lecture15 - nptelnptel.ac.in/courses/103108100/module3/module3.pdf · lecture15 - nptel ... 5

106
1 ! #$%& '()*$+,-+.-+ ,/+-0$*1+0$&

Upload: lamnhi

Post on 02-Jul-2019

251 views

Category:

Documents


1 download

TRANSCRIPT

1

!"#$%&"'()*$+,-+.-+",/+-0$*1+0$&

2

!2 3456"437"6893:";4<7=7>?:8"7=7@:39A4?>7:B@"

34CB4:B9>6"D39CE@7C"F5":87"C7@7=734:B9>"9G"8B?8"7>73?5"

7=7@:39>6"93"F5"7=7@:39>B@":34>6B:B9>6"9G"7=7@:39>6"B>"

:87"B>>73"93FB:4=6 9G"4:9A6H

!2 3456"84<7"4";4<7=7>?:8"34>?7"9G"IJ2K %""":9"IJJ"%"""H"

-9><7>:B9>4="!2 345"6D7@:396@9D5"B6"=43?7=5"@9>GB>7C"

:9"JHI"%"":9"LK"%""H"

J

J

J

J

3

!2 3456"437"?7>734:7C"F5M

IH N9AF43CB>?"4"A7:4=":43?7:";B:8"4"F74A"9G"8B?8"

7>73?5""7=7@:39>6H

LH +OD96B>?"4"6EF6:4>@7":9"4"D3BA435"F74A"9G""""""""""""

!#3456":9"?7>734:7"4"67@9>C435"F74A"9G"!#3456"9G"

=9;73"7>73?5H

PH )6B>?"4"34CB94@:B<7"69E3@7"7AB::B>?"!#3456"CE3B>?"

B:6"C7@45"D39@766"4>C

QH '39A"4"65>@839:39>"34CB4:B9>"69E3@7H

4

R>"4>"!#345":EF7"F9:8"@9>:B>EEA"4>C"=B>7"6D7@:34"437"

7AB::7CH"+=7@:39>6"437""D39CE@7C"4:"4"874:7C"@4:89C7

4>C"4@@7=734:7C":9;43C"4"A7:4="4>9C7"S:43?7:T"F5"4"

D9:7>:B4="CBGG737>@7"9G"IJJ"UVH")D9>"@9==BCB>?";B:8":87"

4>9C7W"D43:"9G":87"7>73?5"9G":87"B>@BC7>:"F74A"B6"

@9><73:7C"B>:9"!#3456H

087"@9>:B>EEA"!#345"6D7@:3EA"7O8BFB:6"4";7=="C7GB>7C"

6893:";4<7=7>?:8"=BAB:"SJT";8B@8"B6"4"@8434@:73B6:B@"9G"

:87"4DD=B7C"<9=:4?7W"B3376D7@:B<7"9G":87">4:E37"9G":87"

:43?7:H

5

-*.0R.))1"$%XR%0R*."'$*1"%."!"2 $%&"

0)N+"YR0Z"%"0).[,0+."0%$[+0

6

087"@9>:B>EEA"34CB4:B9>"376E=:6"G39A"@9==B6B9>6"

F7:;77>":87"7=7@:39>6"4>C"4:9A6"9G":87":43?7:H"+4@8"

@9==B6B9>"376E=:6"B>":87"7AB66B9>"9G"4"D89:9>H"087"

7>73?5"9G":87"D89:9>"B6"7\E4=":9":87"7>73?5"=966"9G":87"

7=7@:39>H"%">EAF73"9G"@9==B6B9>6";B:8"C7@3746B>?"

7>73?5"A45"9@@E3"G93"74@8"7=7@:39>"46"B:"F9E>@76"G39A"

9>7"4:9A"B>:9"4>9:873"H"087"A4OBAEA""D89:9>"7>73?5"

?7>734:7C"@93376D9>C6":9":87"B>6:4>:4>79E6"

C7@7=734:B9>"9G":87"7=7@:39>":9"]739"UB>7:B@"7>73?5"B>"4"

6B>?=7"@9==B6B9>H"

7

087"UB>7:B@"7>73?5"9G"4==":87"7=7@:39>6"@4>"F7"

7OD37667C"46":87"XE4>7"# ZE>:"=4;W

V7 ^""8""""""^""8@ _"

;8737"<"B6":87"4DD=B7C"D9:7>:B4=W"""""""B6":87"G37\E7>@5H

08E6":87"UB>7:B@"7>73?5"B6":87"D39CE@:"9G"4@@7=734:B>?"

<9=:4?7"4>C":87"@843?7"9>":87"7=7@:39>"4>C"""""""B6":87""

A4OBAEA"9G":87"34CB4:B9>":84:"@4>"F7"D39CE@7CH"

0

0

0

8

!#345"=B>7"6D7@:34"376E=:"G39A"7=7@:39>B@":34>6B:B9>6"B>"

:87"B>>73A96:"4:9AB@"93FB:4=6H"0875"9@@E3"B>":87"=9>?73"

;4<7=7>?:8"34>?7"9G"Q"# `"%"""H"087"=B>7"6D7@:34"9@@E3"

G93"4==":87"7=7A7>:6"84<B>?"4:9AB@">EAF736"9G"IL"4>C"

4F9<7H"+=7A7>:6"84<B>?"4:9AB@">EAF736"=766":84>"LP"

689;"9>=5":;9"=B>76"@4==7C"46"a"673B76"4>C"C76B?>4:7C"

46"a 4>C"a H"08767"437"9G"6893:";4<7=7>?:86H"'93"

7O4AD=7"a"673B76"G93":E>?6:7>":43?7:"4DD743"4:"JHIb"

4>C"JHLI%H"J

J

9

(R.+",/+-0$)1"YR0Z"%"1*(&NX+.)1"0%$[+0

a a

09""09

IK""""Pc

PKUV

$7=4:B<7"B>:7>6B:5

IL

b

Q

J

JHL"""""""""JHQ"""""""""JH`""""""""""JHb"""""""""""""IHJ

;4<7=7>?:8W"%9

10

+=7A7>:6"84<B>?"4:9AB@">EAF736"A937":84>"LP"689;"("

673B76";8B@8"437"4=69"C76B?>4:7C"46"IW"

IH""08737"B6"4"

:837689=C"<9=:4?7"G93"74@8"7=7A7>:""F7=9;";8B@8"=B>7"

6D7@:34"C9">9:"4DD743H"'93"7O4AD=7W"F7=9;"KJ"UV"W">9"

=B>7"6D7@:34"B6"9F:4B>7C"G93"A9=5FC7>EAH"Z9;7<73"

4F9<7"cJ"UV"B:"D39CE@76"=B>7"6D7@:34H

11

+=7A7>:" %:9AB@"

>EAF73

a"# ,73B76""

I" I

("# ,73B76""

I" I

Na 11 11.909 11.617 - -

K 19 3.742 3.454 - -

Cr 24 2.290 2.085 21.714 21.323

Rb 37 0.926 0.829 7.318 7.075

Cs 55 0.401 0.355 2.892 2.683

W 74 0.209 0.184 1.476 1.282

U 92 0.126 0.111 0.911 0.720

!#345"7AB66B9>"=B>76"G93"69A7":5DB@4="7=7A7>:6

12

196=75"689;7C":84:":8737"B6"4"=B>743"37=4:B9>68BD"

F7:;77>":87"6\E437"399:"9G"G37\E7>@5"G93"4"?B<7>"a"93"("

=B>7"4>C":87"4:9AB@">EAF73"46"689;>"F7=9;H

@_ ^""4"S"d"# TL

13

087"6893:";4<7=7>?:8"a"673B76"B6"D39CE@7C";87>":87"

8B?8"7>73?5"7=7@:39>"F74A"37A9<76"4>"7=7@:39>"G39A"

:8967"93FB:4=6 >74376:":9":87">E@=7E6"9G":87":43?7:"

4:9AH"08B6"D39CE@76"4>"7O@B:7C"B9>";8B@8"7AB:6"4"

\E4>:4"9G"34CB4:B9>"46"7=7@:39>6"G39A"9E:73"93FB:4=6

E>C73?9":34>6B:B9>6":9"GB==":87"<4@4>@5H

a"673B76"=B>76"43B67"G39A":34>6B:B9>6"F7:;77>"8B?873"

7>73?5"=7<7=6"4>C":87"a"687==H

("673B76"9G"=B>76"376E=:6";87>"4>"7=7@:39>"B6"=96:"G39A"

:87"67@9>C"D3B>@BD4="\E4>:EA"=7<7="CB37@:=5"93"G39A":87"

:34>6B:B9>"9G"4>"("7=7@:39>":9":87"a"=7<7=H

14

/%$0R%("+.+$[&"(+V+("XR%[$%1"-%),R.["

!#$%&,"/$*X)-0R*.

15

R>":8B6"GB?E37W":87"4:9AB@"7>73?5"=7<7=6"437"B>":87"

=9?43B:8AB@"6@4=7H"087"7>73?5"CBGG737>@7"F7:;77>"IWL

4>C"IW"

L437"69"6A4==":84:":875"4DD743"46"6B>?=7"=B>76H

08B6"7>73?5"=7<7="CB4?34A"B6"4DD=B@4F=7":9"4>5"7=7A7>:"

;B:8"6EGGB@B7>:"7=7@:39>6":9"D73AB:":87">EAF73"9G"

:34>6B:B9>6"689;>H

087";4<7=7>?:86"9G"@8434@:73B6:B@"!#345"7AB66B9>6"

437"B>C7D7>C7>:"9G":87"@87AB@4="6:4:7"9G":87"7=7A7>:"46

:87":34>6B:B9>6"C9">9:"B><9=<7"F9>CB>?"93">9>F9>CB>?""

7=7@:39>6H"08E6":87"D96B:B9>"9G"a =B>7"G93":E>?6:7>"93"

4>5"7=7A7>:"B6"64A7";87:873"B:"B6"4>"9OBC7W"6E=D8BC7 93"

DE37"A7:4="93"4>"93?4>B@"@9AD=7OH

16

N467C"9>":87"D39D73:B76"9G"!#3456W"4">EAF73"9G"4>4=5:B@4="

A7:89C9=9?B76"84<7"F77>"C7<7=9D7C"9<73":87"57436H"08767"

B>@=EC7"M

4T !#345"7AB66B9>"6D7@:396@9D5"S!+,T

FT %E?73"7AB66B9>"6D7@:396@9D5"S%+,T

@T !2345"G=E9376@7>@7"6D7@:396@9D5"S!',T

CT +=7@:39>"6D7@:396@9D5"S+,-%T

7T !#345"4F693D:B9>

GT !#345"CBGG34@:B9>

17

!#$%&"%.%(&0R-%("1+0Z*X,

!"# 345"7AB66B9> %E?73"7AB66B9>

!#345"G=E9376@7>@7 +=7@:39>"6D7@:396@9D5

!#345"4F693D:B9>" !"# 345"CBGG34@:B9>

18

!#345"4F693D:B9>"4>C"7AB66B9>"6D7@:34"437"\EB:7"

6BAD=7"F7@4E67":875"@9>6B6:"9G"<735"G7;"=B>76H"!#345"

7AB66B9>"6D7@:3EA"9G"4>"7=7A7>:"A45"F7"9F:4B>7C"F5"

E6B>?":87"64AD=7"B:67=G"46":87":43?7:"7=7A7>:H"Z9;7<73"

:8B6"4DD394@8"B6">9:"<735"@9><7>B7>:"G93"4==":5D76"9G"

64AD=76H

R>6:74CW"7O@B:4:B9>"@4>"F7"4@@9AD=B687C"F5"B334CB4:B>?"

:87"64AD=7";B:8"4"F74A"9G"!#3456"G39A"4>""!#345"

:EF7"93"4"34CB94@:B<7"69E3@7H"R>":8B6"A7:89CW"4==":87"

7=7A7>:6"B>":87"64AD=7"437"7O@B:7C"F5":87"4F693D:B9>"9G

:87"D3BA435"F74A";8B@8"7AB:":87B3"9;>"@8434@:73B6:B@"

G=E9376@7>@7"!#3456H

19

08E6"!$'"B6"4"D9;73GE=":99="G93":87"\E4=B:4:B<7"SD466"G4B=":76:T

4>C"\E4>:B:4:B<7"76:BA4:B9>"9G"4=="FE:":87"=B?8:76:"7=7A7>:6"

84<B>?"4:9AB@">EAF736"?374:73":84>":84:"9G"9O5?7>"SebTH

!$'"B6"4">9>"C76:3E@:B<7":7@8>B\E7"46"4?4B>6:"A96:"9G"

:87"9:873"7=7A7>:4=":7@8>B\E76H

08737"437":;9":5D76"9G"!2345"G=E9376@7>@7"6D7@:39A7:736"M"

;4<7=7>?:8"CB6D736B<7"!#345"G=E9376@7>@7"SYX!$'T"4>C"

7>73?5"CB6D736B<7"!#345"G=E9376@7>@7"S+X!$'T"

6D7@:39A7:736H

RAD93:4>:"B>6:3EA7>:"@9AD9>7>:6"9G"!$'"B>@=EC7"4"69E3@7W"

4":34>6CE@73W"4"6B?>4="D39@76693"4>C"374C"9E:H

20

R.,0$)1+.0%0R*."'*$"!$'

21

,*)$-+,

IH -99=BC?7":EF7

%>"!#345":EF7"B6"4"8B?8"<4@EEAW"674=7C"9GG":EF7"

@9>:4B>B>?"4"874:7C"GB=4A7>:"@4:89C7"SYT"4>C"4"K"O"IJ"

AA"874<5"F=9@U"9G"@9DD73";B:8"4"A7:4=":43?7:"D=4:7C"

93"7AF7CC7C"9>"B:6"6E3G4@7H""043?7:"A4:73B4=6"B>@=EC7"

:E>?6:7>W"@839ABEAW"@9DD73W"A9=5FC7>EAW"389CBEAW"

6@4>CBEAW"6B=<73W"B39>"4>C""@9F4=:H

,7D434:7"@B3@EB:6"437"E67C":9"874:":87"GB=4A7>:"4>C":9"

4@@7=734:7":87"7=7@:39>6":9":87":43?7:H"087"874:73"

@B3@EB:"@9>:39=6":87"B>:7>6B:5"9G":87"7AB::7C"!#3456"4>C"

:87"4@@7=734:B>?"<9=:4?7"C7:73AB>76":87B3"7>73?5"93"

;4<7=7>?:8H"N9:8"@E337>:"4>C"<9=:4?7"AE6:"F7"6:4F=7"

ED":9"JHIfH

22

!#345"?7>734:B9>"F5":8B6"A7:89C"B6"F46B@4==5"4>"

B>7GGB@B7>:"D39@766"4>C"AE@8"7>73?5"B6";46:7C"46"874:H"

Z7>@7"@99=B>?"9G":87"4>9C76"B6">7@766435H

19C73>"7\EBDA7>:6""7AD=95"8B?8=5"67>6B:B<7"

:34>6CE@736"4>C"87>@7"@99=B>?"B6">9:">7@766435H

087"!#345"F74A"D46676"9E:"9G":87":EF7":839E?8"4":8B>"

F735==BEA";B>C9;"93"4"6D7@B4="?=466H"'93";4<7=7>?:8"9G"

`"# cJ""%"W"E=:34":8B>"SI AT"4=EAB>EA"93"D43=9CB9> GB=A6"

437"E67C":9"B69=4:7":87":EF7H

J

23

087"@E337>:"B6"37?E=4:7C"F5"A9>B:93B>?":87"!#345":EF7

X-"@E337>:"4>C"@9>:39==B>?":87"GB=4A7>:"<9=:4?7H"Y87>""

:87"GE==";4<7"B6"37@:BGB7CW":87"<9=:4?7"374@876"B:6"D74U"

<4=E7"ILJ":BA76"D73"67@9>C"4>C"D736B6:6"G93"9>=5"4"

6A4=="G34@:B9>"9G":BA7H

Y87>":87":EF7"B6"9D734:7C"4:"KJUVW":87"?4B>"B6":;9"G9=C"

G93"7=7A7>:6"ED":9"%:H".EAF73"PK"SN3T"4>C"B>@374676":9"

G9E3"G9=C"4:"%:H".EAF73"K`"SN4TH

.93A4==5"!#345":EF76"437"9D734:7C"F7:;77>"KJ"# `J"UV"

FE:">9;"4"C456":EF76";B:8"IJJ"UV"437"4<4B=4F=7H

24

,-Z+1%0R-"*'"%."!2$%&"0)N+

25

$%XR*R,*0*/+,

%"<43B7:5"9G"34CB94@:B<7"6EF6:4>@76"6E@8""46

7:@HW"437

E67C"46"69E3@76"B>"!$'H",9A7"7=7A7>:6"D39CE@7"

6BAD=7"=B>7"6D7@:34"4>C"9:8736"D39CE@7"4"@9>:B>EEAH"%"

?B<7>"34CB9B69:9D7";B=="F7"6EB:4F=7"G93"7O@B:B>?"4">EAF73"

9G"7=7A7>:6H"'93"7O4AD=7"4"69E3@7"?B<B>?"!#345"B>"

JHPJ"# JHQc"%""B6"6EB:4F=7"G93"!$'"6:ECB76"G93"4=="7=7A7>:6"

ED":9"6B=<73H"087"67>6B:B<B:5"BAD39<76"46":87";4<7=7>?:8"9G"

:87"69E3@7"=B>7"4DD394@876":87"4F693D:B9>"7C?7H

PbAlPmICdCoFeH 21082

14761

12553

10948

5727

551

33 ;, , , , ,

J

26

,+-*.X%$&"'()*$+,-+.-+",*)$-+,

R>"69A7"4DD=B@4:B9>6"4>"!#345":EF7";B:8":E>?6:7>"

:43?7:"B6"E67C":9"7O@B:7"a 4>C"a =B>76"9G"1*H"

087"376E=:B>?"G=E9376@7>@7"6D7@:3EA";9E=C"@9>:4B>"

9>=5"=B>7"6D7@:34";8B@8"@4>"F7"E67C"G93":87"7O@B:4:B9>"

9G":87"4>4=5:7H

27

!#$%&"'R(0+$,

R>"69A7"4DD=B@4:B9>6W"O#345":EF76";B:8">4339;"

;4<7=7>?:8"34>?7"437"37\EB37CH"N9:8"GB=:736"4>C"

A9>9@839A4:936 437"E67C"G93":8B6"DE3D967H

dB3@9>BEA"GB=:736"9G"JHJI"@A":8B@U>766"437"6EB:4F=7":9

B69=4:7"a =B>7H"R:"GB=:736"A96:"9G":87"@9>:B>EEA"4>C"a

=B>7H

,7<734="9:873"GB=:736"84<7"4=69"F77>"C7<7=9D7C"G93":8B6"

DE3D967H"gEB:7"9G:7>W":8B>"6:3BD6"9G"9:873"A7:4=6"437"

4=69"7AD=957C"G93":8B6"DE3D967H

28

'R(0+$,"'*$"!2$%&,

29

!#$%&"1*.*-Z$*1%0*$,

!#345"A9>9@839A4:936 @9>6B6:"9G"4"D4B3"9G"F74A"

@9==BA4:936H"*>7"673<76"46"4"6=B:"4>C":87"9:873"673<76"

46":87"CB6D736B>?"4?7>:H"

087"=4::73"B6"4"6B>?=7"@356:4="A9E>:7C"9>"4"?9>B9A7:73

93"4"39:4:B>?":4F=7":84:"D73AB:6":87"C7:73AB>4:B9>"9G":87"

4>?=7" F7:;77>":87"@356:4="G4@7"4>C":87"@9==BA4:7C"

B>@BC7>:"F74AH

N34??h6"7\E4:B9>"689;6":84:"G93"4>5"?B<7>"4>?E=43"

67::B>?"9G":87"?9>B9A7:73 9>=5"4"G7;";4<7=7>?:86"437"

XBGG34@:7C"4@@93CB>?":9":87"7\E4:B9>W

> ^"L"C"6B>"

30

09"D39CE@7"4"6D7@:3EAW":87"7OB:"F74A"4>C":87"C7:7@:93"

AE6:"F7"A9E>:7C"9>"4"67@9>C":4F=7":84:"39:4:76"4:"

:;B@7":87"34:7"9G":87"GB36:H"Z7>@7";87>":87"@356:4="

39:4:76"F5"4>"4>?=7" :87"C7:7@:93"39:4:76"F5"L H

19C73>"!2345"A9>9@839A4:936 84<7"AB@39D39@76693"

@9>:39==7C"A9:936":9"C3B<7":87"@356:4="4>C":87"C7:7@:93"

B>C7D7>C7>:=5";B:89E:"4"?743"F467C"A7@84>B@4="

@9>>7@:B9>H"Z7>@7":875"@4>"6@4>"34DBC=5"4:":87"34:7"9G"

LQJJ_AB>H

31

%."!2$%&"1*.*-Z$*1%0*$"%.X"

X+0+-0*$"%$$%.[+1+.0

32

087"@9==BA4:936"B>"4>"!2345"A9>9@839A4:936 @9>6B6:"9G"

4"673B76"9G"@=967=5"6D4@7C"A7:4="D=4:76":84:"4F693F"4=="

:87"34CB4:B9>6"7O@7D:":87"D434==7="F74A6H

!234CB4:B9>"=9>?73":84>"L%"B6"4F693F7C""F5":87"

4:A96D873B@"?4676H"08737G937"BG"=9>?73";4<7=7>?:8

!23456"437"37\EB37CW":87"64AD=7"@9AD43:A7>:"AE6:"F7"

G=E687C";B:8"87=BEA"93"B:"AE6:"F7"7<4@E4:7C"F5"

DEADB>?H

YB:8"G=4:"@356:4=6W"ED":9"iif"9G":87"!234CB4:B9>"B6"

CB<73?7>:";8B@8"B6"4F693F7C"F5":87"@9==BA4:936H"087"

=966"@4>"F7"AB>BAB]7C"GE3:873"F5"IJf"E6B>?"4"@E3<7C"

@356:4="6E3G4@7H"087"@E3<7C"6E3G4@7"4=69"4@@9AD=B6876"

:87"G9@E6B>?"9G":87"CB<73?7>:"F74A"G39A":87"69E3@7"9>"

:87"7OB:"@9==BA4:93H

J

33

XR''$%-0R.["-$&,0%("/$*/+$0R+,

-356:4=

(4::B@7

,D4@B>?

CW

Y4<7=7>?:8

34>?7W"4""""""""""""""""""""""""""""""""""""""""

A4O" AB>

XB6D736B9>W"J_

4:"A4O

4:""AB>

Topaz 1.356 2.67 0.24 2.12 0.37

LiF 2.014 3.97 0.35 1.43 0.25

NaCl 2.820 5.55 0.49 1.02 0.18

EDDTb 4.404 8.67 0.77 0.65 0.11

ADPc 5.325 10.50 0.93 0.54 0.09

0A

0A

0A

4N467C 9>":87"466EAD:B9>":84:":87"A746E34F=7"34>?7"9G"L B6"G39A"I`JJ"

G93"A4O"

:9"IJ` G93"AB>

F+XX0 ^""+:85=7>7CB4AB>7 C2:43:34:7

@%X/ ^""%AA9>BEA"CB85C39?7> D896D84:7

34

087"E67GE=";4<7=7>?:8"34>?7"G93"4"@356:4="B6"

C7:73AB>7C"F5"B:6"=4::B@7"6D4@B>?"jC"h 4>C":87"C7:7@:93"

D39F=7A6";87>"L B6""AE@8"=766":84>"IJJH"08B6"

84DD7>6";87>" B6"4DD394@8B>?"]739"93"IbJJH")>C73"

:8767"@9>CB:B9>6W"D9=5@839A4:B@"34CB4:B9>"6@4::737C"

G39A":87"@356:4="6E3G4@7"F7@9A76"<735"8B?8H"08737G937"

9>=5"ED":9"I`JJ SL T"437"7AD=957C"B>"!2345";93UH

-356:4=6";B:8"=43?7"@356:4="=4::B@7"6D4@B>?"SCTW"6E@8"46"

4AA9>BEA"CB85C39?7> D896D84:7"9GG73"F7::73"@9>:39="

9<73":87"6@4::73""@9>:39="FE:"B:"376E=:6"B>"=9;73"

CB6D736B9>"4=69H

35

XBGG737>:B4:B>?"N34??h6"7\E4:B9>W";7"?7:W

C >

C LC"@96

Z7>@7"C _C :87"A746E37"9G"CB6D736B9>"B6"B><7367=5"

D39D93:B9>4=":9"CH"Z7>@7"=9;"CB6D736B9>"D398BFB:6":87"

E67"9G"6893:73";4<7=7>?:86H"Z737":9D4]"93"(B' AE6:"F7"

6EF6:B:E:7CH

^

36

!2$%&"X+0+-0*$,

!2345"C7:7@:936"437"E6E4==5"9D734:7C"46"D89:9>"

@9E>:736H"R>":8B6"A9C7W"B>CB<BCE4="DE=676"9G":87"@843?7"

437"D39CE@7C"46"\E4>:4"9G"34CB4:B9>";8B@8"437"

4F693F7C"F5":87":34>6CE@73"4>C"@9E>:7CH"08B6"37\EB376"

34DBC"376D9>67":BA76"G93":87":34>6CE@73"46";7=="46":87"

6B?>4="D39@76693H"08B6":7@8>B\E7"B6"E67GE="G93"=9;"

B>:7>6B:5"!2345"F74A6H

37

[%,"'R((+X"0$%.,X)-+$,

Y87>"!23456"D466":839E?8"4>"B>73:"?46"6E@8"46"43?9>W"O7>9>"

93"U35D:9>W"4"=43?7">EAF73"9G"D96B:B<7"B9>6"4>C"7=7@:39>6"437"

D39CE@7C"G93"74@8"!2345"\E4>:EAH"08737G937W"@9>CE@:B<B:5"9G"

:87"?4676"B>@374676"G39A":8B6"D87>9A7>9>H"R9>B]4:B9>"@84AF736W"

D39D93:B9>4="@9E>:736"4>C"[7B?73":EF76"437"E67C":9"A746E37":8B6"

7>84>@7C"@E337>:H

%":5DB@4="?46"GB==7C":34>6CE@73"B6"689;>"8737H"087"34CB4:B9>"

7>:736":87"@84AF73":839E?8"4":34>6D437>:";B>C9;"9G"AB@4"93"

F735==BEA"93"4=EAB>EA"93"A5=43 6877:H"+4@8"D89:9>"9G"

!234CB4:B9>"B>:734@:6";B:8"9>7"4:9A"9G"43?9>"4>C"@4E676"B:":9"

=9967"9>7"9G"B:6"9E:73"7=7@:39>6H"087"D89:9"7=7@:39>"=9676 B:6"

UB>7:B@"7>73?5"F5"B9>B]B>?"67<734="8E>C37C"4CCB:B9>4="43?9>"

4:9A6H"087"7=7@:39>6"A9<7":9;43C":87"@7>:34=";B37"4>9C7"4>C"

43?9>"@4:B9>6 A9<7":9;43C6":87"@5=B>C3B@4="A7:4="@4:89C7H

38

[%,"'R((+X"X+0+-0*$

39

%1/(R'R-%0R*."*'"X+0+-0*$",R[.%(,

40

08B6"GB?E37"689;6":87"7GG7@:"9G"4DD=B7C"<9=:4?7"9>":87"

>EAF73"9G"7=7@:39>6"374@8B>?":87"4>9C7"G93"74@8"D89:9>H"

087"37?B9>""VI# V

L"W689;6":87">EAF73"9G"7=7@:39>6"

374@8B>?":87"4>9C7";8B@8"B6"G4B3=5"@9>6:4>:"G93"74@8"D89:9>H"

R>":87"37?B9>"VP2VQW:87">EAF73"9G"7=7@:39>6"B>@374676"

34DBC=5";B:8"4DD=B7C"<9=:4?7H"Z737"67@9>C435"B9>"D4B3"

D39CE@:B9>"9@@E36"CE7":9":87"@9==B6B9>6"F7:;77>":87"

4@@7=734:7C"7=7@:39>6"4>C"?46"A9=7@E=76H"08737G937W"E>C73"

:8767"@9>CB:B9>6"4AD=BGB@4:B9>"9G":87"@E337>:"9@@E36H"

087"37?B9>"VK2V`689;6":84:"4AD=BGB@4:B9>"9G":87"7=7@:3B@4="

BADE=67"B6"7>93A9E6"FE:":87"@E337>:"B6"B>C7D7>C7>:"9G":87"

:5D7"4>C"7>73?5"9G":87"B>@9AB>?"34CB4:B9>H"087"@E337>:"B6"

4@:E4==5"?9<73>7C"F5":87"?79A7:35"4>C"?46"D3766E37"9G":87"

:EF7H"08B6 37?B9>"B6"U>9;>"46":87"[7B?73"37?B9>H

41

,-R.0R((%0R*."-*).0+$,

%"6@B>:B==4:B9>"@9E>:73"@9>6B6:6"9G"4":34>6D437>:"@356:4="

9G"69CBEA"B9CBC7"@9>:4B>B>?"JHLf":84==BEA"B9CBC7"

684D7C"B>":87"G93A"9G"4"@5=B>C73"684D7C"POQ"B>@8"B>"

74@8"CBA7>6B9>H"*>7"6E3G4@7"B6"D=4>7";8B@8"G4@76":87"

@4:89C7"9G"4"/10H"%6":87"B>@9AB>?"34CB4:B9>"D46676"

:839E?8":87"@356:4=W"B:6"7>73?5"B6"=96:":9":87"6@B>:B==4:93

;8B@8"B6"6EF67\E7>:=5"37=7467C"B>":87"G93A"9G"D89:9>6"

9G"G=E9376@7>@7"34CB4:B9>H

087"G=46876"9G"=B?8:"D39CE@7C"437":34>6AB::7C":9":87"

D89:9@4:89C7";8B@8"B>":E3>"D39CE@7"4>"7=7@:3B@4="

DE=67":84:"@4>"F7"4AD=BGB7C"4>C"@9E>:7C.

42

!2$%&"'()*$+,-+.-+"1+0Z*X,

%6"7OD=4B>7C"743=B73":8737"437":;9":5D76"9G"!$'"

B>6:3EA7>:6M"Y4<7=7>?:8"CB6D736B<7"SYX!$'T"4>C"

7>73?5"CB6D736B<7"S+X!$'TH

R>"YX!$'"4>"!2345"F74A"G39A"4"34CB94@:B<7"69E3@7"B6"

@9==BA4:7C"4>C"CB6D7367C"B>:9"B:6"@9AD9>7>:"

;4<7=7>?:86H"N9:8"6B>?=7"@84>>7="S67\E7>:B4=T"93"

AE=:B@84>>7= S6BAE=:4>79E6T"C7:7@:B9>"656:7A6"437"

7AD=957CH"

43

R>"6B>?=7"@84>>7="B>6:3EA7>:6W":87"@356:4="4>C":87"

:34>6CE@73"437"67:"4:"6D7@BGB@"4>?=76"S k L 376D7@:B<7=5T

4>C":87"@9E>:B>?"D39?376676"E>:B="6EGGB@B7>:"@9E>:6"437"

9F:4B>7C"G93"D37@B67"A746E37A7>:6H"087"B>6:3EA7>:"@4>"

F7"4E:9A4:7C":9"@9<73":87"7>:B37"P`JJ -H"R>"6E@8"

B>6:3EA7>:":87"A9<7A7>:"9G":87"@356:4="4>C"C7:7@:93""437"

65>@839>B]7C"4>C":87"9E:DE:"B6"@9>>7@:7C":9":87"C4:4"

4@\EB6B:B9>"656:7AH

087"!2345"69E3@76"E67"@839ABEA"G93"=9>?";4<7=7>?:86"

4>C":E>?6:7>":43?7:"G93"6893:";4<7=7>?:86H",E@8"

B>6:3EA7>:6"@96:"439E>C"LK"=4U8 $ED776H

44

1E=:B@84>>7= B>6:3EA7>:6"437"@96:=B73"Se"IKJWJJJlTH"0875"

437"E67GE="G93":87"C7:73AB>4:B9>"9G"ED":9"LQ"7=7A7>:6""

6BAE=:4>79E6=5H"R>":8767"B>6:3EA7>:6W"B>CB<BCE4="

@84>>7=6"9G"4>"4DD39D3B4:7"@356:4="4>C"4"C7:7@:93"437"

4334>?7C"34CB4==5 439E>C"4>"!2345"69E3@7"4>C"64AD=7"

89=C73"H"087"@356:4=6"G93"A96:"9G":87"@84>>7=6"437"GBO7C"

4:"4>"4DD39D3B4:7"4>?=7"G93"4"?B<7>"4>4=5:7 =B>7H

'93"7<735"7=7A7>:":9"F7"C7:73AB>7C":8737";B=="F7"4"

C7CB@4:7C":34>6CE@73W"4AD=BGB73W"DE=67"87B?8:"C7:7@:93"

4>C"@9E>:73"93"B>:7?34:93H"08767"B>6:3EA7>:6"437"

7\EBDD7C";B:8"4"@9ADE:73"G93"D37@B67"B>6:3EA7>:"

@9>:39=W"C4:4"D39@766B>?"4>C"CB6D=45"9G"4>4=5:B@4="

376E=:6H"087"4>4=56B6"B6"E6E4==5"@9AD=7:7C";B:8B>"4"G7;"

67@9>C6":9"4"G7;"AB>E:76H

45

+.+$[&"XR,/+$,RV+"!$'

+X!$'"846"4"D9=5@839A4:B@"69E3@7"6E@8"46"4>"!2345"

69E3@7"93"4"34CB94@:B<7"A4:73B4=W"4"64AD=7"89=C73W"4"

67AB@9>CE@:93"C7:7@:936"4>C"<43B9E6"7=7@:39>B@"

@9AD9>7>:6"G93"7>73?5"CB6@3BAB>4:B9>H

087"4>4=5:B@4="A7:89C9=9?5"B6"<735"6BAD=7H"08737"437"

>9"A9<B>?"D43:6"4>C">9"@9==BA4:936"93"@356:4="

CBGG34@:93H"08737G937":87"7>73?5"374@8B>?":87"C7:7@:93"

B6"IJJ":BA76"A937":84>"YX!$'"B>6:3EA7>:6H"Z7>@7

=9;"D9;73"!2345":EF76"93";74U73"34CB94@:B<7"A4:73B4=6"

@4>"F7"E67C"46"34CB4:B9>"69E3@76";8B@8"437"@96:"

7GG7@:B<7"4>C"A937"64G73":9"E67"H

46

S4T",@87A4:B@"C76B?>"9G"+X!$' SFT"1436"1B66B9>"$9<73"874C

47

087"67>693"874C"B>":87"39<73"@9>:4B>6"`"@E3BEA2LQQ"

69E3@76":84:"7AB:6"!23456"4>C"KHbI"17V D43:B@=76H

!2345"7AB66B9>"B6"6:BAE=4:7C"F5"F9AF43CA7>:"F5" 4>C"

9:873"6EF4:9AB@"D43:B@=76"6E@8"46"D39:9>6":9"

D39CE@7"/43:B@=7"R>CE@7C"!2345"+AB66B9>"S/R!+TH

087"!2345"C7:7@:93"B6"4">7;"399A":7AD734:E37":5D7":84:"

7O8BFB:6"=9;">9B67"4>C"8B?8"6B?>4=":9">9B67"34:B9"G93"

A96:""9G":87"7=7A7>:6H

48

!$'"X+0+$1R.%0R*."*'"1%$0R%."$*-a,

R>:7>6B:5"@9E>:6"D73"67@9>C

+>73?5W"U7V

49

R>"AE=:B@84>>7= +X!$'W"4==":87"7AB::7C"!2345"=B>76"437"

A746E37C"6BAE=:4>79E6=5H"08737G937"B>@37467C"

67>6B:B<B:5"4>C"BAD39<7C"6B?>4=":9">9B67"34:B9"437"

9F:4B>7C"S'7==?7:: 4C<4>:4?7TH"RAD39<7C"3769=E:B9>"4:"

6893:73";4<7=7>?:86"B6"4>9:873"4C<4>:4?7H

50

%"F7>@8":9D"+X!$'"B6"4<4B=4F=7"G93":87""39E:B>7"

C7:73AB>4:B9>"9G"ED":9"IL"7=7A7>:6"34>?B>?"G39A"

69CBEA":9"E34>BEA"B>"B>CE6:3B4="64AD=76H"R>":8B6"

R>6:3EA7>:W":87"34CB4:B9>"G39A"4>"!2345":EF7"D46676"

:839E?8"4>"4DD39D3B4:7"GB=:73"4>C"6:3BU76":87"F9::9A"9G"

:87"39:4:B>?"64AD=7H"087"G=E9376@7>@7"6B?>4="D46676"9>"

:9":87"64AD=7"C7:7@:93"S6B=B@9>T";8B@8"D39<BC76"6B?>4=6"

:9":87"AE=:B@84>>7= @9E>:B>?"656:7AH

087"656:7A"E676"4"389CBEA"4>9C7"!2345":EF7"W"GB<7"

D39?34AA4F=7"GB=:736W"4"87=BEA"DE3?7"656:7AW"4":;7=<7"

D96B:B<7"64AD=7"@84>?73"4>C"4"6DB>>73":9"39:4:7"74@8"

64AD=7"CE3B>?":87"C4:4"4@\EB6B:B9>"D39@76676":9"

37CE@7"64AD=7"B>"89A9?7>7B:5H

51

%"N+.-Z"0*/"!$'"1*X+(

52

+X!$'"D=9:6"7>73?5"<6 B>:7>6B:5"S@D6TH"087"7>73?5"B6"B>"U7VH

gE4>:B:4:B<7"4>4=56B6"@4>"F7"9F:4B>7C"F5"A746E3B>?":87"

D74U"87B?8:6H"%"39E?8"76:BA4:7"9G":87"@9>@7>:34:B9>"@4>

F7"9F:4B>7C"F5W"

/!^"/

,H"Y

!

;8737"/!B6":87"37=4:B<7"=B>7"B>:7>6B:5"A746E37C"B>":73A6"9G"

>EAF73"9G"@9E>:6"D73"GBO7C":BA7"W"Y!B6":87";7B?8:"G34@:B9>"

9G":87"C76B37C"7=7A7>:"B>":87"64AD=7"4>C"/,B6":87"37=4:B<7"

B>:7>6B:5"9G":87"=B>7"E>C73"BC7>:B@4="@9>CB:B9>6"BG"Y!;737"

E>B:5H"087"<4=E7"9G"/,B6"C7:73AB>7C";B:8"4"6:4>C43C"64AD=7"

9G"U>9;>"@9AD96B:B9>"93"DE37"7=7A7>:H

53

%.%(&0R-%("1+0Z*X*(*[&

14:3BO"7GG7@:6M"%F693D:B9>"9G":87"!23456"G39A"4:9A6";7=="

F7=9;":87"6E3G4@7H"087"7O:7>:"9G"4::7>E4:B9>"C7D7>C6"

ED9>":87"A466"4F693D:B9>"@97GGB@B7>:"9G":87"A7CBEA"4>C"

B:6"@9AD96B:B9>H",B?>4="C7@374676H

+>84>@7A7>:"9G"G=E9376@7>@7"A45"9@@E3"CE7":9":87"

67@9>C435"7O@B:4:B9>"9G":87"4>4=5:B@4="=B>726B?>4="

B>@374676H

08B6"7GG7@:"@4>"F7"AB>BAB]7C"F5"E6B>?"4"@=967=5"A4:@87C"

6:4>C43C6"7O@7D:":87"4CC7C"7=7A7>:H"

54

%=:73>4:7=5W"4>""B>:73>4=""6:4>C43C"B6"B>:39CE@7C"B>"4==

:87"6:4>C43C6"4>C"64AD=76H

*>7"@4>"4=69"CB=E:7":87"64AD=7"4>C"6:4>C43C6":84:"

4F693F"!23456"9>=5";74U=5H"Y4:73W"93?4>B@"69=<7>:6W"

6:43@8W"=B:8BEA"@43F9>4:7W"4=EAB>4W"F93B@"4@BCW"F934:7"

?=466"7:@HW"Z737"A4:3BO"7GG7@:6"F7@9A7"7667>:B4==5"

@9>6:4>:H

55

%//(R-%0R*.,

Y87>"!2345"4F693D:B9>"4>C"7>84>@7A7>:"7GG7@:6"437"

AB>BA4=W":87"!$'"=B>7"B>:7>6B:5"4>C"7=7A7>:"@9>@7>:34:B9>"

@E3<76"437"=B>743H".R,0"6:4>C43C6"D39<BC7"6E@8"A4:73B4=6"

;8B@8"@4>"F7"E67C":9"@4=BF34:7":87"B>6:3EA7>:6H"05DB@4="

4DD=B@4:B9>"B>@=EC7M

SBT"""%>4=56B6"9G"39@U"64AD=76"G93""LL"7=7A7>:6H

SBBT""%==95"@9AD96B:B9>"@9>:39="CE3B>?"A4>EG4@:E37H"

SBBBT"(74C"4>C""F39AB>7W"B>"4<B4:B9>"GE7=6W"-4W"N%W"]B>@"B>"

=EF3B@4:B>?"9B=6W"DB?A7>:6"B>"D4B>:"64AD=76H

SB<T"X7:73AB>4:B9>"9G"@8=93B>7W"6E=D8BC76 4>C"6E=D8E3

CB9OBC7"9>"*2:9=EBCB>7W"6B=<73">B:34:7"4>C"69CBEA"

85C39OBC7"BAD37?>4:7C"AB@39D937 GB=:73"D4D736H

S<T"X7:73AB>4:B9>"9G""'7W"-EW"d>"B>"3B@7"64AD=76H

56

%XV%.0%[+,"*'"!$'

SBT 087"6D7@:34"437"37=4:B<7=5"6BAD=7"4>C">9:"6EFm7@:"

:9"AE@8"B>:73G737>@7H

SBBT .9>"C76:3E@:B<7":7@8>B\E7H"Z7>@7"E67GE="G93"

4>4=56B6"9G"D4B>:B>?6W"43@879=9?B@4="6D7@BA7>6W"

m7;7==735 W"4>:B\E7"B:7A6"7:@HW

SBBBT ,D77C"4>C"@9><7>B7>@7"9G":87"D39@7CE37H

SB<T /37@B6B9>"4>C"4@@E34@5"437"@9AD434F=7":9"

76:4F=B687C"A7:89C6"B>"@=466B@4=":7@8>B\E76H

57

XR,%XV%.0%[+,"*'"!$'

SBT 087"@9>@7>:34:B9>"34>?7"<43B76"G39A"JHJI"# IJJfH

SBBT .9:"E67GE="G93"=B?8:"7=7A7>:6"S=766":84>"LP"%:H".EAF736TH

SBBBT ZB?8"@96:"9G":87"B>6:3EA7>:6H

1

ATOMIC ABSORPTION SPECTROMETRY

The phenomenon of atomic absorption was first discovered by Woolaston in 1802 in the spectrum of sunlight. Till then thought to be a continuous spectrum, Woolaston made a remarkable observation that the solar spectrum was in fact interrupted by �“darklines�” which was later confirmed by Fraunhofer in 1814. However, Brewster put forward the idea that these dark lines denoted till then by alphabetical markers are in fact due to the presence of vapors of certain elements in the sun�’s atmosphere. Therefore, it follows that substances emitting specific radiations are also capable of absorbing the same, causing the spectrum of dark lines in the bright background.

2

This phenomenon generally known as Kirchoff�’s law was used to deduce the presence of oxygen, hydrogen, sodium, iron, calcium etc., in the solar spectrum. The experimental confirmation for this came from electric arc or spark, when the spectral source surrounded by atomic vapors also showed dark lines because of absorption of the emitted radiations. Foucalt in France also demonstrated the reversal of spectral lines.

3

FRAUNHOFFER LINES

4

FRAUNHOFFER LINES

5

In 1902, Wood repeated the experiments of Kirchoffand Foucalt and proved conclusively that by introducing sodium vapor in the optical path of sodium emission lines (589.0 and 589.6 nm), a reduction in the intensity of radiation occurs. By analogy with acoustic resonance lines, he also showed the possibility of using these resonance effects to detect traces of mercury. The potential of this technique was not recognized by analytical chemists and spectroscopists till 1924.

6

Angerer and Joose published the atomic spectra of iron group metals, followed by Frayne and Smita for indium, aluminum, gallium and tantalum. Muller and Pringshiem in 1930 published the first atomic absorption method of measuring the mercury content in air. Even this did not evoke interest in the analytical chemists for the determination of other elements.

7

Walsh, in 1955 developed the first real application of atomic absorption to chemical analysis. In the same year Alkamade and Miatz described a double beam method of spectral selection with two flames, the first being the source and the second as atomizer. Since then the atomic absorption spectrometry is in the forefront of chemical analysis. The first commercial atomic absorption instruments appeared in 1960s.

8

Spectacular advances in instrumentation, electronics,

automation and computers over the years have made

atomic absorption spectrometry, one of the most

reliable analytical techniques of modern times

perhaps equalled only by atomic emission

spectrometry in terms of simplicity, sensitivity,

specificity and speed of operation.

9

The development of electrothermal atomization by L�’vov and Massmann pushed the detection limits of atomic absorption technique to nanogram and picogram and sometimes even up to femtogramlevels.

Hydride generation atomic absorption spectrometry for arsenic, antimony, bismuth, selenium, tellurium, germanium, lead and cold vapor mercury determination have proved attractive accessories for atomic absorption technique to make it the first choice of analytical chemists throughout the world.

10

The popularity of the atomic absorption spectrometry

can be gauged by the fact that more than 100 books,

10,000 publications and 5000 symposia and

conferences till date have appeared with applications

in biological, chemical, nuclear, industrial products,

soils, environment etc.,

11

THEORETICAL CONCEPTS OF ATOMIC ABSORPTION

The simplest concept of atomic structure is that of the positively charged nucleus containing protons and neutrons surrounded by an equal number of electrons orbiting in space in the electric field created by the protons. According to quantum mechanics, such a system can exist in a stable state only if its energy is quantized even at the lowest energy level or ground state. All other levels are excited levels, which can be induced by mechanical or electromagnetic means. The energies associated with these atomic states are in the range of a few electron volts represented by Grotiandiagram. Such a diagram for sodium is shown in the next slide.

12

ENERGY LEVEL DIAGRAM FOR SODIUM

13

Emission of light occurs when an atom reverts to a state of lower energy. Bohr�’s equation expresses the conservation of energy by the relation:

= E1 �– E2 / h (1)

or = c / = hc / E1 �– E2

where c is the velocity of light (2.99793 x 108 m/s), h is the Plank�’s constant (6.62 x 10-34 in SI Units), v is the frequency, is the wavelength and E1, E2 are the energy levels of excited and ground states.

14

Inserting the numerical values, we get:

= 1.23978 / E

Thus a transition from the resonance level of sodium (2.102 electron volts) to ground state would correspondto the emission of:

= 1.23972 / 2.102 = 0.5986 µm or 589.6 nm

15

When a photon of frequency v interacts with an atom of energy E2, the atom may be able to absorb the photon thus raising it s energy to E2 + hv, provided the new energy level is equal to one of the excited energy levels of that atom, Then we can write:

= E1 �– E2 / h (2)

Comparison of equations 1 and 2 shows that �“An atom can only absorb the radiations that it is able to emit�”.This forms the basis of spectrometry.

v

16

The fundamental difference between emission spectrometry and absorption spectrometry may be defined as:

(i) For emission to occur, a number of atoms must be in the excited state.

(ii) For atomic absorption to occur, a number of atoms must be in the ground state.

The second condition is easily attained compared to the former in that, free atoms in the ground state can be easily generated in flame compared to the excited state, by flame emission.

17

The characteristic absorption wavelengths for an atom can be calculated once the energy levels are experimentally determined. But several wavelengths are never observed which proves that some sort of selection rules be developed. These rules were evolved empirically at first, and subsequently confirmed by applying quantum mechanical principles to the concept of transition probabilities.

The probability of a spontaneous emission by transition between energy levels E1 and E2 is defined as the fraction of number of atoms that drop to lower level per unit time.

18

Mathematically,

dN1 2 = AN1 dt (3)

where A is the coefficient of proportionality termed as Einstein emission coefficient. Higher the probability of transition, the greater is the intensity of emission. The strongest emission lines correspond to values of A in the range of 108 to 109 / sec.

19

Similarly if N2 atoms in the lower transition state are

irradiated by a radiation of frequency derived from

equation (1) and the volume flux density ( ), the

number of d N2-1 of atoms that will absorb the

radiation in time dt is proportional to N2, ( ) and dt.

Hence,

dN2 1 = B2-1 , N2 ( ) dt (4)

v

vv

v

20

The term B2 1 is known as Einstein�’s absorptioncoefficient. Now a days, the term oscillator strength is being used to denote the relationship between B and the total number of electrons.

B2 1 = e2 / m h c f2,1 (5)

where, e and m are the electronic charge and mass. Thus for sodium D lines, oscillator strength is 0.23 and 0.47 and for potassium they are 0.35 and 0.70.

21

The emission lifetime of any transition is approximately 10-8 sec. However, if there are sufficient numbers of atoms, steady state emission or absorption phenomena can be observed within the experimental time frame. For atomic absorption to occur , intense emission of the desired element must be generated first. The radiations generated from electric dipole, magnetic dipole, electric quadrupoleinteractions give rise to such lines among which electric dipole are most important. Both Einstein emission (A) and absorption coefficients ( ) are non-zero, only if the levels involved are of opposite parity and if J = ±1.

22

Using these selection rules, resonance level of an atom may be defined as that of lowest excited energy level that can interact with the ground state by a transition of electric dipole type. The corresponding wavelength is known as the resonance line. Therefore, it follows that for a particular atom the resonance line is the most intense of highest oscillator strengths and only this line is useful for analysis provided the wavelengths are in the 200-600 nm range.

23

In practice, it is impossible to get a truly monochromatic line, but the energy is distributed symmetrically over a narrow waveband. The width of a spectral line is defined as the value of where the intensity is 50 percent of the total. This is called as half width. The shape and size of an absorption or emission band is affected by several factors such as natural broadening, Doppler broadening, pressure broadening and electric or magnetic field broadening etc.,

24

PROFILE OF A RESONANCE LINE

25

NATURAL BROADENING

Due to the short lifetime of energy states, Heisenberg�’s uncertainty principle is applicable for all transitions. Thus a small broadening effect of the order of a few millionth of a nanometer at 250 nm occurs rising to about 10-4 nm at 1 m. This natural width is influenced further by a variety of factors, chief among them being the disordered thermal motion of the atoms and various types of collisions of atoms.

26

DOPPLER BROADENING

27

If an atom emitting a radiation 0 moves with a velocity relative to the observer, the observed wavelength is given by,

= 0 + 0 / c (6)

where c is the velocity of light in the vacuum. Further,if the atoms are in thermal equilibrium at temperature T, their velocities will have a Maxwellian distribution.

v

v

28

The monochromatic absorption coefficient K as a function of may be expressed as:

K( ) = K0 exp { [ -( - 0) / d 2 (ln 2) ½ ] 2 } (7)

where d is the Doppler halfwidth related to T and the atomic mass M by the equation:

d = 7.16 x 1070 ( T/M )1/2 (8)

The line is thus shown to have a Gaussian profile. It is possible to calculate the values of d at 2000, 2500 and 3000 K and the line widths for these temperatures are of the order of 30-50 mA.

0

29

PRESSURE BROADENING

Since the atoms in the vapour state are in a perpetual state of motion, collision of atoms is inevitable causing radiation quanta of slightly differing frequencies to be absorbed or emitted. Several types of particles may be involved in the collisions. Interaction of electrically charged particles causes line broadening known as �‘Stark effect�’. Collisions with uncharged atoms lead to van Der waal�’s effect. Collisions between atoms of the same type leading to resonance broadening effect is referred as �‘Holtsmark�’ effect. Since it is difficult to differentiate between these three effects they are collectively referred as �‘Lorentz�’ broadening.

30

The broadening of spectral lines reduces the lifetime of the excited state of the atoms. It also increases the line profile of the radiation. The monochromatic absorption coefficient of the em radiation at a wavelength is given by:

K( ) = K0 / 1 + [2 ( - 0) L] 2 (9)

where K0 is the maximum absorption coefficient and L is the half width. The profile of this distribution is flatter than Doppler broadening but both are almost of the same order. The half width L is thus a fraction of the frequency of collision (Z), which in turn is a function of the temperature and the effective cross section defined by:

= Z 02 / C (10)

31

It may be noted that both Doppler and Lorenz broadening occur simultaneously resulting in a similar but broader profile known as Voigt profile (K ) which may be mathematically expressed as:

(11)

Where a = L / D ( ln 2 )1/2 ,

w = �– 0 / D 2 (ln 2 ) 1/2 ,

y = 2 / D (ln 2 ) 1/2 and

= distance to the point at which K( ) and K0 are the calculated and the maximum value of the coefficient.

dy y) - (w a / e / a K )( 22

-

y2-oK

32

The curves are symmetrical with a maximum at 0. Apart from Doppler and Lorenz effects, line broadening also occurs due to hyperfine structure exhibited by many resonance lines due to nuclear spin. Isotope shift of the resonance lines also contributes additionally to the line broadening. These effects are also significant but not as prominent.

In essence, the sum total of all these line broadening effect is of the order of 0.0005-0.005nm, which increases with increasing temperature and pressure. The significance of peak width at half the peak height has a profound effect on the emission characteristics of radiation sources, (especially hollow cathode lamps) which will be discussed later.

33

MEASUREMENT OF ABSORPTION

Based on quantum physical description given earlier, rigorous mathematical expressions have been derived to determine the absorption coefficient, its variation with N.f.l, effect of monochromator band width and also of optical density. However, for practical analytical purposes a physical understanding of these phenomena is more relevant which may be Interpreted as follows.

34

A very narrow frequency interval is essential for the absorption of resonance radiation. However, it is impossible to isolate and obtain high intensity of illumination in the range of 0.0005 �– 0.005 nm from continuum radiation sources. It would be too weak tobe of any practical use. To overcome this difficulty, Walsh recommended that the radiation source should be made of the analyte element only. Therefore only the resonance line need to be separated from other spectral lines by a monochromator.

35

Assuming that a monochromator isolates a spectral band S covering the absorption line 0 (resonance line), the

total spectral energy received by the detector is :

(13)

= I0 S (14)

= Area of the rectangle ABCD

2/

2/00

0

0

dI S

S

I

36

Now if a homogeneous gas having an absorption K( ) is interposed in a length of the radiation beam, the energy within the band will decrease by the same amount but the spectral profile will have the same shape.

3737

Instead of considering the radiation per unit volume, if the total radiant flux ( ) is considered, then it may be proved that the absorption factor and hence optical density is proportional to the concentration of the free atoms and to the path length in the absorbing medium provided that the concentration is low and the spectral bandwidth is narrow. This is nothing but Beer �– Lambert�’s law which can be expressed as:

tr = 0 e�–xv N l (16)

Where 0 and tr are the radiant fluxes before and after absorption in the path length l, xv is the spectral absorption coefficient and N is the number of atoms.

3838

This expression may be rearranged in the familiar form,

Absorbance = A = Log 0 / tr = 2.303 xv N L (17)

The total number of free atoms in optical path cannot be determined but it is not necessary for routine applications, as atomic absorption is a relative technique like any other spectroscopic techniques.

3939

The physical conditions for highest sensitivity may be summarized as follows:

The absorption line should have lowest energy state and highest population of the atoms in the ground state.

If several resonance lines are there, the one with highest oscillator strength has to be chosen.

Employing a source of radiation, that emits a line of the same wavelength but with lower half width.

Path length may be increased within practical limits in the absorbing medium since B-L law states that the absorption also increases according to the path length.

4040

Employing these conditions, we can in principle, construct an atomic absorption spectrometer using a hollow cathode lamp made of the same element as the analyte, an atomizer to produce a population of ground state atoms, a monochromator with an entrance and exit slit for collection, dispersion and selection of resonance line, a detector for the measurement of radiation intensity followed by an amplifier and a read out device. A schematic diagram of such a system is shown here.

Source AbsorptionCell Monochromator Detector

AmplifierDisplay

4141

Depending upon the choice of the components and method of operations several variants of atomic absorption spectrometers result, which are enumerated below,

1) Single beam DC instrument �– This is the simplest arrangement. The earliest AAS instruments were of this type.

2) Single beam AC instrument �– By applying the pulsed current to the radiation source or by mechanically chopping the radiation before it enters the absorption cell.

3) Double beam AC instrument �– By using a rotating mirror/chopperarrangement, the radiation is passed alternately through theflame and around the flame. Then it is possible to construct a double beam instrument. Both beams are recombined by a semitransparent mirror placed behind the flame. The electronicsof the system is designed to yield directly the ratio of the transmitted radiation flux to that of the incident radiation. The stability is also better.

42

SCHEMATICS OF ATOMIC ABSORPTION SPECTROMETERS

4343

4) Multi element Simultaneous AAS �– Use of radiation sources containing resonance lines of several elements focused in to the absorption cell permits simultaneous determination of several elements. However the optics and electronics need to be suitably modified to handle various signals readout and printouts.

5) Electrothermal AAS �– By substituting the absorption cell (i.e flame) with an electrically heated graphite furnace, very efficient means of producing atomic vapor can be achieved. This technique has gained wide popularity since last 15 years permitting the quantitative determination in ppb levels (10-9 g).

4444

6) Hydride Generation AAS �– Arsenic, antimony, bismuth, selenium, tellurium, germanium, lead etc, are capable of forming their respective hydrides in acidic medium. These compounds easily dissociate into their metallic and non-metallic components which, when introduced into the flame (absorption cell ), permit not only their separation but also estimation in ppb levels (10-9 g).

7) Mercury cold vapor AAS �– Mercury has a unique property of being reduced to metallic form directly from its combined state and also has a significant vapor pressure which permits its determination at room temperature. It only needs to be transported to the absorption cell. This technique is known as cold vapor technique.

4545

Over the years atomic absorption spectrometry as an analytical technique has been accepted as a standard method of analysis all over the world. An enormous amount of literature on the instrumentation, radiation, sources, atomization techniques, optics, signal handling and data presentation has been developed. The advent of computers has made it possible for maximum use of automation, instrument control and statistical data evaluation. On an average, more than 500 research papers are being published on the application of AAS to various matrices every year.

Now we shall discuss the detailed aspects of atomic absorption spectroscopy.

46

AAS is the measurement of the absorption of em radiation by the atoms in the gaseous state.

Free atoms do not undergo vibrational & rotational transitions but only electronic transitions. Such excited electron may return to ground state by atomic emission, atomic fluorescence or atomic absorption phenomena.

The various energy states of an atom are described by n,land inner quantum number J. Selection rules permit L = ±1 and n = any number.

47

For sodium atom the most loosely bound electron is designated by,

3s2 S1/2 3 p2 p1/2 ,3/2 589.593 nm / 588.996 nm4 p2 p1/2,3/2 330.294 nm / 330.234 nmn p2 p1/2,3/2

In emission spectrum all possible lines are obtained.

48

Since all elements can be excited to their next higher energy level ,in theory any element can be determined byatomic absorption spectrometry.

However, below 200 nm, analysis of As, Se, I, S , P etc., is difficult owing to the incipient absorption by oxygen and hot flame gases. Cerium ,Thorium and other refractive elements also present difficulty. Artificial and radioactive elements can not be analyzed by atomic absorption spectrometry.

49

THERMAL EXCITATIONIt must be appreciated that for atomic absorption to occur ,we have to produce a population of atoms in the ground state. This can be achieved by exposing a sample of the analyte to high temperatures. At high temperatures prevailing in the flames, compounds decompose into ions, which in turn pick up electrons to produce atoms.

The ratio of number of atoms Nj in an excited state j to thenumber of atoms in the ground state N0 is given by,

Nj Pj

N0 P0

where Pj & P0 are the statistical weights of the excited and ground states , k is the boltzmann�’s constant and T is the absolute temperature .

= . e-Ej/KT