bue te He te allowed values
cf the spin quenfeer mum lber
> Ne she fee )
> hee 4 a ©
Vv
fuatting wis valve in eg @) we
a # punt! _— ©
an w
dechor 3 dimension
which is the from ovengy 4,
This eu Aelates Phe Ream? ene Ae the ceveenlnetion x.
Rept New, Aho rw dh obits per unk energy ie Dewily of, slate is
ee a [ sar ing | [* ev ®
an? \ Re
46
Je
Ne BG)
ey thick the deny , arte
fe errs in Tare
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Arausers
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Hom om Leatin: only fpachen ef, the ond To elednon ane eratted
a G Te
avd dors paenalon Tv.
Then the efleclranie —thiamal —Kinehe every Uta the andu ¢
Uy 2
Cae ble) ( de Ce-&) i |
0
Now fyehdiedin qu ® ond Tue je
— hf coroner] (— ee)
ar olf Er
i vd
Gt xe ©4) ant petty the valve of f in oe @ ,Y
=
7 x
2 de 3? 2
> te = FT n¢ee) | "S
~&h -
A xe dy 2
Che bai be al [ 2 f e*aly 3
Slept,
Bul pftp)> 3H 2 EN,
2G abel
> = oT? Nb fT
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di
tahch shes thal Hoa csposly fa dineckinel prspeationel ko dbe
fore prmsbew-
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Question. Derive electra and termed
that te the enimenlal vies port 1
iawn.
Skpl The memento, de free electron ib Aeleted do the wave vector by
area hk,
Sr an Ehednie field £ ard Magneto fi 6
the force on an election of change oa ig
fF. -eL E+ lees].
D The newlen's secemd Saw ef, rrofion becomes
(ee mde . att ee ef exdjo] —o
Shep.
a In the absence ef celliters | tre fermi aphew maven K-dhace aa
critean accle by 6 contfont appied ledtsic field.
There fore at Bo)
Snteguebng @ wal tre, tor gd
k(t) —kG)= -ebt
4
AM Ledn me 2 the jplor will be duploted fe a news combs al
Sk 2 -eCl/+,
Steps
ie I the collisions ane proret , Abhos 1b wroinlinal jn a dhewky Ade,
Therefore : a tec)
ney isfocarel of, she -fprmd Sphete i shady Blade ta gher by {-
‘fee -eez
. a aus 4h
Tne incremental velecity Wo ue hile f ol ia|
oa fret ye
2 Ws ste @
Co po URES ore ae!
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toil valine, hen
Fhe clectale cusnevt densiby ia
je nqve neve —
7
Aue q = ot —
fare Gard A we gd
f 3 G J
Efecicd — anductivity
es ver 6
Thermal conductivity Medal
We chrow Red
thesmed conduckivly ef Medals ia givers as
ke= 4 Se vf 6
et = teal expacily per exit volome
De mean fur poth
ver pert velaity,
Plo cy = TE Nyt
7% As
xe nig cot tet Ai
ra
= y- WN ke T
Vp?
Lor 1B me gt
& fe hele
>
ke = (tn be? iy Le UT
: 4 = ) Le7 a
>
me
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Relolion bf Thermel ond Checlaical Conctuel
bising equ vil ry Ow vl
(e (ene / ee)
my am mm
on hy ke?
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am “heb
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Se
be a hal’
om 3 ‘ hus
a Le Me Uhrh 4 Lonena nuveber
oT
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—s
Gitewn —webvon of fpce ebednra in vnnguehe field and erffain Hall af?
Maher ttebion of free electanns in rmngrelic fields,
fon in abn described — vel
£ Melon in a ff divest na bay the vebs He
Heel Gnngidin Abe cpidien of rekon {er ds acewtad dle yf ofan “phere Of
forties eled on by 2 eer fond by ppebon 00 seppeverted by
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pe
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in ae —3
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tren ne clo velit
Ter = u- ~et%6 wt 5) Ut SEG
[= Eb eT z OG t pid
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AA TAT mopvele {eld Bo
4
pet 24, camend Boca flew cob ef the Aad in They ehnech,
we mut have by oe
There fore
cbf! velo
Uys xs x - were My = ~ EE Gy pete
2 be Se —ty at By: wet —O
Trodowe ,we get ten @
y= Ime Oe
e
fatty fre vabie f(D in above be (uy), we gt
Se me (456)
e
> & Hut Gy
tle we 2B = eyelet fpepeeneg
G, >= ~C8te, me
“| we ©
g H Gy 2 Hall vaste;
opt. Tre Hall coefficient a as *
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become canunt and dowel ge vrly in the dinedlion of, the elethie fret
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cowed by “the ofpticatien ch ven oki fied, ther
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wiz ek + gn ———®
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Fact IP om be nagtected.
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te dechm and bole, the drorveve gamete Resishonee. deer no!
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Rasitp Explain Thermodlectale effects. &
frsvien
Theme cletaic_¢Ifeel *
— The elfeel in whieh foterkol iffrmmee i+ crate
Wr two clifferent medals in cenfect and curser i
Setuh helweer them ia called Meme elerbde affet
Shep
> lensidarng vw different medal A ond Bin cenbact, Jel athe efedten densi in
Q ink
A be poles ther B, Thoofone elecnere prone pert Hen 6
ci) Bue fo Fhese differences iy eledhenie proure , aechont with diffuse from A
48 smbing A positive ond B regatve and thewely resting. © difheurce
4) paenbal at te jones of the to metal,
@) TWA potential dl ffororee will Tend te preven further electamt pening
from Ait By whe Hh peachy -he mesimum [cen valver a
Abce af, equilibsiom ach in ond mipshin of chednany Abed cope
Tor Cffeds of Thamedlechit phenomena
Steps. extanal J
(> Uther Aho potential Ui ffermce ts apple he the pont ar the cunent
Abels floating from A do 6
fe che Hrarete, ef, dechew farm B to A
But
we amurned dhe eleclon deesity of A te be qoeals thon B
Therefars
, elednons bye 8 to A involves woah do “be cere agains the difhereoe
I dedneve ptt ard Barer craps all be abated af He functor
(A the aitechow af eaaserd is tweed, the jorelon ye feated
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Evie ge
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if, dree are on elecnens por wit vebime of, a
elechowe poser iA
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73
a) corduchr, the
3
Since Amos dT
2) pe 4 naT ——
5 Moe, GE) thy ane ‘eledhn pia aif votre each lh charge @, Se charge
pe wit yume i ne.
Se He Volume Veosres posing to ori cheng
\
vet —
as She
the woth doe uber arid chorge pow Hivrough dhe purcien is equal fe the
wok doe by ue ledrem tn meng frow dugher to Lower elechonic prenire
he Ae Sins
» orf" Anat (1)
ve
Dae gat ie #9 2 O byy
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37e v
w
As Ves Yme 2m
vi Vea Ta
ne
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Thema ee
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a” flee. So kinehe Heong ch ele cls
Ameer
incrented oh
3 Energy. of, cleaems te ving Aowanls refer pend wiht be incseated with ox
censepuend sheng elect
Bul of dhe tome me _ due fo huighen alechunic
pet
elechon will move dewerdt gold fant ushiwr Srergy co bt, teading fe
colby elfted -
Thus , the elechon theany ig tenable fo deciele thick of, Ahae suo fheceaies is
poesne al halle and
hey
grote.
*
Bolte nann equation, row will ‘aaa calculate eleclasca} and fhevie!
x
Question. Usin
conductivity ef orebly ard inguleon. § @
Qottarann equation
Skept Ll A be athe coasdiiala ef on cleciion
and w be the veledly Comparer
‘Thon athe clltaibuhon fumthin 4 dvtn y= fe)
i in the value dad dy ord velo Aaige Av is poy
“he rod eledhent
Fs, ¥) Ase = veo ef paabicle, tr dade oO
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Tepa. censiddoing effect 4 a time dialotac nt dt on the Ustarh
fuonchien 7
Here fgre vole elemenl along dre dishibutin with erllistoy 's
F (44d, rade, vedo) — fa) (oF)
wher Eat re. of, colUsinns
Thus
a(t) 4 Ab ppelf + ae goed > 405 oa
oF
Wt accetychin dv be cleneted by a, Men ohare jun becenret
a
a as
| 4 apf + a peld —o
This is Boltarmann eqeahm,
“st Ac accelertom abv combercrts ts jon
‘mks - ef —€UxH
Theufere , when the electnie fretd ib alone x dindon and toe Flee, 4
and 4 is independent of 4, + and 2, then ee @ become
A)ag= ot uth - be Hf
2 = fife -udl -e6 gf
2 Sefer -t(u ¥- 63 |
3) §-f-efe s-26. —@
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Hen the averse 7 4 el eckan per unit velume (4
< Fo Apa dpy dpe
Treneferr cused deny *
d,s -heu
cae fer) dpe ty dey Coed
= ca) ~ a (([°e® Apedhy Ag —_—_—@
SkpX. Fan tha cone, Gablewam epushem BO) beens
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Gila “a,
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a» gfe rated) uf, (g- <)- aff
Be” (Be Fp
Sivee eek pe > ee ‘feew
fattuy this vale in eg, we gd
i ste (J “dbo
; As uv? ond tp anis = air
3
oe Abo ate
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Then
ips o€y
Thow
Eledaiced eondlcvdy is
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oe de 2 en T/A
S mf Aan
Fo,
Thermal Conelu chvi
From Finebic Sheany of qa
kz 4G-4y% ——@
for eledtr a
a
Cpe 2 eT
ier Ee
24 2
= fm uy
ant age YH GH
Therefor epu-O be con
ke L (at n't uy %|
BUA Yara
iJ ”
—
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setiiviby i etl 0
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The eledtrical Resishivity sw mela 14 que by
fm
nee
Sci) Tha clectavend Kesighily eh reat medals ia dominated of avom Hem fpernbaae
Conk) by Alanon the caption lene ith Rate Hoes ond
ot Liysd helio — fom. (wt) by ction wwith impunity horns ond
rrechavieal imperfect in the Lattice
Gry), Eleeie fet te suilched eth,
the met Aelonahen sabe is
ple ee
Tt ca ee
hue Zp= tllinin times fon deadlening by Pheew
t= testy by im en fechow,
gt Thode tre vek Retails
Be Si tSi
cles Resoiby coued by themed phovor
Ay = Resstivihy duc 4 Seating of, afechrn toro by
impuly ofomy ohh dish thy povstaly af.
the fobice.
Matthiewer's Rule
Ht Afska that ushon the canceelaaton of impel odoms Us
ee and
4p inde herd ant of, domptonbone ,
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Energy bond dhe a
Blech dheosen, elechow iv paricdse folerhel ard My
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Bemicardactert, — Semiemducloa ; bat gop, eqpatien of, motion , Bore scheme,
aie well pelentiol « Copy tee
nsutalens ond
cendauchon
4 Femi sonfeca, sledaen Aste ard ofen cakibe; Coladaben of, emmy bed ; ay
binding wrelired , Wigner - Seite mdfed, pseudo potentials ( Quditetive onli). taw of
wa ochen in gem ervdluctens, Iopusily, conductivity ard inposty Altes, The
spe ele dite
Affeds thaty sod corsneon of, fond infos by cyelohin Aeserarce ‘ord de-Hos
var Aebhen elf
Questions.
Bt
Oe
G3.
Qe
as
O66.
aa,
ae -
43.
lo
aw
Gla,
QZ
a
MS
rite ard éefin the anpificance of, fe thensent
bad id Bloch Yieorew 2 Cansiden an alechm In povicdie potential and shoo
Hood Here Yo om -evergy tt at gene betvidary ©
Galeadcle evry bovds by urnsidesing Aecloom in feed Ayvare ell petarbed,
How uit) your wake dltincten Yes th, imately oval gemdeerbacte. (G)
Diafinguish Wo rete, ingulohmn and serw'cerdudons on Hy bail o of bard
Wieory. @
Derive Band gap ard tint He fein! few in zamreerduchos . ®
Duss ty “hiring rmared for eafulation of enogy bord in materials. &
How will p caleytote eno bard Howeh Wigner sete meld, &
pews Lass of rast ackion in sem—cencluctoss @
Discus Twpevly skal and burly emducivily, @
fepiwn the ele uf fans fore! in pemiconducters 2 6)
ik Bhord yale ont Fone Schemes. ©!
ire Study ord contin chen of, form) Auiface by De-Ham Von phan aed @
Discus shew De-ttas Van Apher fect el ws th lady and emily chor
oh fermi Arrfve. Give o compile gxbesimentel delat, 6
Discuss the conbAuction fami Aurpece & aque daltice.
ExHaln the — concebl ch © nad Surhace.
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