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NWX^]KJJ@LWKUAX QWKX & GWKLL^ JK\ ]AB@WX
Q-Wkys
Hctr`munth`c 9
W`ctlbc hc ;182 mhsn`vbrbm tab Q-Wkys wabc ab wks stumyhcl tab pabc`dbc`c `f
mhsnakrlb `f bjbntrhnhty tar`ula rkrbfhbm lksbs.
\ahjb bxpbrhdbcthcl whta nkta`mb tugb ab f`ucm takt wabc k gbkd `f fkst d`vhcl
bjbntr`cs strhob k s`jhm tkrlbt, kcm hcvhshgjb, ahla pbchtrkthcl rkmhkth`c krb pr`munbm.
Gbnkusb `f tabhr ucoc`wc rkmhkth`c ckturb W`atlbc nkjjbm tabsb rkmhkth`c ks Q-rkys.
Q-rkys krb bjbntr`dklcbthn rkmhkth`c / wkvbs `f vbry sa`rt wkvbjbclta. ( 4 ; ;55)
Ur`munth`c `f Q-rkys 9
]ab Q-rkys krb pr`munbm wabc fkst d`vhcl bjbntr`cs strhob k tkrlbt `f suhtkgjb
dktbrhkj. \abc fkst d`vhcl bjbntr`cs krb summbcjy st`ppbm gy tkrlbt, k sdkjj pkrt `fohcbthn bcbrly lbt n`cvbrtbm hct` Q-rkys.
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NWX^]KJJ@LWKUAX QWKX & GWKLL^ JK\ ]AB@WX
D`mbrc N``jhcl ]ugb 9
A]
N``hcl
dbnakch
D
]
F
\
Q-rky
Fhl 9 N``jhcl ]ugb
N`cstrunth`c 9
k) Ht n`cshst `f ahlajy bvknujktbm ljkss gujg n`ctkhchcl nkta`mb kcm kcthnkta`mb
`r kc`mb.
g)
Nkta`mb n`cshst `f tuclstbc gy pksshcl kcm bjbntrhn nurrbct t` lbt tabrdh`chn
bdhssh`c f bjbntr`cs.
n)
]ab fhjkdbct hs surr`ucmbm gy dbtkj nup D kt cblkthvb p`tbcthkj t` tab
fhjkdbct. Abcnb bjbntr`cs bdhttbm fr`d tab fhjkdbct krb n`jjhdktbm hct` fhcb
pbcnhj `f bjbntr`chn gbkd.
7/23/2019 7.XRAY & BRAGG'S LAW
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NWX^]KJJ@LWKUAX QWKX & GWKLL^ JK\ ]AB@WX
m)
Abrb bjbntr`cs krb knnbjkrktbm t`wkrms kc`mb (tkrlbt) gy vbry ahla
p`tbcthkj mhffbrbcnb (kr`ucm fbw ov) gbtwbbc nkta`mb & kc`mb.
b) ]ab tkrlbt ] n`cshst `f n`ppbr gjkno hc wahna k pjknb `f tuclstbc hs fhttbm.
(bl. ]uclstbc \, D`jygmbcud D`)
Wbquhrbdbct f ]krlbt Ht sa`ujm akvb
k) Ahla kt`dhn wbhlat 9
]` rbmunbm akrm Q-rkys .
g) Ahla dbjthcl p`hct 9
^` takt ht sa`ujm c`t dbjtbm mub t` tab g`dgkrmdbct `f fkst d`vhcl
bjbntr`cs wahna nkusb j`t `f abkt lbcbrkth`c .
n)
Ahla tabrdkj N`cmunthvhty 9
]` nkrry kwky lbcbrktbm abkt.
h.
Gbnkusb wabc fkst d`vhcl b-s strhobs tab tkrlbt, kr`ucm 88% `f bcbrly hs
n`cvbrtbm hct` abkt kcm `cjy ;% wahna lbts n`cvbrtbm hct` Q-rkys .
hh. ]ab tkrlbt hs pjknbm kt =2 whta tab pkta `f b- gbkd .
hhh.
]ab tkrlbt hs n``jbm gy fj`whcl n` jbm wktbr hct` a`jj`w tuvb kttknabm whta
tab tkrlbt.
7/23/2019 7.XRAY & BRAGG'S LAW
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NWX^]KJJ@LWKUAX QWKX & GWKLL^ JK\ ]AB@WX
F`r hcmustrhkj purp`sb, tab pkrkdbtbrs `f Q-rkys wahna cbbms t` gb n`ctr`jjbm
krb
H)
Hctbcshty
HH)
akrmcbss.
H) Hctbcshty 9
Ht hs pr`p`rth`ckj t` tab cudgbr t` b-s strhohcl tab tkrlbt kcm ht nkc gb
n`ctr`jjbm gy vkrhcl fhjkdbct nurrbct.
HH) Akrmcbss 9
k) Ht hs k qukjhty `f Q-rkys wahna rbprbsbct tab pbchtrkthcl p`wbr, mbpbcms up`c
tab p`tbcthkj mhffbrbct gbtwbbc tab nkta`m kcm tkrlbt.
g)
Ahlabr hs tab knnbjbrkth`c v`jtklb, hlabr hs tab spbbm `f strhohcl bjbntr`cs
kcm n`csbqubctjy d`rb pbchtrkthcl Q-rkys krb pr`munbm kcm tbrdbm ks akrm Q-
rkys(^a`rt wkvbjbclta)
n) J`wbr hs tab knnbjbrkth`c V`jtklb, j`wbr hs tab spbbm `f strhohcl bjbntr`cs
kcm j`wbr pbchtrkthcl Q-rkys krb pr`munbm whta n`dpkrkthvbjy j`cl
wkvbjbclta , tabsb Q-rkys tbrdbm kss`ft Q-rkys.
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NWX^]KJJ@LWKUAX QWKX & GWKLL^ JK\ ]AB@WX
Q-Wky ^pbntrk
H.
Nakrkntbrhsthn `r Jhcb ^pbntrk
9
Hcnh.
k)
Fbw fkst d`vhcl bjbntr`cs akvhcl vbj`nhty kg`ut `cb tbcta `f tab vbj`nhty f
tab jhlat dky pbchtrktb tab surfknb kt`ds `f tab tkrlbt dktbrhkj kcm oc`no `ut
tab ahlajy g`ucm bjbntr`cs bvbc fr`d tab hccbr- d`st sabjjs (jhob O, J sabjj,
bnt.) `f tab kt`d.
g) C`w, vknkcnhbs s` nrktbm dky gb fhjjbm gy tab b- fr`d ahlabr sabjj.
n) ]aus bjbntr`chn trkcshth`cs tkob pjknb.
m)
]ab bcbrly mhffbrbcnb hs rkmhktbm hc tab f`rd `f Q-rkys `f vbry sdkjj gut
mbfhchtb wkvbjbclta.
b) ]ab wkvbjbclta mbpbcms `c tab tkrlbt dktbrhkj.
f) ]ab spbntrk n`cshst `f sakrp jhcbs kcm hs tab nakrkntbr `r tkrlbt dktbrhkj,
Abcnb tab spbntrk oc`wc ks nakrkntbrhsthn `r Jhcb Q-rkys spbntrk.
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NWX^]KJJ@LWKUAX QWKX & GWKLL^ JK\ ]AB@WX
l)
Hf hcnhmbct bjbntr`c oc`no `ut bjbntr`c fr`d o sabjj kcm tab vknkcny hs fhjjbmgy tab b- fr`d J-sabjj, tab spbntrkj jhcb rbprbsbcthcl tahs trkcshth`c hs nkjjbm ojhcb
_BBO4 a;T 4
a) Hcstbkm `f J-sabjj hs vknkcny hs fhjjbm gy b-fr`d D-sa tabc ht w`ujm akvb gbbc
o
jhcb
_BBO4 a7T kcm
Abcnb 3 --- _o jhcb Q rkys krb d`rb bcbrlhkcm sa`rt wkvbjbclta T
h) Q-rky kcm spbntrk `f mhffbrbct bjbdbcts krb f`ucm t` shdhjkr t` bkna `tabr,
kjj krb akvhcl O.. J, D sbrhbs gut ht wks `gsbrvbm gy d` takt frbqubcny `f jhcbs
f`r bvbry sbrhbs fr`d tab bjbdbct `f ahlabr kt`dhn cudgbr hs lrbktbr takc takt
pr`munbm gy kc bjbdbct `f j`wbr kt`dhn cudgbr.
i) Knn`rmhcl ` D`stjy,
Frbqubcny bdhttbm gy spbntrkj jhcb kc nakrkntbrhsthn Q-rky spbntrud hs
fucnth`c `f kt`dhn cudgbr. ( g)
7/23/2019 7.XRAY & BRAGG'S LAW
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NWX^]KJJ@LWKUAX QWKX & GWKLL^ JK\ ]AB@WX
Fhl.
frbqubcny `f spbntrkj jhcbkt`dhn cudgbr
g snrbbchcl n`cstkct.
\kvbjbclta
_Fhl 9^pbntrud `f nakrkntbrhsthn Q-rkysT
o) Hc nksb f nakrkntbrhsthn Q-rky spbntrud, spbntrud hs `gsbrvbm hc tbrds `f
sakrp pbkos.
j)
]ab pbko mbpbcms up`c, bcbrly jbvbjs `f kt`d kcm bcbrly jbvbj pkttbrc hs
nakrkntbrhsthn `f tab pkrthnujkr typb `f bjbdbct t` wahna tab lhvbc kt`d
gbj`cls t`
d) Ht dbkcs takt pbko mbpbcms `f tab tkrlbt dktbrhkj usbm, kcm hs hcmbpbcmbct
`f tab bcbrly f hcnhmbct bjbntr`c h.b. hcmbpbcmbct `f tab `pbrkthcl p`tbcthkj .
HH. N`cthcu`us Q-rky ^pbntrud 9
k)
K fbw fkst d`vhcl bjbntr`cs pbcbtrktb mbbp hct` hctbrh`r `f tab kt`ds `f tkrlbt
dktbrhkj kcm krb kttrkntbm gy tab kttrknthvb f`rnbs `f tabhr cunjbh.
g) Mub t` tabsb f`rnbs, tab bjbntr`cs lbt mbfjbntbm fr`d tabhr `rhlhckj pktas.
7/23/2019 7.XRAY & BRAGG'S LAW
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NWX^]KJJ@LWKUAX QWKX & GWKLL^ JK\ ]AB@WX
n) Hc tahs wky, tab bjbntr`cs krb mb-knnbjbrktbm h.b tabhr vbj`nhty hs rbmunbm kcm
tahs lhvbs rhsb hs j`ss `f bcbrly.
m)
]ahs j`ss `f bcbrly murhcl rbtkrmkth`c hs lhvbc `ff hc tab f`rd `f
bjbntr`dklcbthn rkmhkth`c h.b Q-rkys `f n`cthcu`us vkrhcl wkvbjbclta.
b)
]ab Q-rkys n`cshst `f n`cthcu`us rkclb `f frbqubcnhbs upt` dkxhdud
frbqubcny `r dhchdud wkvbjbclta
f) Jbt tab vbj`nhty b-nakclb fr`d vt` vmub t` mbfjbnth`c
J`ss `f bcbrly 4 a 4 dv dv --- (;)
l) ]ab ahlabst frbqubcny `f tab bdhttbm Q-rkys n`rrbsp`cmhcl t` tab p hct wabrb
bjbntr`c hs n`dpjbtbjy st`ppbm h.b
v 4 5 dv 4 ax 4 --- (7)
a)
\abc bhs knnbjbrktbm gy k p`tbcthkj V, tabc ohcbthn bcbrly hs ,
dv
4 bV ---(>)
4
416.6
.6 8
4=
--- (=)
7/23/2019 7.XRAY & BRAGG'S LAW
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NWX^]KJJ@LWKUAX QWKX & GWKLL^ JK\ ]AB@WX
bqc (=) sa`ws takt , kcm 4 5, V 4 wahna hs c`t
p`sshgjb.
h)
]abrbf`rb n`cthc`us Q-rky spbntrud, tabrb kjwkys bxhst k c`c Ybr` .
25 ov
=5ov
>5 ov
\kvbjbclta
_ Fhl 9 N`cthcu`us x-rky T
i)
Kjj nurvb stkrt whta c`c zbr` vkjub `f dhchdud wkvbjbclta nkjjbm .o)
Kjj tab nurvbs kttkhc k pbko kcm kftbr takt fkjjs `r lrkmukjjy.
j)
U`shth`c `f pbko mbpbcms up`c tab kppjhbm v`jtklb .
d) Ks `pbrkth`c v`jtklb hs hcnrbksbm, pbko sahft t`wkrms sa`rtbr wkvbjbclta.
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NWX^]KJJ@LWKUAX QWKX & GWKLL^ JK\ ]AB@WX
Mhffbrbcnb gbt
c
n`cthcu`us nakrkntbrhsthn Q-rky spbntrk. 9
N`cthcu`us Q-rky ^pbntrud Nakrkntbrhsthn pbntrud
h. Ht hs n`cthcu`us spbntrud h. Ht hs k jhcb spbntrud
hh. ^d``ta nurvb `gtkhcbm hh. Nbrtkhc sakrp pbko `gtkhcbm.
hhh.
Mbknnbjkrkth`c f bjbntr`c hhh. ]rkcshth`c `f `rghtkj bjbntr`c hs
rbsp`cshgjb fr`d ahlabr t` j`wbr `rght hs
rbsp`cshgjb.
hv.Fhl. sckp sa`t
Mhffrknth`c `f Q-Wkys 9
k)
Mhffrknth`c ;5 mbfhcbm ks gbcmhcl `f rky kr`ucm tab n`rcbr `gstknjb wa`sb
mhdbcsh`c krb `f tab `rmbr `f tab wkvbjbclta f rky .(dkob tahs tktbdbct
shdpjb)
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NWX^]KJJ@LWKUAX QWKX & GWKLL^ JK\ ]AB@WX
g)
Ks x-rky krb bjbntr`dklbcthn wkvbs iust ks jhlat wkvbs, tabydust bxahght
hctbrfbrbcnb kcm mhffrknth`c.
n) ]` stumy tab mhffbrbcnb `f x-rky, lrkthcl whta pbrh`m `f 7t` 2 hs rbquhrbm.
m) Ht hs bxtrbdbjy mhffhnujt t` prbpkrb lrkthcl whta suna k sdkjj pbrh`m `f `rmbr.
b)
Hc ;8;>,Dkx Jkub sullbstbm takt nrystkj dhlat knt ks k ckturkj tarbb
mhkdbcsh`ckj lrkthcl suna k sdkjj `rmbr ,gbnkusb hctbrpjkcbr mhstkcnb hs
pbrh`m kcm `f tab `rmbr `f fbw kclstr`ds ucht .
f)
Abcnb ,wabc x-rkys dkmb hcnhmbct up`c nrystkjs , wb lbt kc `rmbrbm,
rblujkr mhffrknth`c pkttbrc `r `cnb nkc sky takt Nrystkj knt ks tarbbmhdbcsh`ckj rbfjbnth`c lrkthcl whta Q-
rkys
GW LL^ J \9
K N
U
W
GUjkcb H
^ ]
Ujkcb HH
[
Ujkcb HHH
Ujkcb HV
7/23/2019 7.XRAY & BRAGG'S LAW
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NWX^]KJJ@LWKUAX QWKX & GWKLL^ JK\ ]AB@WX
k) Jbt us n`cshmbrbm k sbt kt pkrkjjbj jktthnb pjkcb `f nrystkj sbpkrktbm gy
mhstkcnb mkpkrt.g)
^upp`sb k ckrr`w gbkd kt Q-rkys `f wkvbjbclta ' gb hcnhmbct up`c tahspjkcb kt kc kcljb .Ks sa`wc hc fhlurb (-hs k ljkcnhcl kcljb)
n)
]ab gbkd whjj gb rbfjbntbm hc kjj mhrbnth`c gy tab kt`d `f vkrh`us kt`dhn pjkcbs.
m) Gbnkusb tab rbfrknthvb hcmbx `f dkttbr f nrystkj hs vbry cbkrjy bqukj t` uchty ,
abcnb tabrb hs prknthnkjjy c` gbcmhcl `f tab rkys bctbrhcl r jbkvhcl `cb nrystkj
.
b)
\abc k gbkd `f d`c`nar`dkthn Q-rkys fkjjs `c k nrystkj , bkna kt`d
gbn`dbs k s`urnb `f snkttbrhcl rkmhkth`cs.
f)
N`cshmbr k rky KG rbfjbntbm kt kt`d K hc tab mhrbnth`c GN fr`d pjkcb H kcm
kc`tabr rky U[ rbfjbntbm kt kc`tabr rky [ hc tab mhrbnth`c [W fr`d pjkcb HH .
l) C`w fr`d kt`d G, mrkw tw` pbrpbcmhnujkrs G^ & G] `c tab hcnhmbct rky
U[ & rbfjbntbm rky [W rbspbnthvb .
a) Ukta mhffbrbcnb gbtwbbc tw` rkys hs (^[ +[])
h)
]ab tw` rbfjbntbm rkys whjj gb hc paksb `r `ut `f paksb whjj mbpbcms up`c
pkta mhffbrbcnb .
i) \abc pkta mhffbrbcnb (^[ +[]) hs k dujthpjb `f wa`jb wkvb jbclta c,tabc tw` rkys whjj rbhcf`rnb bkna `tabr kcm pr`munb hctbcsb sp`t .
^[ + [] 4 c--- (;)
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NWX^]KJJ@LWKUAX QWKX & GWKLL^ JK\ ]AB@WX
Fr`d tab fhl ?
G^[ & G][
shc 4 4 shc 4
4
^[ 4 m shc [] 4 m shc
^[ + [] 4 c
m shc + m shc 4 c
--- (\abrb c 4 ;, 7, >, ..)7m shc 4 c
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NWX^]KJJ@LWKUAX QWKX & GWKLL^ JK\ ]AB@WX
GWKLL^ UBN]W@DB]BW
9
Q-rkys n Nrystkj
^
;
^
7
]ud tkgjb ^
>
^
=
H`chzkth`c
nabdgbr
Fhl. Grklls pbntr`dbtbr
k) ]ab snabdkthn krrkclbdbct `f Grklls spbntr`dbtbr hs sa`wc hc fhl .
g) K d`c`nar`dkthn Q Wky gbkd `gtkhcbm fr`d Q-Wky tugb hs dkmb t` pksstar`ula sjht ^;&^7wahna krb dkmb `f up `f jbkm.
n)
]ab gbkd dkmb t` fkjj `c k nrystkj N (usukjjy Cknj `r ONJ) d`uctbm `c k
nbctrb `f nhrnujkr turc tkgjb `f spbntr`dktbr.
m)
]ab rbfjbntbm Q-rkys krb n`jjbntbm gy h chskth`c nabdgbr ,tab turc tkgjb hs
r`tktbm thjj wb lbt sakrp hcnrbksb hc tab hctbcshty .
b) ]ab summbc hcnrbksb hc tab hctbcshty `f Q- Wky sullbstbm takt Grklls jkw hsskthsfhbm kt lhvbc kcljb `f hcnhmbct gbkd .
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NWX^]KJJ@LWKUAX QWKX & GWKLL^ JK\ ]AB@WX
f)
]ab pbko hc h`chskth`c nurrbct wahna rbprbsbct tab hctbcshty nnurs d`rb
takc `cb ks hs vkrhbm gbnkusb Grklls jkw stktbs 9
7m shc 4c --- (wabrb c 4;,7,> .)
\b akvb ;, 7,>
l)
Ht tab hctbcshty (`r h ckskth`c nurrbct ) hs pj`ttbm klkhcst ljkcnhcl kclbj tab wb
lbt lrkpa ks sa`wc hc f`jj`whcl fhl .