Guia de Fisica II - William Taipe

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o~ bonez

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mksemeofrk seofo bgbk tkz hg ~eaueofro optzo~eþf<

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JEJHEKAZGCEG<

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OPTOZEMOFRK F´ 4:< MKSEMEOFRK GZMÞFENK ÊMTHO 7& KJLORESK^ Borozmefgz hg nkf~rgfro bo ohg~renebgb boh muohho mobegfro hg Ho bo @kkio& U nkmtzkjgz optozemofrghmofro oh tozekbk bo k~nehgneþf boh muohho& :& C_FBGMOFRK^ ROÞZENK^< _f muohho ~u~tofbebk sozrenghmofro bo uf ~ktkzro ~ef fefaufg mg~g nkhagfbk bo ~u oprzomk reofo ufg hkfaerub ‐H― (hkfaerub of zotk~k%& Nugfbk ~o nuohag ufg mg~g boh muohho ~u hkfaerub ~o efnzomofrg of H ) ∃H

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bo owuehejzek; Oh muohho olozno ufg cuoz|g zonutozgbkzg C = -ip bkfbo p o~ hg be~rgfneg wuo ~o bo~thg|g oh muohho bo~bo hg tk~eneþf bo owuehejzek  i o~ hg nkf~rgfro ohç~reng boh muohho& Oh ~eafk foagresk efbeng wuo hg cuoz|g gtufrg of ~ofrebk nkfrzgzek g hg ~erugneþf bo hg mg~g& Hg cuoz|g zonutozgbkzg `gno wuo hg mg~g k~neho gzzejg  gjglk& Oh tozekbk bo k~nehgneþf botofbo bo hg mg~g  bo hg nkf~rgfro boh muohho& R =

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Muohho

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4&7?4402?17

NKFNH_ÊKFO^< •

Oh tozekbk bo k~nehgneþf boh muohho o~ bo 4&57072 mobegfro hg ceauzg : bo hk~ o~wuomg~&

•

Oh tozekbk bo k~nehgneþf `ghhgfbk hg nkf~rgfro bo k~nehgneþf o~ bo 4&1304?& nkf uf ozzkz bo 4&7?440&

•

Hg nkfrgfro bo ohg~renebgb boh muohho fk o~ nkzzonrgmofro nghnuhgbk tkz wuo ope~rof cgnrkzo~ bo ozzkz gh mkmofrk bo hg rkmg bo bgrk~ of oh hgjkzgrkzek&

1&

JEJHEKAZGCEG<




x QEHHEGM RGETO

7:

OPTOZEMOFRK F´ 4>< TZEFNETEK BO GZW_ÍMOBO^ 7& KJLORESK^ Nkmtzkjgz optozemofrgh mofro oh tzefnetek bo Gzwuímobo~& Borozmefgz hg bof~ebgb boh híwuebk (gaug% bo mgfozg optozemofrgh&

:& C_FBGMOFRK^ ROÞZENK^< Oh tzefnetek bo Gzwuímobo~ o~rgjhono wuo oh omtulo wuo optozemofrg uf kjlork nkmthorg k tgzneghmofro ~umozaebk of uf chuebk o~ eaugh gh to~k boh chuebk bo~thg|gbk tkz oh kjlork& O = m c a

Bkfbo χ c o~ hg bof~ebgb boh chuebk

S o~

=

χ c Sa

oh skhumof ~umozaebk boh kjlork 

a

o~ hg gnohozgneþf

bo hg azgsobgb&

T

O

Oh skhumof ~umozaebk o~ eaugh gh çzog bo hg ~onneþf G muhrethengbk tkz hg ghruzg ~umozaebg `& Oh omtulo jkgfro tuobo bo~nzejez~o nkmk< O = χ c ( G`% a

ê oh kjlork ~o sg ~umozaeofbk of oh chuebk meofrzg~ ~o o~rç mebeofbk oh omtulo hg tofbeofro bo O czofro g ` o~ tzktkznekfgh g hg bof~ebgb boh chuebk&


Jg~o  ~ktkzro

•

ôf~kz bo cuoz|g

•

Zoneteofro 7444 mH

•

^kcrqgzo Bgrg^rubek

•

Nehefbzk morçhenk nkf ofagfnò

•

Agrk

•

Zoahg azgbugbg

•

Gjzg|gbozg çfauhk bozon`k

•

@ehk

•

^ktkzro



x QEHHEGM RGETO

7>

2& MORKBKHKAÍG< 2&7& O^W_OMG BOH OPTOZEMOFRK Oh o~wuomg boh optozemofrk o~ bo hg ~eaueofro ckzmg<

Ceauzg 7 2&:& BGRK^ OPTOZEMOFRGHO^ To~k boh nehefbzk

4&51 F

Beçmorzk

>&0 nm

4&4>0 m

Ghruzg

1 nm

4&41 m

Zgbek

7&5 nm

4&475 m

Çzog bo hg jg~o

77&>2407? nmV:

4&4477>240 mV:

Bgrk~ rkmgbk~ nkf oh o~wuomg bo hg ceauzg 7 F´ Rof~eþf (R%

Tzkcufbebgb (`%

Omtulo (!O!%

F´

Rof~eþf (R%

Tzkcufbebgb (`%

Omtulo (!O!%

7 4&51

4

4&444

7

4&51

4&4444

4&44

: 4&03

7

4&774

:

4&03

4&4744

4&77

> 4&13

7&?

4&:74

>

4&13

4&47?4

4&:7

2 4&3?

:&:

4&>:4

2

4&3?

4&4::4

4&>:

? 4&??

>&?

4&2:4

?

4&??

4&4>?4

4&2:

3 4&2>

2&?

4&?24

3

4&2>

4&42?4

4&?2

1 4&>>

3

4&324

1

4&>>

4&4344

4&32

0 4&:>

3&?

4&124

0

4&:>

4&43?4

4&12

5 4&71

1&?

4&044

5

4&71

4&41?4

4&04



x QEHHEGM RGETO

72

?&

ZO^_HRGBK^< Borozmefomk~ hg tofbeofro bo hg nuzsg bo hg cuoz|g bo omtulo czoro g tzkcufbebgb& Oh gfçhe~e~ hk zoghe|gmk~ mobegfro oh mårkbk bo mífemk~ nugbzgbk~< ⌥ pu⌬ √ ⌥ p⌬ ⌥ u⌬ ⌥ p : ⌬ √ ⌥ p⌬ : ⌥ p: ⌬⌥ u⌬ √ ⌥ p⌬⌥ pu⌬ g= ⌥ p : ⌬ √ ⌥ p⌬ :

j=

F´

`

O

`,O

7

4&4444

4&444

4

4&4444

:

4&4744

4&774

4&4477

4&4447

>

4&47?4

4&:74

4&44>7?

4&444:

2

4&4::4

4&>:4

4&44142

4&444?

?

4&4>?4

4&2:4

4&4721

4&447:

=g)jp

3

4&42?4

4&?24

4&4:2>

4&44:4

O=g)j`

1

4&4344

4&324

4&4>02

4&44>3

0

4&43?4

4&124

4&4207

4&442:

5

4&41?4

4&044

4&43

4&44?3

Tzkmobek

4&4>3>

4&2:44

4&4:75

4&4475

g

=

j

= 74&?3>:??7?

`V:

4&4>3:471:5

Eaughgfbk hg tofbeofro nkf hg optzo~eþf tGa bof~ebgb =

5?4&22?5?5

ia+mV>

G`kzg nghnuhomk~ mobegfro oh ~kcrqgzo bo Bgrg ^rubek



x QEHHEGM RGETO

7?

G`kzg nghnuhomk~ hg bof~ebgb boh gaug eaughgfbk hg tofbeofro nkf χ Ga  bo~tolgfbk tkz χ & Eaughgfbk hg tofbeofro nkf hg optzo~eþf Bof~ebgb =

tGa

5?4&22?5?5 ia+mV>

Nkmtgzgfbk oh sghkz nghnuhgbk nkf oh sghkz fkzmghmofro gnotrgbk nghnuhgfbk oh tkznofrglo bo becozofneg& Oh sghkz gnotrgbk roþzengmofro o~ bo 7444ia+mV>  oh sghkz nghnuhgbk of oh hgjkzgrkzek o~ bo 5?4&223ia+mV> Nghnuhomk~ hg becozofneg  hk~ ozzkzo~ boh optozemofrk< Sghkz roþzenk

Sghkz optozemofrgh

Becozofneg

ozzkz

Ozzkz (/%

7444

5?4&22?5?5

25&??242455

25&??2427

4&425??242



x QEHHEGM RGETO

73

3&

NKFNH_ÊKFO^< •

Hg bof~ebgb boh gaug nghnuhgbg o~ bo 5?4&2 nkf uf ozzkz tkznofrugh bo 4&425/&

•

Hg becozofneg bo hg bof~ebgb boh gaug ofrzo oh sghkz gnotrgbk  oh sghkz nghnuhgbk nkf oh optozemofrk o~ bo 25&??&

1&

JEJHEKAZGCEG<




x QEHHEGM RGETO

71

OPTOZEMOFRK F´ 42< SOHKNEBGB BOH ^KFEBK OF OH GEZO 7& KJLORESK^ Borozmefgz hg sohknebgb bo tzktgagneþf boh ~kfebk of oh gezo  gfghe|gz hg ckzmg bo kfbg~ ~kfkzg~ o~rgnekfgzeg~ of oh Rujk&

:& C_FBGMOFRK^ ROÞZENK^< Hg sohknebgb boh ~kfebk o~ be~refrg g rzgså~ bo becozofro~ mgrozegho~& Hg sohknebgb boh ~kfebk botofbo bo hg ohg~renebgb  hg bof~ebgb boh mgrozegh& Tkz olomthk hg ohg~renebgb boh òhek o~ ng~e eaugh wuo hg ohg~renebgb boh gezo tozk ~u bof~ebgb o~ mun`k mofkz& Nkmk nkf~onuofneg hg sohknebgb boh ~kfebk of oh òhek o~ ufg~ rzo~ sono~ mç~ zçtebg wuo of oh gezo& Of hk~ ag~o~ hg sohknebgb boh ~kfebk botofbo bo hg romtozgruzg& Of oh gezo hg sohknebgb gumofrg gtzkpemgbgmofro 4&34 m+~ tkz ngbg azgbk Noh~eu~ bo gumofrk bo hg romtozgruzg& Roþzengmofro ~o tuobo nghnuhgz hg sohknebgb boh ~kfebk tgzreofbk bo hg be~rgfneg wuo zonkzzo  oh reomtk of wuo zonkzzo o~rg be~rgfneg& Of hg tzçnreng oh nçhnuhk ~o jg~g g mofubk of oh efrozsghk bo reomtk wuo `g ofrzo oh ~kfebk tzkbunebk  ~u onk& Hg sohknebgb boh ~kfebk o~ eaugh gh bkjho bo hg be~rgfneg besebebk ofrzo oh reomtk rkrgh&


Rujk bo ngzrþf

•

ôf~kz bo ^kfebk

•

Jg~o  ^ktkzro

•

^kcrqgzo Bgrg^rubek

•

Nefrg gbò~esg

•

Gjzg|gbozg rzo~ bobk~

•

Nefrg Mårzeng

•

2&

MORKBKHKAÍG<

2&7& O^W_OMG BOH OPTOZEMOFRK Rgto uf oprzomk boh rujk nkf nefrg gbò~esg&

_reheno uf ~ktkzro  ufg gjzg|gbozg tgzg mkfrgz oh ~of~kz bo ^kfebk of oh nofrzk boh oprzomk gjeozrk boh rujk&



x QEHHEGM RGETO

70

N`g~wuoo ~u~ bobk~ czofro g hg tgzro gjeozrg boh rujk&

2&:& BGRK^ OPTOZEMOFRGHO^ Tkz oh o~wuomg boh optozemofrk kjrofomk~ hg ~eaueofro azgceng mobegfro oh ~kcrqgzo Bgrg^rubek bkfbo zoghe|gzomk~ hk~ gfçhe~e~ tgzg kjrofoz oh reomtk wuo bomkzg oh ~kfebk of ez boh tufrk bo ~of~kz bo ~kfebk  ~u zorkzfk gh me~mk tufrk&

REOMTK( R %

4&4773~oa

ROMTOZGR_ZG ( R ´ %

:4Ń

BE^RGFNEG BOH R_JK ( b %

7&51m



x QEHHEGM RGETO

75

?&

ZO^_HRGBK^< Nghnuhomk~ hg sohknebgb boh ~kfebk mobegfro hg onugneþf s=

Bkfbo

B

B R

o~ hg be~rgfneg zonkzzebg tkz oh ~kfebk tgzg fuo~rzk ng~k o~ eaugh gh bkjho bo hg

hkfaerub boh rujk :b  

R

o~ oh reomtk wuo bomkzg of zonkzzoz rkbk oh rzgonrk boh rujk bk~

sono~& s=

:b R

Nkf o~rg onugneþf kjrofomk~ oh sghkz bo hg sohknebgb boh ~kfebk of oh gezo kjrofeofbk uf sghkz fumåzenk bo >>5&3??71:2m+~& Oh ozzkz nkmorebk of oh hgjkzgrkzek g hg nkfbeneþf bo romtozgruzg bo :4Ń o~ oh ~eaueofro< Sghkz roþzenk

Sghkz Optozemofrgh

>2>

3&

>>5&3??71:2

Ozzkz

Ozzkz(/%

>&>2?

4&4451?7302

NKFNH_ÊKFO^< •

Hg sohknebgb boh ~kfebk g hg romtozgruzg bo :4Ń of oh gezo o~ bo >>5&3?m+~ nkf uf ozzkz bo 4&4451/&

1&

•

Hg sohknebgb boh ~kfebk botofbo bo hg romtozgruzg boh gezo&

•

Oh ozzkz wuo ~o nkmoro of o~ro optozemofrk o~ towuo÷k&

JEJHEKAZGCEG<




x QEHHEGM RGETO

:4

OPTOZEMOFRK F´ 4?< HOU BO JKUHO „ TZOÊÞF U SKH_MOF 7& KJLORESK^ Nkmtzkjgz optozemofrghmofro hg Ho bo Jkho „ Mgzekro `ghhgfbk hg zohgneþf wuo ope~ro ofrzo hg tzo~eþf  skhumof bo uf ag~ (gezo% g ufg romtozgruzg nkf~rgfro  borozmefgz optozemofrghmofro hg tzo~eþf grmk~cåzeng of hg neubgb bo Tufk&

:& C_FBGMOFRK^ ROÞZENK^< Hg Ho bo Jkho o~rgjhono wuo hg tzo~eþf bo uf ag~ of oh efrozekz bo uf zoneteofro o~rç zohgnekfgbg nkf oh skhumof boh ag~& Of krzg~ tghgjzg~ ~e ngmjeg oh skhumof ngmjeg hg tzo~eþf& Tgzg ufg ngfrebgb borozmefgbg bo ag~ g ufg romtozgruzg borozmefgbg hg tzo~eþf boh ag~ o~ efsoz~gmofro tzktkznekfgh gh skhumof& _fg ckzmg bo sozecengz o~rk o~ bejulgz hg azçceng bo hg efsoz~g boh skhumof boh ag~ czofro g hg tzo~eþf boh ag~&


Lozefauehhg (nkf ~of~kz%

•

ôf~kz bo tzo~eþf

•

Rujk~ (nkf ~of~kz%

•

^kcrqgzo Bgrg^rubek

•

Nkfonrkz bo glu~ro zçtebk (nkf ôf~kz%

•

Ahenozefg

2&

MORKBKHKAÍG<

2&7& O^W_OMG BOH OPTOZEMOFRK Glu~ro oh skhumof bo gezo of hg lozefauehhg g :4 mH& (Fkrg< Tgzg celgz hg tk~eneþf efenegh boh te~rþf bo~nkfonro oh nkfonrkz boh ôf~kz muosg oh te~rþf g hg tzemozg tk~eneþf (:4 mH%  suohsg g nkfonrgz oh nkfonrkz gh ôf~kz%&



x QEHHEGM RGETO

:7

2&:& BGRK^ OPTOZEMOFRGHO^ Bgrk~ boh Rujk wuo nkfonrg hg lozefauehhg nkf oh ~of~kz bo tzo~eþf< Rujk

37

nm

Beçmorzk

4&>:

nm

Grmk~cozg

3>&?

iTg

Skhumof

2&54?5::?3

nmV>

2&54?5::?3

mH

Bgrk~ bo tzo~eþf  skhumof boh optozemofrk ~oaüf oh o~wuomg boh optozemofrk<

Skhumof(mH%

Tzo~eþf (iT%

Skhumof efsoz~g

Tzo~eþf (iT%

:2&54?5::?3

3>&0

4&4247?745:

3>&0

::&54?5::?3

35&3

4&42>3?30>7

35&3

:4&54?5::?3

13&1

4&4210>>>>?

13&1

70&54?5::?3

0?&:

4&4?:05>210

0?&:

73&54?5::?3

5?&:

4&4?57?4030

5?&:

72&54?5::?3

74?&>

4&4314012:0

74?&>

7:&54?5::?3

7::&5

4&41120>043

7::&5

74&54?5::?3

720&7

4&45735>:51

720&7

0&54?5::?3

715&2

4&77::020>

715&2

3&54?5::?3

::0&3

4&72204>:23

::0&3

Hg tzo~eþf grmk~cåzeng of hg neubgb bo Tufk nghnuhgbk tkz oh ~of~kz bo tzo~eþf o~ bo 3>&?iTg

?&

ZO^_HRGBK^< Zoghenomk~ oh gfçhe~e~ bo hg~ azçceng~ bo tzo~eþf s~ skhumof&



x QEHHEGM RGETO

::

Bkfbo tuobo kj~ozsgz wuo hg tzo~eþf o~ efsoz~gmofro tzktkznekfgh gh skhumof boh ag~ (gezo% bo o~rg azgceng~ tkbomk~ bonez wuo TS

=

nkf~ nkf~rg rgfr froo

Nghnuhomk~ oh tzkbunrk bo tzo~eþf tkz skhumof tgzg ngbg ng~k bo hg bo bgrk~ optozemofrgho~ huoak `ghhomk~ uf tzkmobek bo o~rk~ zo~uhrgbk~<

Skhumof(mH%

Tzo~eþf (iT%

I

:2&54?5::?3

3>&0

7?00&55103

::&54?5::?3

35&3

7?52&:?::7

:4&54?5::?3

13&1

734>&202:3

70&54?5::?3

0?&:

7374&10234

73&54?5::?3

5?&:

7345&22>0>

72&54?5::?3

74?&>

7?35&?5>3?

7:&54?5::?3

7::&5

7?03&7>100

74&54?5::?3

720&7

737?&7317>

0&54?5::?3

715&2

7?51&1::?7

3&54?5::?3

::0&3

7?10&35>54

Tzkmobek bo I

7?5?&2:110:

G`kzg azgcewuomk~ tzo~eþf s~ efsoz~g bo skhumof

& O&T& N~& CÍÊNK MGROMÇRENG^


x QEHHEGM RGETO

:>

Bo bkfbo kjrofomk~ hg tofbeofro bo hg azçceng oh nugh o~ hg nkf~rgfro boh tzkbunrk

TS

o~ro

sghkz hg tkbomk~ `ghhgz tkz oh mårkbk bo mífemk~ nugbzgbk~ k u~gfbk oh ~kcrqgzo Bgrg^rubek& 7   S 

T = I 

Tkz oh mårkbk bo mífemk~ nugbzgbk~ kjrofomk~ hg tofbeofro m = 7?5?&2:110:=I & Oh ozzkz wuo boh optozemofrk o~ oh ~eaueofro< Sghkz Roþzenk

Sghkz Optozemofrgh

7?5?&2:110:

3&

7?04

Ozzkz

Ozzkz (/%

7?&2:110:>?

4&44531

NKFNH_ÊKFO^< •

Of uf ag~ ag~ (gezo% g romtozgruzg romtozgruz g nkf~rgfro bo :4Ń hg tzo~eþf o~ efsoz~gmofro tzktkznekfgh g ~u skhumof&

•

Gh zoghe|gz uf gfçhe~e~ azgcenk bo tzo~eþf s~ skhumof efsoz~k ~o kjreofo hg nkf~rgfro boh tzkbunrk TS nkf uf ozzkz bo 4&44531/&

•

1&

Hg tzo~eþf grmk~cåzeng~ bo hg neubgb bo Tufk o~ bo 3>&?iT&

JEJHEKAZGCEG<




x QEHHEGM RGETO

:2

Guia de Fisica II - William Taipe

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