SyLLABUS

SEM- V
PAPeR -V
Paper Nanme i Modan physter
UNIT UNIT NaMes
Spectuankam
roscop1Mechantes
fuanhun
Nudlear physte
Soltd Slate phystes,
 UNIT- D
SPECTROscOPY AroMIc - MoLcCULAP-SPCctRA
Taycics
Bohr's atomte Moalal
* The -Atom Cons1sl op Cenhol pouthvaly
chovçad parltele caltd he alucleus
+ The elethon Revolving ound the auclats fn
dhe elzrhon
* The orbtlal angulav Monenhum olSntegral
ts Consevvedl and ca, vat to an Mul4
-ple o! b.
27

n=t 2, 3.- -
27

* The of nar9y dakes place only wokur

vadfaton ol
an electron Hat) trans MPHed eom kaher enei
to louoer energy

*
Bohr's Model o hydoqes abom -
electoslathe ’ Centr'gtge orre
-foyce
(ze),o

*-fcondinq to Bohr s mod:l ol hydngen stom

an elacton fn
9n an Atom moved in a
Oyb?t. above the erteis Under Hhe tnfrene
of elechotd alic foca o -Haction ?s balana by
Cuntitigud
 -tlctodote fore Centigiguel -fore,

my2-0

Cn tnlaqat
fntogval ot ond mu ltpla

myyenh
27

Tadtahon e emiHed olectn an

* elechromagntte
ronmted rom hg energy to louoer 2rar
E-E= k9
from eo
nb

nh

-Substtute ea n eay
e2
47 Eo
m

47£,Tn

e2 rón'h

2
e

7mYn

e'x 7mYn = n'h

 exntn
n2hEO (5
uohere

e = b02X Io9
m= a.lX to-3|

C)2(6. 625x103)( 8- &5 XI62)

Ct. Go2xI6)a. l4) (a.1 XIo3)

0.529 A°
known as Bohr'e radtus

V=

Lem
nh
am(o. 53)
V= C)(6. 62 5 X|0 34)
a7( 4.1xIg31) (o.53) 2nho
V 6. 625x 10-34

8(3.14)(9- xID)(o.53) 2nho

we knoo that he total energy o aleehon
poBential energy (Re) and prnehe energy
um of
(k-e) Drtahte fom the uclerus s
* he Prletal at a
P e - e2
47En
Sub ea n ea hen
PE

Pe

e2m

Pe ) 46or
4Kkonh'Co
We knouo hot b:e 2
mv 0
Sub ea, G in ea 2

k.e = Lm nhem m
2
2
2nheo
me 4
met
&n'h2s,

The total enarqy is given by

En ke + P.e.(o) ÞE tke-)

and
me
th= -me
4 n²hEo

820

-
rom eq
-3|
&n'hE
-13.6 h 6. 6SXIo
En eo.g5%ó2

=-13. Gev

n=
-13.6

(a)2
n=3

(3)2
hadoton are amiled i?
* lectro
elechon
mognete
tr ansmied rom hs her ene94 to a

lower
enrgy
E - E eh
Me
-me - h
&nheo
met met
+
&nthtto

med -hi9

h
n, 2

8h5e
 Rrdberg centtant Pa

Stve types
Tkey are
Sertes
&eries
11) Balwner
ti) Parehan Sertes
Sertes
&ortes.

kaymen &eites (
S.
n,el , n= 2, 3, 4,

The Reciprocal wave length

n=l, n a

3x1. 094XD1

* ThR Seriu lies n Ultra voflet eqion

 Balmer Series G
* in hfs eries n, 2, n, 3, 4,S
Rectprocal oave lengi

n,= 2 n 3

5
36 X .oxiot

GS63x (o m
6563X 1o m
= 65 6BA!

Series teee Pn

fr) Pas chan Series (

Benel n=3, n= 4Sbi

The Recfpro cal wavelength

n,= 3 ) n,=4.

L44
 |44

A = 18762-A
On
Bovies

)Bracket Sertes ¢

* TRe Rectpro cal voovekength

The

n,

RH

26-167
400 * This Sgrious

ingered sgon
400

400

A= 405|4A°

-thfs 8ertes
 he Redpro calwoavelengh

362
400

A= 4582A
Tü 8e viou lee neav
tojorted vegion
bIMITATIONS De BoHe's MopeL

Bohr' model doasn explatn the Variaton

fodenity ot hu Spechal IPne grhe stute
*.Bokrs mo del ooeyn! enpla?in the
Spehal Itne
Bohr' mb de Teeuau ethort
does b't explan Kenarn

Shope
S
gven
lhe pole
cles Pieces
 n n 9ven de
* Stlver mateital kapt
as shoo fn the gure
*rom -he Oven h Selver otoms are alous
hrough the &l9des (S,7S)
to travall
Dut tro
-5 beamn ol 8lver atoms Comes
he Slteles s,&, &S,
Re Svos boam s allowad to pasg thrc
Aald by the Gpotal derignoJ
h magrete
magrahe pole Cm, m) adge and
*Ons ol the pole shops
Shap o kntle
anolher pole shape te D-shapa.
t
+The magnate pola wtll ereate aa gield
dmecton o plane o paper.
* The vaþlac od atomic baam coming out trom
uoitl gall on the Bereen P).
poles ofH
preen a o) mag
-neie eld boudle ghucured 3houon in
abova q
Thxenyi
pB

(B! de Jeoso)

* kd p. b the pole chengh and ' be the

odoc mogne
 *ket B 1s the Shonqth oj applrecd magne Reey
ieldl and dB e the 6told gvadiond in M-dim
etton.
* Then ,luo Mutually prpendratoy fovre oill ort
on -the ahomfe magnot
One end of the pole
(PB) and anolhet end o!. u pole fovre athr
dB
*Due
* to this eppohle and Unegual forres an

external toraue PBlcore ack on 4he atom?e

magnt on the atonne
* he etfed oy the torqe
magnd ie to produco Some motion
* s F means fove on X- dnecton Ps th
ato mte magnet it
i gtuen by
fore acttng
Plcore.
da
Hhe Vatouty op ato mfe magnatie
L' he dittana lravolled by atomfe magnat,
m fe fhe maus o th mag
* Then, he tine travelled by atomie magnehe
hield.
L
4) >
4 the are levahon of atowtc maqnee
 -kshe drparsmund atomi
magnetre teld han
mand in he

m)/)
pl cos0,6
moment (u)
* 1agnahe
ea &ub tn a
())
2m

2m da >

Can jtnd
trom above expLriment wa
alured. drsplacement oo atomfe maard in
Ahe magnehe eld.
Eroblem i a1e Vand
1. he nerrq4 o4 too or bit are J.
L, 46 Rspudhvaly
Number o tuo Drbtle
Auantum
--ln C
Ans Gtven Value
Eini-c.
Aat nurgy (E)e I. 24ev
Suond Enrgy Ces) l.9 6ev, T00

n
q6
n,
 492

(4
n

Mn 14|

of Rlechon fu
8 calculate the Energy
aSecond orbsts
în

-13.6
-En=

- t - l 3 , 6 ev

E -l3.6evl
Se(ond orbit )n=2

2
-¬, =-3.& ev
4

and Second
3 Calut ad e the Momentun
Ovbtt.
nh
27

ovbit )ne)

27

Second ovbit n= 2
ph
 leton bohy'S
4 Caladate the value o

- 6
1. x 10e
charge (e) 34 T/
(A)G. 62 sIo
Planke o ntlant 9.1X 0-31
electron CM,)-
Masof Mogneton e
(u). eh
-formula elachon Bokr 47

*lectron Bohr yayeron

6. 62XIn34
X
+(3.14) (94X 103)
-S3 31
16X6. 62 X D
4(3.14) (a.)
-22
t, 6X 6.62 X t0
4(3.14) (9.)
Cu) 9.242 x (024

Ratom
The total no.o orbilal fon n Sto |
5.
-2n2
he mani mum no.o orbitalb
90)2= 2
= a(2)'= 2(4)&.

a(4) - 2(4)-32
ot6)- al26)-50
Vebrational &patroa of dratomfe moleutle;

* vbraltng dtotonste moleuler tg tontder

Can we calualated Utng nachon louo ot boho
* ) dotomte molacule th tuso atom ot
masses m,& m2
* led 'o' be the Ea,uiltbotum dislano boho
two masses
* -pplytng -force an atoms and distanca
between tuoo oto ms
The tauation o Mohon of rrt atm of
Cm) is gtven by
mas Cm,)

dt
*The eyuati on o Moton o Sacond otom
o gvon by
m, dia -k(7-T
*-from he g

* The Syslem s Balancad above cente oh

 miV m,( - )

m,v,t m,V, m,T

(9

&ub in eoy

m,-m, = m,72
m,re m j t m,

m,t m,
m/mmitm,_
eneral Eauaton o 8?mple hormonfe mokion
mda
o'k
both stds dfvde o?th m.

dt -k

m
dt 2

Cw. a71g)
d42

dt'
 I0) (4)X s14) 4
I,6X1ox
o.02.
Spaaton
Au]- Component
47M
Magnete
9.Ixo [MJ -elechon ofMas
I.6x1o-!9 ]
-Ceelechon Charqeo
lnes Tven
Rnes. opectal
ponent &eparaton
o! ind Tesla o2
O.
oR 0.
20004 Cor), 2000 o!hield Magnete a iH .
n'5
2435)
Q6.3S
n-l3. 6
26?5 36
X
=-13.6 Q6.35
2635
-13. I3.4 1a.75
+
12.75--
6)l3.
-13.G
2n
-13.6
-13.6
13:4) I9.95-
(- h9
-fovmula
19.35ev Ce,e] stale xetted knergy
ol
-13,
bv6 energy
Tel state 6round
qiven
2ncted
sato
to the ut Aind l2.45
ev enerqy
o!
obsere late ground nium electro he 6.G
 4l3.19) (9.tx10 31) b.lx0, 0 x

vabues ol , s,T,
8.nd he
pousble o two Jnells
4he 6.XO, 0
vohreh ave

he
Jr0, s - 6,1x O.02 )
a nohen nel,
|9.66 v4.

100

2 2

S6
fnd
b> when
J=o,,s-' then

2- 3
2
2 2
elechov
9. lermine he possible evms
atom Covrespon dPng to 3e3
-iven
n 3
tab u
-the Orbil al Quantum Numbey 1) Con
 values l=0, I, a. vohen
-he posible valur of J + S

3 ,%

2 2

5 3

20. Caleulate the Magnete

Magnethe mount o! poton
gtven that o proton(m)e 1. 63 x102*ta
charge o protong I. 6x1O192
-forqula
6,iven

plante Cons!ant Ch a. sxio34

formula ( ) eh
Mognette momunl oh proton
47Mp

Ioxs4
1.6x 6. 6 2x
22
y06
S3 27
6 X6. 62
l
le 6x6. 62 X 10 4x3.|4X1.67
4 X3. |4 X .67
 196x
o27
19 5.

Dertve brog's
Crydali

plane a

pane
cho matfc X-Taye falls
* When a mopo
Cystal Source of Seatterino
* ach aom becomee
becC
tadfations
from the plones eaual dtslanc.
* Tha atoms
SatHeinq of -Tay fom ths planas
* the hie plongs
be to cated upon behlechon oom
parallel planes are procuees
producu maximum
* T5?s
ntensty
* Contder a Set of paralle planr od a Cryud
Saperated by a dislance (o) a part.
* ket a
the tncident upon HRs plane at an angk l8
as shoon An above iq
all dnechirn
beam wo|l be reflected fn
Hhe atom o! vartous ahomie planes
by epleded at ato m'A' in
P9
Hhe diaecton HR ronm plane I. in
oajlacted at on atom (B/
* jnother ray 98
the dir eeton BS bro
.order t Calwlate the path dFhhere
 draw
înefdent o ray Q8 and hetleded ray BS.
Aipeetvely trom ato mA
* ho padh droltnce hotueen uto rayA
CB + BD
Rnow the Concion fr mazimum to he
Sntegral nmulliple o woavalength
CB+ BD n 0
* from riangle DACB hn qet
AB

YOm AABD then

Sfne BD
sAB

BD Bne3)
eq sub tn qO.
-ABine + ABno nA
QABine n
ad sin e- nd
he above ea fs tnown as brag's kaus
Stat
* -the Phenomen ot he Spltinq o Spedtalheld
Ines Tn the Prerene of Kxbev nal Elechf
is knous n as Slavk fect
* tlctite -Aeld about vl per meder the
matn fe atures bcerved in cae of Balmer Sertes
OH he Spechal
ho kleche ield o cbout 1o'vlm the
-)taum pien ingseau in propotional to the
 faschan- Back tectt qradually
pield is
+ When theMagnehe hu Couple
fnereased on
behoeen
4he omte
Lec yoco
&pochra
s break Coupleing
douon & h Jt.

oh spectrol Components (3)

Cae les number as Pasrhen - p.
bavved -%i: fe known Bi
ttpoct. -Peld dired,
of 4s along
*The Maqnttde
L=

L27
due to feld
* Th
change -Ener1
gven by

*Anamolus lemenEeet Comparatvely weal

* I! the maqnahe teld te
to
than three Compor
each Ine epl?k into more
-nt is known as -Anamolus
emen Efhet.
Explaîn the Anam olus - emun Ethet,
* To
eleton Sptn Ps Con8iderable along with orbid
Mohon

ele ctron can be oblainad te change

trequeny
 UNIT- 1
QUANTUM MecANICS
Rbrogler's
Co)
lengh oouatton
De-broglerlsHypotheis i
hypehrns a
*Aeording to Ae-brogleis oith a uoa Ve
moving partele fe asoiated
|is hen qes) knouon as Be-brogerle wavo
* The woavalength ol Matter obve te gren
by
Wava angth Cx)
ohere h ’ plant con ank
P» Momartum

vohere m- paittele mus

v-yavtcle vebety
to
Jecordtng -Cquatono-Enstetn
Erergy auohon (or) nelathon
mass

E: onc2
wherem- partcle mat.
C =

*-9coreling to plant'e theory o adiadion

E =h

me' hs
hu
 * Material mauCm) and moving th valout
(v) then

Enargy s the, kfnehe Enargy(too he

maetal parttele han
Imy?= E

m2v2

(mv)= ame
2

P V2rmé

*Ey Sub gn ea

Walalenqh C)
ol Matter Waver -
* Boparhas dapend1 on the
Valbety o Mater
waves

Veloity of Matfer patiele.

 -he velocity o igh. greater thu
machdal Mohon of Patele Cp), woave
Velo cty lw)
knou he Enlen's mas Energy relahon
and plank's Wheory of radtaton
Emc2 -

h9me
2

but we know he velorty ormua

W 9A
mc

where c light velouty

* Phase Vabocityor)
Wave
velocty
Wave veloeity
ejsnation
The rato o angulor treaency and
propaqatfon Contdant 6 called tohae veloetyo
* H s denoted by (P) g (v)
Vp - Propagration
Anaulas juqwunylu
Contantl r]
 (mv)
Y- aBinlwt-ta)
plae of Condaot phau (wt ba
for he
Contant.
dtyberendiatng above oq wilh suped
* On
-tfne.
wt- ka 0.
=0

da
dt

k.

*A0upvelocty g)t
enerqy fn the qry
the energy
wohich he
Hhe velocty tnown as froup velodty
fe trantmihed i
# den oted by Vg
* Conder tuo wavee
havtng dame Amplkd
dtperernt angular requnciea (w,>w,)
ta)
and phale Vetocthes Cv, v,)
dizplaremunt
* The nOave ea uaton ol the
gven by
y= a sin (w,t- tz)
Y, a in Cwt-t x)
dtjarenre o the flngular reguney
popaqatron
Constant
to)
 (Pa

Heisenbetg- (Vacandatrahy pinctpler

a) Posthon momanum Dnretainty
sH mpotble o mafov bollh poshon and
mometun o a parttcle Stmull antunus oth
dentvad acuracy
mec uremend of pothon Unedatnthy
* AP S +he Dncertatnty n lhe measuI2ment o
mOmentum
* Then th princi ple can be expreked Mathe ma
-Heally ad he produet of Uncertavnihee ?e
alwaye equal to tlhe Order ol plonk's Condot
CH)
pter'e cont n
A. Dp= h t plem'k
D.

- -tre Uncertainty
* Constcer a Cale af a gree parkele hest mace
mortng along 2- dtmachon wfth, Yalotily CVa)
* Then he kine
kinehe energy og he parhele
grven by

drventh ahing
&Pa APx

Mo

APa = wfox A6
 A
APr
Vy -th wauremeu
Unierlavnthy
Aime

=AE. At.
Eauahon oj poviton g
know-heGeneral
| gomantM.

trom ea
4n

Comptoneffeet e
photon

Lntden - Say
-Ireldar
dire on

olethon

when a beam of laht monocyo matQc vadiation

aa Substane.
mgjh treyuery is Satesed. by
4h &coltercd adiation Contoins ton Comporgnt
 one håving a (layer) lower treqemy and
anolhur having &a&ama jroaqueny ond gerne Wave

-Jength (2) au tha

k One having -lu &oma woave Donqb C)
fhetdent gadaton and othes a Jonge voavel.
beam
-4h CA) then ho! o he Tnodont
* when a beam of Jtght f Tnodent on photon
too ays are pro durei
1) Beatterad photon.
1 ableet on elechon tnecon at
Hhis (ef) slatte fnteraton g
Counter ehhect
hid drtharen@ In woavelengh talld Comphon
-tPect.
the depurena og the wowlengih gruen by

* Compton
A-h[i-core)
mol

moe
he elechou,
ohere

wave

-Ihe tactor
caled the Copton
mol

length. 4hen Compton thtyt

cote
* Compton ghigt (A) hMol f-
 mo

A(o)

CompBon sh1 MTnimag

when =0

MoC

moc

9.XD3)
elechon maus =

tgat valoaty
AX = 0.02426A.

TR 1e known a Compfon voavelength ol the elechs

when = |eo
hen Compton hrht te ma imum

moc
ah

9X 6.625 XI034
- A 0.05A
4xX103l x3xto

be eauly detocted Ao
Complon ethotwavalenqlh not gndem
Can

ra d: tion oof
angston:
 Compton t"obrved by vHble Jrgt
Cow pton she_t A Moc

TFne depandent Schrodinger wave 4uaton

Sshodnger Wave
yuaton fe propad
equotion
L developme nt o brolre tdent oh
wave
properhes D matter.
+for thfs purpote fehyoclinger thtroduced
a Mathemateat tun tton ( p) knouon
juncton.
P=Aei(ka-wt)
x
9n difRere ntiatng ababove <9, wo?th Seped to
1(rx-ot)

dterentating above eqy n wotlh rupdt ,

-A qatn
i(k-ot)
2
Cik)lik) A e'

ilkz-t)
-K² A e

A2
rom ey
k' value
-472

P P
472
 472p,

(
4772

on
rjerent atng gn wilh serped fo hrmele)
-Aerllca- ot)
w27g
eh

t
knous Hhat totad ener9y = kinehc en ergyg
potenkad enera

wfth on boh ile

Muleply
p2
2m

or Sub in cay

at
 ot

n he Case
lhroe drmuntonol
-B2

H
Ham
tonian, 2m
oprrtion

Tine tndegthd. Schadtoae ave eauation

don'
* In many Sthuotion pertial
dspend On fme
* In hote -tocus that are achng on potential
enegy Pe' at v'v depend on the positon o the
partcle
* 1 nder bis Co ndslions o(a,+) Qan

he. produd o! a tuncton ol poerhon (x) ad

he other unchon o time (t).
P ( 2)+)= Ae

(p= Ae
e-fut
(Pfca) eivot
to
fwett),
-fw dla)-it

-i2 E
h.
 ép ib

to

again
-Puot

ecerd'ng
to tne dependent schyodirgy
wave uakon.

&ub n

-iwt + V

Lam

2m

ulpytngq ofth m aboue

wave
 In Case dimen gions
A anm(e -v) -0
for a tree
ree partele the polenkal ()- 0.

trom cqca
0.

2)

2m

2m
eenar9y
ane tontan

* Phalo elechte ehac -

Quartebub light
Sgurte
otfe
hrorr
cfonr Surhaces)
3( melal
6lGalvanonate
B

VRheheoslot)

frcquency fs
* when a beam ot Ieht &uttable
&uate -{hen elzchont are

incident on a melal
surtaie -thfs
imnited hom lh melal
phenomno is Knoon as photelachie etat
Tie ehaiHed ele chons ave callod pleto els cho!
 olechons (voak he photu CurYen),
Ipatmendal hudy photo elechte

* The expcRnuntal aveangmnd hudy p

eleehfe
TRe apevahey Conee ol malnly to parl

eleche Cirutt
Suntor
*rom above 4tg AB are -the me-lal
plates fnede e uata bulb
plate fr connated to he neqatve eimid
+h
o the batery and B plade t Conheded
poftive temtral ol the balery through
qalvanometer.
* In above fg plug key («) and Rheorlat (RA)
are Connecled n thad etreutt
* în he abtence ofog Itgbt no elechonr plouo in
Hh creutt and the?y i no
fa lvanometer.
* When Monochomatic tight Sourte fe allowed to
qall on plate a Hhen elechon's are ium miBed and
-havel tousardr plale (2) hen Cuvent i slatr
rom above Chutt
* tron 6alvonometer Curred ts knoon as
Photo Cursent
from chavo dtihuk oh photo elechons the
humber elecksonu mmiled t1ow
hien tinhe iciy dapnd upon. four
factos
 1) the polental d}herene behween e two eleoho
(AB)

Tuddent Tadiahiou
| phelo etal
iThe polknta dehherence between h tuo elechod

when the poihve polenhal o

olechode fs pnercated photo
elechie curent Pe alto
Sncveaed oppin

* for a pavhcular. poshve

poBental photo elechie cuned veacheu maxlinu m
value 4hio Value ol h Curret io tnown ag
Sutls Satuvation Cuvrant
The nqatve polental of k elechòde at
* cuvvent becomes o' isir
tv
wh?ch te pheto ele chie
Called stopptng poanhal.
SncdenTodtatons
tSnenib
* he tinengthy oy 1nadant radtahoy,Phota
fs fnereased the phote eletric
Curent aleo fnereare for all
peitive va lue of pokntal
* 7he Saturation Current fs Stopp'na

pohnt

pacporton al to the intniy j (vo)

D nerolent adtation
*polental % negotve hen paeto elechte Cument
voHage radtaton
&ec1eiseg then
frauny t tnetdent
* The ninimum tr4q uenty o he
fncteent Yadiaton whih can (aue o
plhoto ltchic eitou kneon
-hrerhold Sequny
 * 4 denoteo by

behecen Stopp?ng
|* -4 fraph
poltntal (ve) and he
11oen of a numbor ob
photo Melhod
* Thyeshol eqon y fr a funchon of! photo
mlals

*enstein's Photo eleedte esua kong

Erenstetnt erplanahou Thro
to
*forording
hpect On phon' fe Completly
elechfe otochon.
obsarvad by on
be spit into ton
* The photon energy may
part
ved to eparad Ha
part o phot enargy fr
*4 &urares
electon rom the metal
called Work unchon:
* T6es en erqy R
qver
*-nother pat photon energ7
ktnetle Cnesgy to the electon,
hy ot Ke

where e-h
Wo= Work funchon
ke = kinehe ener9y

his huot mv
* When the photon enerqy 38 &uch a vale
Hhatt can only emt the elechon fom muta
Surtace hsn the kineie anerqy ot electon wi
 be 2e10. (ke o)

my? o

hu Wo ()

hu= Wo + mu
mv2 hy-wo
my2 hs- ho

tunchon bu
for a parhud ar photo metal ook
ConsBant
trom ea

* The veloctthy ot photo elactont fr dfoedy

requenyD4 (aen înudent
Propertonal to the
Tadliaton.
be the 8toppfnq polental tner
Vo

mve hu-ho
eVo b19-ho

Vo - hu ho

Vo
 are dhe Elensden'e

dtarent typu op photo olectie e,uation

y- axi

polental trom 4hot pavamete od

Shoppng

Shppirg
pote
nhal

foumuy (v)
 UNIT-Iv
SouD STaTE P ysics

* The olrl
charactomzodbl! by a partod Co
neavly prohoet pefodteity
tnooh -gtornte ghucure
* Theso Cryclallne
poin t hatng shoarp
hey shouo Ailoret
Tange o!
diachons propechet în dilforent
Can
Sudy early the crypt atra mateial
* în Solfds he atoms ara
arra nged tn an
ireqular haton Care kncuon as '-Amor phous.
* monphous materta Hhro he ato ms are
<Stongly bounded.
point.
are
having otde sange o} Melting
+ These are
Drooke Mat ertala.
Rxample qlas, Rubbar, Plasha
* Ont Cell
+ Unf! cell may ba degined as hat volume
of a Solfd fiom obfeh ha
anter Crystat (o
be Constucled by translaton nepeaton n
demeng)ons.
* lbree dmenetonal
dme bst cell is Shoon
nttona/ bA ab

base vacos a,b,

*A -ormd bu 4he
cdqus and tnudirg angles (*i P,)
* P,S anglesbohoen b and e c and
agb rupsctvaly
tndeees ol a plana is he
The Milley
Mller
eale of
-cals tha interships tohich the plane
he aats ohen Teduced to Smaller4
efh
numbers
*he Milley ndfees ard he hree &mal
the tbie axis.
postble indeeu on

P
= Qai 3bi6c

Q:8i6.

2,

6.l2
2 4,
(hie: )=|3: 2:)]

4 ? 6 12

4
 3:2:

3:6 9

6 3 8,

[biki] - l6:3:2]

[h:le:) -(6:3:2]
Destve doue's eg uation for X- Tays drtbrachon

Piohole

quahg line

Crydad Laue'r
patlen
plateL
 Conthuchon):
Basltphon ( nal oyangnenl ot Koue's
oTangmenl
The <porime
x
shown n n obove ig
qatkod ir
held Statonary în the heo
7Fe
* The Cvytal te

he crystal the x-rays ar

Qre

* Ater pasing
drefracocd photo raphie plate
important becaue
* Tha diameler of pinhole îe
diamater in înterjar ene
|Smaller fr the
the Srysta are

* The x-vay wohtch penitrale

Scattered poom drtterent atomic drthracton
Centres.
*Te value oh drttrent angles wll be difjuroat
for aach Set o! pland and oach Sel of paralbl
planas fl have fk Ouon þavtoudoa value of
the dstance.
02 knoo that atoms of CIystal hava an
ardoly orarqemart tnfn allall thit
4his dimenions in
Spare
* The diPracton o a-aus oil) occur m
mory tomlyls o atom?e plond al On ce.
de 1achon patler
pattern Conist o a

Cental &pot and a ted o Splts

a
A:songed în a dauels patlern.
cenenttical, pal'en is knDon
Kaue's
¥ each sport fn the kavotr Dalten Cowupond
to an ?nferhoranto maytrum -or a Bt ot
Coystol plone Satsang he brog't oayuoton
(nd= 2dtote) for a parltalo wonvelength
Sleted hoom the netdent beam
Theong
imagne
IPne bas
IRne qrting uoflh atorns on he
dFffachng centre's
deta be 4ha dfrlance of he ablAB])
and ' be the oava length o! the
Snetcant XToy
ket ' e) be the angle ot inetelant , 9 ba
|Hh ongle dihrochion &hougn fn above t9.
* Tha path dPheranca betoeen the tuo
dihhvact ed
AN- MB= n
* from 9 trange (A, N, B) AANB
AN
Cos O
AB
AN ABCOsO
AN acos 9

AOMB
BM
cose AB
pM acose
 and are
subshhhng
acos - acoSO
altosg- cosOo) = nd
fncident and
*for dvechonal Coiro of the
Cose,
oplarod by
doclod

ala- o) =nd
* for -Ihroe
muhually perpendiular oris
condihons khow be Sahshied.
Hhrae
a(x- Ko) - n
aCp- Po)= n,
al&-y,) - ns called aue's
he aboya . 2g,uatons
eauahons.