Giao trinh vat ly nguyen tu hat nhan ThaiKhacDinh

8/14/2019 Giao trinh vat ly nguyen tu hat nhan ThaiKhacDinh

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TRNG I HC SPHM TP. H CH MINH.

TI LIU LU HNH NI B - 2003


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LI NI U

Vt l nguyn tv ht nhn l hc phn nm trong chng trnh o to cho sinhvin ngnh vt l ca cc trngi hc Sphm. Hc phn ny gn lin vi nhngthnh tu rc rv ng dng to ln ca ngnh Vt l nguyn tv Ht nhn i vicuc sng ca con ngi, i vi cc lnh vc kinh tv khoa hc, kthut hin i khc.

Gio trnh ny gm hai phn: Vt l nguyn tv Vt l ht nhn.

Phn Vt l nguyn t cung cp cho sinh vin cc kin thc c bn v cc munguyn t theo l thuyt cin, c s ca l thuyt lng tnghin cu cu trcnguyn t; lin kt nguyn t trong phn tv nhngnh hng bn ngoi ln nguyntbc x.

Phn Vt l ht nhn trnh by nhng vn c bn v cc c trng ca htnhn, cc mu cu trc ht nhn, sphn r phng x , cc phn ng ht nhn, nnglng ht nhn v mt svn vcc ht cbn.

Gio trnh ny l ti liu tham kho cho sinh vin cc trngi hc sphm vsinh vin ca cc trngi hc, Cao ng khc.

Mc d cgng v nghim tc vi cng vic bin son, nhng chc chn khngtrnh khi nhng thiu st. Chng ti mong cc bn c lng thv ng gp nhiu kin cho ni dung gio trnh, gio trnh ngy cngc hon chnh hn.

Chng ti xin chn thnh cm n cc ng nghip ng gp cho ni dung cabn tho v xin cm n Bann Bn Pht hnh ca Trngi hc Sphm Tp. H Ch

Minh to iu kin gip cho gio trnh ny sm ra mt bn c.

CC TC GI


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PHN THNHT

VT L NGUYN T

Chng I

CC MU NGUYN TTHEO L THUYT CIN

Vo nhng nm cui ca th k XIX v u th k XX, cc khm ph v tia phng xv Electron trong nguyn t pht ra ngoi lm o ln ton b nim cho rng nguyn tl phn t vt cht nguyn vn nh nht khng phn chia c.

S xut hin ca tia phng x v electron chng t kch thc ca nguyn t cha phil gii hn nh b nht. Bn trong nguyn t cn cha ng nhiu ht c kch thc cn nh

b hn. Nhng ht y lin kt vi nhau to nn cu trc phc tp bn trong nguyn t.Cho n nay khoa hc i n nhng kt lun chnh xc v cu trc nguyn t nhng

cha phi hiu ht cc chi tit ca n. Do vy chng ta ch cp n nhng quy lut cbn nhn bit c qua thc nghim v cu trc nguyn t xy dng cc m hnh nguynt. Chng ta bt u xt cc mu nguyn t tn gin n phc tp theo l thuyt cinv bn cin.

1. MU NGUYN TTOMXN (THOMSON).

nim v mu nguyn tc V. Tomxn xut ln u tin vo nm 1902. Sau t lu, vo nm 1904 J. Tomxn xy dng l thuyt v mu nguyn t da trn tng

ca V. Tomxn.Theo J. Tomxn quan nim thnguyn t c dng hnh cu nhim indng u khp vi bn knh c10 -8 cm.

Cc electron c kch thc nh hnkch thc nguyn t rt nhiu, c phn

b theo cc quy lut xc nh trong khicu tch in dng y. Mt khc electronc th chuyn ng trong phm vi kchthc ca nguyn t. V phng dinin th tng tr sin tch m ca cc

electron bng v ngc du vi khi cunhim in dng. Do vy nguyn t lmt h thng trung ha vin tch.

Hnh 1.1 Mu nguyn t Tmxn

V d: Nguyn t Hydr l nguyn tn gin nht th khi cu tch in dng (+e)cn electron tch in m (-e). Nu electron v tr cch trung tm nguyn t mt khong r,trong khi bn knh ca nguyn t l R ln hn khong cch r. Khi electron s chu tc


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dng ca lc tng tc tnh in Culon t pha khi cu nm trn trong vng gii hn bibn knh r. Lc tng tac nay hng ve tam cau co tr so bang:

F = Ke. er2 = K

e2

r2 = f.r

trong 0

1

4k

= l h s t l trong hn v SI v K = 1 trong hn v CGS. Tr s e

= e.

Ti tm nguyn t (r = 0) electron trng thi cn bng (F = 0), khi lch khi v trcn bng (r 0) electron s thc hin dao ng iu ha quanh v tr cn bng di tcdng ca lc gin hi (f.r) vi f l h sn hi. Do electron ng vai tr nh mt daong tiu ha khi dao ng quanh v tr cn bng s bc x sng in t vi tn s:

1

2

F

M

= vi m l khi lng ca electron.

Vi gi tr r = 10 -8 cm th tn s bc x nm trong vng nh sng nhn thy.Nu trong nguyn t phc tp cha Z electron th cc v tr cn bng r0 sng vi v tr

cn bng gia lc ht tnh in ca electron bt k no vo tm ca khi cu nhim indng v lc tng tc y ln nhau ca cc electron cn li ca nguyn t.

Da vo mu nguyn t, Tomxn tnh ton i vi nguyn t Hydr bc x nng lngin t c bc sng trong vng c tr s c = 0,6 (m th kch thc ca nguyn t bng:

R = 3.10 -8 cmKt qu ny ph hp vi kt qu cho c t cc l thuyt khc, iu chng t s

ng n ca mu nguyn t Tomxn.Ngy nay mu nguyn t Tomxn c xem nh mt biu tng v nguyn t mang

ngha lch s nhiu hn l ngha vt l v n qu n gin khng kh nng gii thchnhng tnh cht phc tp ca quang ph bc x ca nguyn t Hydr v cc nguyn t phctp khc.

2. MU NGUYN TRDEPHO (RUTHERFORD).

Khi nghin cu cc hin tng xuyn thu qua cc lp vt liu ca cc ht mang intch chuyn ng vi nng lng ln lm thay i quan nim v cu trc ca nguyn t.

Nm 1903 Lenard nhn thy cc chm ht nng lng cao d dng xuyn qua cc l kimloi dt mng. iu chng t phn nhim in dng trong khi cu nguyn t khng th

phn bu trong ton b nguyn t m chnh xmt vng c kch thc nh hn rtnhiu so vi R = 10 -8 cm.

Nhng nhn xt ca Lenard c Rdepho khng nh bng nhng th nghim v hintng tn x ht ln l kim loi vng dt mng trong nhng nm (1908 1910).

Tia chnh l chm ht nhn ( 2He4 ) mang in tch (+2e) pht ra t cc ngun phng

x vi vn tc kh ln.


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V d: Cht phng x RaC cho cc ht phng x vi vn tc v 2. 109 cm/s tngng vi ng nng E 7. 106 eV.

Nu hng chm ht bay trongchn khng t nguon phong xa N quaqua khe hep cua bo loc L hng thang

vao la kim loai vang dat mong V. phasau la vang dat mong at knh anh K thni nao co hat ap vao knh anh se elai vet en tham so vi nhng chokhng c ht p vo.

Kt qu th nghim cho thy du vt cc ht li trn knh nh khng phi l mtm en m l mt vng lm tm hnh trn. Hin tng ny phn nh s tn x ca chm ht khi xuyn qua l vng mng. Rdepho kho st hin tng tn x ca chm ht khixuyn qua l vng mng v nhn thy cc ht b tn x di nhiu gc khc nhau t= 00 cho ti =1800

i vi nhng ht b tn x di gc ln =1800 khng th gii thch c nuda vo mu nguyn t Tomxn. Do vy, Rdepho buc phi a ra gi thuyt mi v cuto nguyn t. Nm 1911 Rdepho gi thit l trong nnguyn t c mt trung tm tchin dng v hu nh tp trung ton b khi lng ca nguyn t c bn knh nh hn bnknh nguyn t gp nhiu ln gi l ht nhn nguyn t. Kch thc ca nguyn t xc nh

bi khong cch t tm l ht nhn cho n cc electron phn b xung quanh ht nhn. Nhvy mu nguyn t Rdepho hon ton khc so vi mu nguyn t Tomxn.

khng nh gi thuyt v mu nguyn t ny Rdepho xy dng l thuyt tn xht ln ht nhn nguyn t v kim nghim li bng thc nghim. Ni dung chnh ca lthuyt tn x ht ln ht nhn nguyn t l kho st nh lng s phn b ca cc ht btn x theo gc tn x v i chiu vi kt qu thc nghim.

Theo l thuyt tn x ht ln ht nhn mang in tch dng do Rdepho xutth: Ht vi khi lng m mang in tch (+2e) bay vi vn tc v thm nhp vo vng tcdng ca trng lc Culon ca ht nhn mang in tch dng (+Ze) gy ra. Nu gi s htnhn (+Ze) ng yn v ht bay ti gn ht nhn s b lc y ca ht nhn nn quo

bay ca ht ( c dng l mt nhnh ca Hyperbon. (Hnh v).

2

Hnh 1.3. Minh hoa ly thuyet tan xa hat len hat nhan

N

b

r

+2e

+Ze

F

P

nF

0P

P

P

2


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Lc tng tc y tnh in Culon bng:

F = K(+Ze)(+2e)

r2 = K2Ze2

r2

trong K l h s t l, r l bn knh tng tc gia ht nhn (+Ze) v ht anpha (+2e).

Trn hnh v minh ha cho l thuyt tn x ht ln ht nhn trong trng hp ht bay

ngang qua cch ht nhn mt khong b gi l khong nhm. Nu ht bay vi khong nhmb nh s chu lc y tnh in Culon ca ht nhn mnh lm cho gc tn x ln, ngc likhi bay vi khong nhm b ln s chu lc y tnh in Culon t ht nhn yu lm cho gctn x nh. Nh vy gia gc tn x v khong chm b c quan h t l nghch. Chng tac th thit lp quan h gia b v da trn nh lut bo ton ng lng v mmen nglng i vi trng lc xuyn tm trong qu trnh tn x ca ht anpha (+2e) ln ht nhntch in dng (+Ze).

Gi 0P mv=

l ng lng ban u ca ht bay ti ht nhn (trc lc tn x), saukhi tn x trn ht nhn theo kiu va chm n hi gia ht v ht nhn nn ng lng htanpha l vm

=p . Ket qua cua qua trnh tan xa lam xuat hien so gia vec t ong lng gia

vec tban u 0P mv=

v vc tsau khi tn xP mv=

(Xem hnh v minh ha). Tr s cavc ts gia ng lng bng:

p

= 0p

2 sin

2 = vm

2 sin

2

Mt khc theo nh l v xung lng ta c:

p

=

0

t

Fn dt

Trong Fn = F. cos l hnh chiu ca lc tng tc y tnh in ca ht nhn(+Ze) ln ht (+2e) ln phng ca vct s gia ng lng p

. T hnh v cho thy

2 2

= +

nn do :

Fn = Fcos = F.sin

2 +

biu din:d

dt

= hay

ddt

= v

2

2

2ZeF k

r=

Ta c: 2 20

sin2

2 .p Ze d r

+

=

Cn tch phn ly t = 0 ng vi ht bay ln t bn tri b tn x theo mt nhnhHyperbon i ra xa v cng men theo ng tim cn ng vi gc = ( - ).

Do tng tc gia ht vi ht nhn trong trng lc xuyn tm nn mmen nglng bo ton:

L = mv.b = m.r2 = const


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Suy ra: v.b = .r2.

Do ta c:

p =

2Ze2

v.b

0

-

sin

2 + d =2Ze2

v.b 2cos2

ng nht hai biu thc:

2 .sin2

p mv

= v22

2cos. 2

Zep

v b

= ta c:

2mv.sin2 =

2Ze2

v.b 2cos2

Suy ra kt qu:

cotg 2 = mv2

2Ze2 b

Hm cot2

g

l hm nghch bin, vy khi b gim th tng v ngc li khi b tng th

gim. Kt qu ban u ny phn nh qu trnh tn x ca mt ht ln mt ht nhn khph hp vi d bo.

Trong thc t chm ht gm nhiu ht bay ti b nhiu ht nhn trong l kim loi gytn x, do vy vic gi thit mt ht b mt ht nhn gy tn x ch l trng hp n ginha vn xem xt ban u.

By gita xt c chm ht bay ti l kim loi. Ta gi thit cc ht trong chm htbay song song v cch u nhau. Chm ht c tit din ngang l S. Nhng ht no baytheo khong nhm b ti ht nhn s b tn x di gc , cn nhng ht no bay theokhong nhm (b - db) s b tn x di gc ln hn ( + d).

Trong thc nghim khng thxc nh c tng ht b ht nhngy tn x nhng xc sut ht btn x hon ton c th xc nhc. Xc sut ht b tn x trnmt ht nhn l t s gia din tch

ca hnh vnh khn bao quanh htnhn: dS = 2.b.db v tit din Sca chm ht v nhng ht ; notin n gn ht nhn trong l kimloi vng Au

(hnh 1.4) trong vng khong nhm b bin thin t b n (b + db) s ri vo din tch hnhvnh khn dS = 2.b.db l vng b ht nhn tn x. Cn nhng ht nm trong tit din

db

d

Au

b

dS = 2bdb

Hnh 1.4


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ngang S ca chm ngoi gii hn ca din tch hnh vnh khn dS = 2.b.db s khng btn x mnh nh trong vng din tch hnh vnh khn ang xt. Do vy, xc sut s ht b

mt ht nhn gy tn x l:2 . .b db

S

. Nu c n ht nhn gy tn x th xc sut s bng:

dW =2.b.db

S N.S. (1.1)

Trong :

- N l mt nguyn t trong l kim loi vng gy tn x (l s nguyn t cha trongmt n v th tch l kim loi

nN

V= ).

- l b dy l kim loi.- S l tit din chm ht ph ln b mt l kim loi. Kt qu ta c:

dW = 2.b.db.N.

T biu thc:2

2cot 2 2mvg bZe

=

suy ra: 1

sin2

2

d2 =

mv2

2Ze2 db

Thay th vo biu thc (1.1) ta c:

dW = N..

2Ze2

mv2 2 2 cotg

2

d

2sin2

2

tin tnh ton ta c th biu din h thc:

cotg2

sin2

2

=cos

2 sin

2

sin4

2

=sin

2sin4

2

Suy ra:

dW = N..

2Ze2

mv2

2

2.sin.d

sin42

= N..

Ze2

mv2

2

d

sin42

trong d = 2 .sin.d l gc khi bao ly gc tn x ca chm ht t gc n( + d).

Cng thc ny gi l cng thc Rdepho i vi qu trnh tn x ca chm ht lnl kim loi. Cng thc ny l kt qu ca l thuyt tn x ht ln cc ht nhn nguyn ttrong l kim loi.

Nm 1913, cng thc Rdepho c kim chng bng thc nghim. Nh vy githit v s tn ti ca ht nhn trong nguyn t hon ton c th chp nhn.


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Da vo m hnh nguyn t c ht nhn ngi ta tin hnh xc nh bn knhtng tc ngn nht gia ht nhn v ht khi ht bay trc din vo ht nhn. Bn knhtng tc ngn nht c xc nh:

mv2

2 = K(+2e).(+Ze)

rmin= K

2Ze2

rmin

T nhn c kt qu rmin i vi mt s kim loi c gi tr vo crmin 1,13.

10 -13 cm. T kt qu ny cho php suy on sb kch thc ca ht nhn nguyn t. Nhvy nu kch thc nguyn t vo c10 -8 cm th kch thc ca ht nhn vo c10 -13 cm,tc l bn knh ht nhn nh hn bn knh nguyn t khong 5 bc.

Da vo cng thc Rdepho v o c bng thc nghim i vi s ht b tn x dinhiu gc khc nhau (quan st di knh hin vi cc du vt ca ht li trn mn cmquang) ngi ta xc nh gi tr ca Z ng bng s electron c mt trong thnh phn cacc nguyn t trung ha v hon ton trng khp vi s th t ca nguyn t ha hc trong

bng tun hon cc nguyn t ha hc ca Mendelep.

Theo mu nguyn t c ht nhn cc electron phn b trong khng gian bao quanh htnhn. Kch thc cu hnh ca cc electron bao quanh ht nhn c trng cho kch thc ca

nguyn t. Theo l thuyt in ng lc hc Irnsoi th mt h gm cc electron mang intch m v ht nhn mang in tch dng c tr s bng nhau khng th tn ti trong mt hcn bng tnh ti m ch c th tn ti di dng cn bng ng. Vn dng l thuyt nyRdepho bt cc electron phi chuyn ng quanh ht nhn theo cc quo khp kntheo kiu tng t nh cc hnh tinh chuyn ng quanh mt tri. V vy, mu nguyn tcha ht nhn ca Rdepho c gi l mu hnh tinh nguyn t.

cho h nguyn t bn vng v mt chc th khi cc electron chuyn ng trnquo trn vi bn knh R v vn tc v phi m bo sao cho cc lc ly tm qun tnh caelectron cn bng vi lc ht tnh in Culon ca ht nhn:

mv2

R = K

Ze2

R2

Mt khc nng lng lin kt gia electron v ht nhn trong nguyn t bao gm ngnng v th nng tng tc gia electron v ht nhn:

E = E + Et =mv2

2 KZe2

R

n gin ta gi thit ht nhn nguyn t hu nhng yn, ch c electron quayquanh ht nhn.

T biu thc trn ta suy ra:

mv22 = K

Ze22R

Th vo biu thc nng lng lin kt ta c:

E = KZe2

2R KZe2

R = KZe2

2R

trong K l h s t l ( K =0

1

4trong hn v SI hay K=1 trong hn v CGS); cn

e l in tch ca electron.


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Nhng theo quan im in ng lc hc th mt h nh vy khng th tn ti bnvng v khi electron chuyn ng quanh ht nhn tng ng nh mt dng in trn khpkn c mmen lng cc in v mmen t. Mmen lng cc in ca nguyn t I s quaytheo kiu nh mmen ng lng ca con v quay trong trng lc hp dn ca qutxung quanh trc thng ng vung gc vi mt t. Khi mmen lng cc in I quay s

bin thin tun hon theo thi gian, bc x sng in t nn nng lng lin kt E s b gimdn, ko theo lm cho bn knh quo ca electron gim dn. Cui cng th electron s ri

vo ht nhn nguyn t. Nh vy nguyn t khng tn ti bn vng; iu ny hon ton muthun vi thc t. Nguyn t l h tn ti bn vng nhng theo mu nguyn t Rdepho thkhng bn vng. Nh vy tng xy dng mu nguyn t theo kiu chc thin th khngthnh cng.

Nhn li hai mu nguyn t Tomxn v Rdepho, ta nhn thy c nhng mt c vmt cha c. Trong mu nguyn t Tomxn bt cc electron bi trong qu cu nhimin dng, cn trong mu nguyn t Rdepho bt cc electron quay quanh ht nhn ukhng hp l. Nh vy chng t khng th p dng rp khun chc cin cho th giinguyn t. Mun thot khi nhng b tc ny ch c cch phi t b cc phng php truynthng ca vt l hc cin, sng to ra l thuyt mi. N.Bohr l ngi i theo hng tm

kim l thuyt mi cho th gii vi m th gii nguyn t.Nhng hn ch ca mu nguyn t Rdepho c khc phc trong mu nguyn t N.

Bohr.

3. MU NGUYN TN. BOHR.

Nm 1913 N. Bohr xy dng mu nguyn t Hydr l nguyn tn gin nht. xy dng mu nguyn t mi ny N. Bohr s dng nhng kt qu ca quang ph bc xnguyn t Hydr, vn dng tng lng t ca thuyt Plank v thuyt photon nh sng

ca Anhstanh.I. TNH QUY LUT CA QUANG PH NGUYN THYDR.

Vo nhng nm cui ca th k XIX, khi nghin cu quang ph ngi ta nhn thy ccbc sng trong ph nguyn t hp thnh nhng dy vch xc nh gin on gi l dy ph.Nm 1885 Banme (Balmer) l mt nh ton hc Thy S thit lp c biu thc m tcc vch trong dy quang ph bc x ca nguyn t Hydr trong vng nh sng nhn thy.Dy quang ph ny mang tn dy quang ph Banme. Trong dy quang ph Banme vch c

bc sng di nht v r nht = 6564 A0 c k hiu l H , vch tip thp k hiu l H, vi bc sng =4863 A0. Theo chiu gim ca bc sng cc vch ph cng b tr st vonhau v cng sng yu dn cho n mt vch gii hn m t khng cn phn bitc cc vch ring l na m ch thy mt dy mlin tc.

Cng thc Banme cho dy quang ph Hydr trong vng nhn thy c biu dinbng cng thc:

=1 = R

1

22 -1n2

Trong :

* gi l s sng l s bc sng trn mt n v di; n = 1, 2, 3, 4, l ccs nguyn t nhin* R l hng s Ritbe (R = 1,096776. 107 m-1 )


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T cng thc ny, tnh c gi tr ca vch u tin Hng vi n = 3, vch th haiHng vi n = 4, vch th ba Hng vi n = 5, vch th t Hng vi n = 6 v vch giihn (vch ranh gii) H ng vi n .

Tt c nhng gi tr tnh ton theo cng thc Banme ph hp tt vi cc kt qu thcnghim

Cc dy quang ph bc x ca nguyn

t Hydr c minh ha hnh 1.5. Ngoi dy Banme, ngi ta cn tmthy cc dy quang ph khc trongvng hng ngoi v t ngoi cng cquy lut tng t.

Trong vng t ngoi c dy Lyman vi cc s sng:

2 2

1 1 1

1v R n

= = vi n = 2, 3, 4,

Trong vng hng ngoi c cc dy quang ph:

- Pasen:2 2

1 1 1

3v R

n

= =

vi n = 4, 5, 6,

- Brakt:2 2

1 1 1

4v R

n

= =

vi n = 5, 6, 7,

- Phund:2 2

1 1 1

5v R

n

= =

vi n = 6, 7, 8,

Hp nht cc cng thc trn thnh mt dng chung c gi l cng thc Banme tngqut:

2 2

1 1 1v R

n m

= =

vi m > n

Nu gi nguyn tr s n = 1 thay i m = 2, 3, 4, ta c dy Lyman ; n = 2 vthay i m = 3, 4, 5, ta c dy Banme ; nu gi nguyn n = 3 v thay i m = 4, 5, 6, ta c dy Pasen v v.v ta s c tt c cc dy quang ph.

S tn ti ca tnh qui lut quang ph nguyn t Hydr cng nh quang ph ca nhiu

nguyn t phc tp khc l nhng bng chng v mt qui lut mi m, l tnh gin onkhng lin tc ca quang ph nguyn t.

Vung t ngoaiVunghongngoai

Vung nhn thay

H HH

Hnh 1.5


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II. THUYT N. BOHR.

Ni dung ca thuyt N. Bohrc xy dng trn hai nh v mt iu kin vlng t ha mmen ng lng quo. Nhng nh ny c a ra da trn csvndng khi nim lng t nng lng ca Plank ( = h) v khi nim photon nh sng caAnhstanh (Einstein) kt hp vi nhng ni dung ca l thuyt Rdepho v tnh qui lut ca

quang ph nguyn t Hydr.1. nh thnht v cc quo dng (trng thi dng ca nguyn t).

Electron trong nguyn t chuyn ng theo cc quo trn c nng lng hon tonxc nh gi l cc qu o dng hay trng thi dng. Khi chuyn ng theo cc quodng trong nguyn t electron khng bc x nng lng in t.

2. iu kin lng tha v mmen ng lng quo.Khi electron chuyn ng trn qu o dng phi tha mn sao cho mmen ng

lng quo ca n lun lun bng mt s nguyn ln ca hng s Plank chia cho 2 ( tc

l =h

2 ) :

L = m.vnrn = n vi n = 1, 2, 3, 4,Trong :

m l khi lng ca electron. Vn l vn tc ca electron. rn l bn knh ca quo dng. n = 1, 2, 3, 4, c gi l lng t s chnh.3. nh v tn s (cch bc x).Nguyn t ch hp th hay pht x nng lng di dng bc x sng in t theo c

ch nh photon nh sng khi n chuyn t trng thi dng ny sang trng thi dng khcc xc nh:

h = Eni

E

nk

viin

E l nng lng trng thi u vkn

E l nng lng trng thi cui. Nuin

E >

knE ng vi qu trnh pht x v nu

inE n


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Biu thc ny c dng trng vi cng thc Banme tng qut nu t ni = m v nk= n. V bn cht th n = 1, 2, 3, trong cng thc Banme ch l nhng con s s hc thunty khng cha ng ni dung vt l nhng trong l thuyt N. Bohr n c mt ngha vt l, l lng t s, c trng cho cc trng thi nng lng trong nguyn t. Mi vch quang

ph Hydr thu c t thc nghim tng ng vi qa trnh chuyn gia hai mc nnglng tng ng trong nguyn t. Nhcch ny m tnh qui lut ca quang ph nguyn tHydr v cc in tng t Hydr c lm sng t. ng gp ny ca l thuyt N. Bohr tht

l ln lao v gp phn thc y ngnh quang ph hc pht trin mnh m v t nhiuthnh tu bt ngtrong khoa hc k thut.

Thng qua hng s Ritbe biu thc nng lng lin kt ca electron trong nguyn tc th biu din di dng:

En =

R.h.cn2 Z

2

Trong :

h = 6,6. 10 -34 J.S l hng s Plank. c = 3. 108 m/s l vn tc nh sng. n = 1, 2, 3, 4, l lng t s chnh.Ni dung l thuyt N. Bohr v cch to ra cc dy quang ph c th minh ha trn

cng mt gin sau: (Hnh 1.8)

Hnh 1.8

En l nng lng lin ktelectron trong nguyn t:

En =

- R.h.cn2 Z

2 < 0

n = 1 l mc cbn. n = 2, 3, 4, 5, ( l ccmc kch thch.

Bn knh quo r1 ng vimc E1 v r2 ng vi mcE2 , r3 ng vi mc E3 , r ng vi nng lng .Khi electron s ri xanguyn t v bin nguyn tthnh in dng.

Bn cnh nhng thnh cng ni bt, l thuyt N. Bohr gii quyt nhiu vn v cutrc v quang ph bc x nguyn t; tuy nhin l thuyt N. Bohr cng bc l nhiu hn ch.

n = 3

E1

n = 2

n = 1

n = 4n = 5

n

E2

E3

E4

O

EnE > 0

r1

r2

r4

r3Da L man

Day Banme

Day Pasen

Day Braket


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Trc ht l thuyt N. Bohr ch p dng thnh cng cho nguyn t Hydr, i vi ccnguyn t phc tp l thuyt N. Bohr cha th gii quyt c.

L thuyt N. Bohr cha ng mu thun ni ti cho nn ni dung ca n cha ththon chnh th hin s kt hp va l thuyt cin ln l thuyt lng t di dng ccnh c tnh cht p t.

L thuyt N. Bohr cha cp n cng v b rng ca cc vch ph, c bit

vn cu trc tinh t ca cc vch quang ph khng th l gii c.Cho d l thuyt N. Bohr cn b hn ch, nhng nhng g m l thuyt N. Bohr lmc, c th ni l nhng vic lm mang tnh cch mng trong vt l hc. L thuyt N.Bohrc xem nh mt qu trnh chuyn tip t vt l hc cin sang vt l lng t hini.

5. KIM CHNG L THUYT N. BOHR BNG THC NGHIM.Nm 1914 Frank v Hc tin hnh th nghim cho php xc nh trc tip s tn ti

ca nhng trng thi nng lng gin on ca nguyn t v cch bc x v hp th can. Th nghim tin hnh nh sau: Trong mt ng chn khng bng thy tinh c b tr Catt

(K), Ant (A) v cc li (L). tng ca th nghim ny l dng chm electron pht ra t Kc tng tc trongin trng va chm trc tip vo cc nguyn t ca cht kh cn kho st c bm votrong ng thy tinh ban u ht ht khng kh c chn khng nht nh.

S th nghim c biu din theo nguyn tc sau:

ng thy tinh hnh tr c chn khng vi p sut 0,10 mmHg. Gia Catt (K) v li Lc ni vi th tng tc V1 , giali v Ant (A) cng c nivi in th nh hn V2 (khngln hn 0,5V).

Trong ng thy tinh c cha hithy ngn, khi electron thot ra tK s va chm vo cc nguyn tkh thy ngn theo hai cch:

- Cch va chm th nht l va chm n hi, trong cch va chm ny nng lng caelectron khng b bin i m ch thay i hng bay. Th tng tc V1 c thiu chnh linhhot iu khin dng in Ant.

- Cch va chm th hai l va chm khng n hi, kt qu ca loi va chm ny lmcho nng lng ca electron b bin i do truyn nng lng cho cc nguyn t kh thyngn.

Theo l thuyt N. Bohr th nguyn t hi thy ngn ch nhn tng lng nng lng doelectron truyn cho ch khng phi nhn mi gi tr bt k. Kt qu nguyn t thy ngnchuyn ln mt trong s cc trng thi kch thch c th c i vi nguyn t thy ngn.Trng thi kch thch gn nht chnh lch so vi trng thi cbn mt gi tr nng lng c4,86 eV. Chng no cc electron pht ra t K cha c tng tc ln, tc l cha t tr

R R

- + + -

G

V V

L AK

e

Hnh 1.9. S o th nghiem Frank Hec


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s eV1 = 4,86 eV th va chm gia electron vi cc nguyn t thy ngn ch l va chm nhi v dng in Ant tng ln. Khi va tng gi trng nng ca electron n 4,86 eV, tcth din ra va chm khng n hi gia cc electron vi cc nguyn t hi thy ngn.

Trong va chm khng n hi electron truyn ton b nng lng cho nguyn t thyngn lm cho nguyn t thy ngn b kch thch lm cho mt trong s cc electron nguyn tthy ngn chuyn t trng thi c bn ln trng thi kch thch. Do mt nng lng nn

electron sau khi va chm khng n hi khng thn Catt c. Do vy khi hiu in thgia Catt v li (L) bng 4,86 eV th dng in Ant phi gim xung. Hin tng s txy ra khi nng lng ca electron bng eV1= 2. 4,86 eV ; eV2=3. 4,86 eV ; tc l eV1 =n. 4,86 eV, th electron c th tham gia va chm khng n hi hai, ba hay nhiu ln.

ng c trng Von Ampe I=f(V) m t s ph thuc ca dng in Ant v hiu intht vo Catt v li (L) khng nh tnh ng n v trng thi nng lng dngtrong nguyn t ca l thuyt N. Bohr

Trong th nghim Frank v Hc khi tng hiu in th V ngi ta nhn thy nhng stdng in ng vi cc gi trin th V=4,86V ; V=9,72V; V= 4,58 V; ng thi cng

pht hin thy trong ng thy tinh c bc x t ngoi pht ra vi bc sng = 2537 A0.

Cc nguyn t kh thy ngn sau khi c kch thch bi cc va chm vi electron,trv trng thi cbn v pht ra cc phtn c nng lng h = 4,9eV ng bng nnglng hp th ca electron.

Nh vy th nghim ca Frank v Hc xc nhn s tn ti ca cc mc nng lnggin on ca nguyn t, tc l khng nh tnh ng n ca hai tin cbn trong lthuyt N.Bohr. Th nghim Frank v Hc cng chng t rng nguyn t khng phi ddng nhn ty tin nng lng ca electron t bn ngoi cung cp cho nguyn t, chng nonng lng ny cha ng bng nng lng cn thit chuyn n t mc ny sang mckhc, tc l t trng thi dng ny sang trng thi dng khc.


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Chng II

CSCA L THUYT LNG T

1. L THUYT PHOTON.

Csca l thuyt photon c xy dng trn tin cho rng: nh sng v cc loibc xin tc cu thnh t cc ht mang nng lng nh v gin on gi l ccphoton hay lng t.

Mi photon mang theo nng lng ph thuc vo tn s bc xin t tun theo hthc:

= h = hc

Trong :

h = 6,626. 10 -34 J.S l hng s Planck. c = 3. 10 8 m/s l vn tc lan truyn ca bc xin t trong chn khng (k

c vn tc lan truyn nh sng).

l tn s. l bc sng.

Mi photon s tng tc hon ton hoc khng tng tc vi vt cht, ngha l nhoc c th truyn ton b nng lng ca mnh hoc khng truyn mt t nng lng noc.

V cc photon chuyn ng vi vn tc nh sng nn theo thuyt tng i Einstein,khi lng ngh ca chng bng khng, do nng lng ca cc photon ch c th c

ngun gc ng hc. Nu mt photon tn ti th n s chuyn ng vi vn tc nh sng, nuphoton khng chuyn ng vi vn tc nh th na th n cng khng cn tn ti.

i vi photon khi lng ngh m0 = 0, h thc nng xung lng tng i tnh cdng:

E = p.c

Kt qu ny suy ra t h qu ca thuyt tng i:

m =m0

1 -v2

c2

nu nhn hai v ca biu thc ny vi2

42

1v

cc

ta c:

m2 c4 m2 v2 c2 = m20 c

4

Mt khc theo h thc lin h gia nng lng v khi lng:

E = m c2 v E0 = m0c2


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Vi ng nng bng: E = mc2 - m0c2

Trong E l nng lng v E0 l nng lng ngh tng ng vi khi lng ngh m0.Do ta c: 2 2 20 ( . )E E p c= +

Khi m0 = 0 th nng lng bng: E = p.cTheo quan nim lng t th cng ca bc xin t (trong c cng nh

sng) t l vi s photon p ln mt n v din tch t vung gc vi phng truyn cabc x:

I = N.h

Trong :

h l nng lng ca mt photon. N l thng lng photon (s photon ti trn mt n v din tch trong mt n

v thi gian) p n im ang xt.Da vo thuyt photon ngi ta gii thch c nhiu hin tng nh hin tng

quang in, hin tng tn x Compton v.v


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2. HIU NG QUANG IN.

Hiu ng quang in l hin tng gii thot cc electron t b mt kim loi khi ccc bc xin t thch hp chiu vo n. Cc electron bt ra t b mt kim loi gi l quangelectron.

C th nghin cu bng thc nghim hin tng quang in da vo sin t

(hnh 2.1):Trong mt ng thy tinh ht ht khng kh ri b tr vo hai in cc Ant (A) vCatt (K). H thng ny c mc vo mt s c hiu in th u. Khi di mt chm bcxin t thch hp vo Catt (K) trong mch xut hin dng in qua n k G. Thay ihiu in th u gia Catt v Ant c ghi nhn qua vn k V. T kt qu thc nghimnhn c ng c trng Von Ampe c dng l mt ng cong c biu din qua th hnh 2.2.

T thng c trng Von - Ampe I = f(u) ta nhn thy:1. Ban u cng dng in tng

theo hiu in th u; khi t n gitr u xc nh th dng in trnn

bo ha (Ibh) tc l khi u c tngthm th dng in vn khng tngna.

2. Ngay ti tr s u = 0 cng dng quang in vn c gi tr khckhng I0 0. iu ny chng tkhi cc electron thot ra khi Catt c sn ng nng ban u

E0 =mv2

2 .

3. C th trit tiu dng quang inban u bng cch tc dng vo haiin cc Ant v Catt mt hiuin th ngc gi l hiu in thcn (uc) ; hiu in th cn uc c gitr sao cho cng cn ca in trng

bng ng nng ban u cc i cacc quang electron:

mv2max2 = e.uc

Hin tng quang in c gii thch theo thuyt photon nh sau:Cc electron t do b nht trong kim loi khng th tng thot ra khi gii hn ca kim

loi. thot ra ngoi kim koi, t nht electron phi c ng nng bng cng thot A1 tngng vi tng cht liu ca kim loi xc nh. Bnh thng ng nng chuyn ng nhit


22/125

trung bnh ca electron trong kim loi nh hn cng thot A1. Tuy nhin khi di bc xint c tn s thch hp vo b mt kim loi, cc electron trong kim loi hp th photon. Mielectron hp th mt photon, tc l n nhn thm nng lng = h. Nng lng ny mt

phn chuyn thnh cng thot A1 v phn cn li chuyn thnh ng nng ban u caelectron. ng nng ban u cng ln khi electron nm cng gn b mt kim loi do electron nm trn b mt kim loi s c ng nng cc i. Theo nh lut bo ton nnglng ta c:

h = hc = A1 +

mv2max2

Biu thc ny gi l phng trnh Anhstanh. Da vo phng trnh trn c th giithch cc qui lut ca hiu ng quang in.

1. nh lut gii hn quang in.

Nh bit, ng nng khng bao gic gi tr m m lun lun dng nn ta c:

hc - A1 =

mv2max2 > 0

Suy ra: hc - A1 > 0 hay h

c > A1

Nu t 01

hc

A= ta c < 0 hay >0

Gi tr0 hay 0 gi l gii hn quang in, y l iu kin cn thit hiu ngquang in c th xy ra.

Nh vy i vi mi kim loi xc nh, hiu ng quang in ch c th xy ra khi dichm bc x c bc sng phi nh hn bc sng gii hn 0 hay c tn s phi lnhn tn s gii hn0.

Mi kim loi c mt gi tr0 (hay0) c trng ca n.

2. nh lut v dng in bo ton.

Dng quang in bo ha t c khi c bao nhiu electron bnh bt ra khi Catt(K) u hng v Ant (A) do vy dng in s cc i v khng i theo thi gian.

Nhng s quang electron thot khi b mt Catt t l vi s photon m kim loi chto Catt hp th. S photon li t l vi cng ca chm bc x di vo Catt, chnh vth m cng dng quang in bo ha (Ibh) t l vi cng ca chm bc x di ti.

ng cong bo ha (1) ng vi cng chm bc x di ti Catt nh hn so vi ngcong bo ha (2) ng vi cng chm bc x di ti Catt ln hn.

3. nh lut ng nng cc i ca quang electron.

ng nng cc i ban u ca quang electron ch ph thuc vo tn s ca chm bcx di ti kim loi m khng ph thuc vo cng ca n. Theo cng thc Anhstanh tac:


23/125

mv2max2 = h - h0 = h( - 0)

Nu n quan h gia cng cn v hiu in th cn ta c:

h = h0 + e.uc

Suy ra: e.uc = h( - 0)T cho thy ng nng cc i ca quang electron ch ph thuc vo tn s bc x

di ti b mt kim loi.

3. HIU NG TN X COMPTON.

Nm 1922 Compton lm th nghim cho mtchm tia X vi bc sng xc nh di vo cccht liu: paraphin, grapht, v.v , v nhn thy khitruyn qua cc cht liu ny, chm tia X b tn x(truyn lch phng so vi phng ban u).

Trong ph tia X thng thng, ngoivch phng vi gi tr bc sng ti cn xuthin vch phng vi bc sng c gi tr lnhn (tc l ( > ). Cc kt qu thc nghim chothy bc sng khng ph thuc vo cu to cacht b di bi tia X m ch ph thuc vo gc tn x (Xem hnh 2.3). tng ca bc sng do kt qutn xc xc nh:

= - = 2c sin22hoc cn c th biu din di dng: = - = 2c (1 - cos)Trong :

00,0243c h Amc

= = gi l bc sng

Compton m = 9,1. 10 -31 kg l khi lng

ca electron. c lvn tc nh sng h l hng s Planck.

Da vo thuyt photon ca Anhstanh c th gii thch hin tng tn x Compton.

Hiu ng tn x Compton c th xem l kt qu ca qu trnh tn xn hi ca chmphoton tia X di ti cc in t trong nguyn t cht gy tn x.

Trong ph tia X, vch ng vi bc sng c th xem nh tia X b tn x trn ccelectron nm cc lp in t bn trong nguyn t b tr gn st vi ht nhn, nhngelectron ny lin kt mnh vi ht nhn nh khng th no nh bt chng ra c, cn vch


24/125

ng vi bc sng > tng ng vi s tn x ca chm tia X vi electron lp ngoilin kt yu vi ht nhn nguyn t (c th xem nh electron t do) nn chm tia X nh btelectron lin kt ra khi phm vi nguyn t. Kt qu ca qu trnh tn x ny chm photon tiaX nhng mt phn nng lng nh bt electron, phn cn li mang theo khi b tn xcho nn nng lng ca n gim i lm cho bc sng tng ln, kt qu ta nhn c >.

Trong thc nghim Compton s dng tia X vi bc sng = 0,7A

0

tn x trnGrapht. V nng lng tia X tng ng vi gi tr c1,8. 104 eV, gi tr ny ln hn rtnhiu so vi nng lng lin kt ca electron cc lp bn ngoi ca nguyn t Ccbon lthnh phn chnh ca Grapht. Chnh v vy m c th xem cc electron l p ngoi canguyn t l t do so vi nng lng chm tia X di ti Grapht.

Da vo nh lut bo ton nng lng v bo ton ng lng trong qu trnh tn xchm tia X ln electron trong nguyn t, thu nhn cng thc tn x Compton.

Tia X xem nh photon ti c nng lng E = h ='

hc

v ng lng: P =

h

Theo nh lut bo ton nng lng ta c:

hc + m0c

2 = hc + mc2 (2.1)

v nh lut bo ton ng lng:

p

=p

+pe

(2.2)

T cng thc (2.2) suy ra:

pe

=p

-p

(2.3)

pe c gi trc xc nh bi cng thc:

p2e = p

2 + p2 - 2ppcos

X

X

P =h

E = h

eHnh 2.4. S tan xa tia X len e

P =h

E = h

e

Ee = mc2

Pe = mv

y


25/125

Trong m0 l khi lng ngh ca electron v m l khi lng ca electron chuynng vi vn tc v. Ly phng trnh th (2.1) bnh phng tr hai v cho phng trnhth hai (2.2) bnh phng hai v ta c:

m0c2 ( - ) = h (1 - cos)

m0c2

c

-c

=h.c2

. (1 - cos)

m0c2

-

. c =h.c2

. (1 - cos)

Suy ra: = - =h

m0c(1 - cos)

Hay: = - =h

m0c2sin2

2

Trong ta t c =0

h

m c

dn n kt qu (1 cos )c = .

Nh vy l thuyt photon gii thch y hiu ng tn x Compton.

4. SNG DBRI (DE BROGLIE) CA HT VI M.

1. Lng tnh sng ht ca nh sng.

Vt l hc khng nh nh sng c bn cht hai mt gi l lng tnh sng ht:

- Tnh cht sng th hin s giao thoa, nhiu x, phn cc - Tnh cht ht photon th hin hiu ng quang in, hiu ng tn x Compton.Theo l thuyt photon, nh sng c cu thnh t nhiu phn t b nh gi l photon

nh sng. Mi photon nh sng mang nng lng v ng lng (hay xung lng) hon tonxc nh theo h thc Anhstanh:

E = h (2.4)

p =h (2.5)

ep

Hnh 2.5. Bao toan ong lng

'p

p


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Cc i lng: nng lng E v xunglng p c trng cho tnh cht ht, cn bcsng v tn s c trng cho tnh chtsng. Hai c trng sng v ht c lin hvi nhau thng qua hng s Plank h.

Hm dao ng ca nh sng c th

biu din thng qua nng lng v xunglng. Nu xem s lan truyen cua anh sang las lan ta trong khng gian ca sng phng,th mt dao ng sng n sc ti O c

biu din:

u0 = A cos2 t

trong A l bin , l tn s; th sau thi gian t sng nh sng s truyn n v tr M cchO mt khong d s c dng sau:

uM = A cos2

t - dc

trong c l vn tc nh sng.

Gia tn s v bc sng nh sng c quan h:

=c

OM =r

d = r cos = (r

.n

)

vi n

l php tuyn vc tn v hng theo phng truyn sng. Dao ng sng ti Mc biu din:

uM = A cos2(t -

r

.n

)

Di dng phc hm sng nh sng c biu din:

Nu th E = h vo biu thc ta c:

= A.e-

i(Et -

p

.r

)


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trong 2

h

= l hng s Planck chia cho 2.

Nu biu din thng qua vc tsng k

l vc thng theo phng truyn sng c tr

s2

k

= v p k=

, hm sng c dng:

= A.e- i

Et -k

.r

2. Lng tnh sng ht ca ht vi m sng DBri.

Nm 1924 DBri khi qut ha lng tnh sng ht ca nh sng cho cc htvi m nh electron, photon, ntron v.v

DBri cho rng khi mt ht chuyn ng t do c nng lng v xung lng xcnh s tng ng vi mt sng phng n sc lan truyn theo phng chuyn ng ca ht,c m t bi hm sng:

= A.e- i

Et

-k

.r

gn lin vi bc sng v tn s xc nh:

=hp vi p = mv

=E

h

Sng DBri l loi sng khng c ngun gc dao ng c hc, cng khng cngun gc in t, n l loi sng gn lin vi ht vt cht khi chuyn ng. Khc vi sng

nh sng ch, gia tn s v bc sng DBri khng c quan h =c

. Bc sng D

Bri lin h trc tip vi khi lng v vn tc chuyn ng ca ht:h

m

= .

5. KIM CHNG GI THUYT SNG DBRI.

Mun khng nh tnh cht sng ca mt i tng no , iu cn thit l phio c bc sng ca n. Cng vic ny c Ing thc hin vo nm 1801 khngnh tnh cht sng ca nh sng v Laue tin hnh vo nm 1912 xc nhn bn cht sngca tia X.

khng nh bn cht sng ca electron ngi ta kho st hin tng nhiu x can qua n tinh th, tng t nh kho st hin tng nhiu x tia X.

Nu qu tht electron c bn cht sng th n phi cho hnh nhiu x.


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Chng ta s bnh gi bc sng DBri ca electron chuyn ng trong intrng vi hiu in th u c gi tr bng:

m2

pE

mE2

h

mv

h 2=== nangongvi

ng nng ca electron do nng lng in trng cung cp v bng

mv22 = e.u

nu thay cc tr s khi lng m, in tch e v hiu in th u tnh bng Von v bc sng

tnh bng A0, ta c bc sng: =12,25

u(v)A0

Nm 1927 C.J. Davinxn tin hnh th nghim cho electronnhiu x trn n tinh th Ni(Niken).Khi Davinxn iu chnh chmelectron c tng tc bi hiuin th u nh bin tr R xuynqua khe lc L hp vi b mt tinhth Niken mt gc tha mn iukin nhiu x Vunph Brc:

2 1 2 sind n = = = vi n = 1, 2, 3,

Trong :

l hiu ng i ca hai tia bng mt s nguyn ln bc sng. d l hng s mng tinh th Niken ng vai tr l cch t nhiu x (d = 0,91 A0

cng bc vi bc sng DBri ca electron). Qu nhin hai chm tia phn x caelectron t b mt mng tinh th cho cc cc i nhiu xan xen vo nhau.


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Kt qu ny khng nh tnh cht sng ca electron.

Cng trong nm 1927, clp vi Davinxn; P. Tomxn tinhnh kho st nhiu x chmelectron xuyn qua l kim loimng.

Bn cht vt l ca chmelectron n nng nhiu x trn lkim loi mng c P. Tomxn lgii nh sau: trong l kim loicha nhiu tinh th nh hngngu nhin, trong s c nhngn tinh th sp x p theo mt trtt xc nh, cho nn khi iu chnhcc thng s thch hp P. Tomxn thu c hnh nhiu x c dngnhng vn trn ti sng an xen

vo nhau.

Sau Tomxn tip tc th nghim vi bt nhm p thnh l mng ri cho chm tiaelectron n nng xuyn qua vi bc sng thch h p cng bc vi bc sng tia X, P.Tomxn cng thu c cc cc i nhiu xi vi chm tia electron. Cng trn mu nhmy P. Tomxn cho chm tia X xuyn qua th cng thu c cc cc i nhiu x, hon tonging nh cc cc i nhiu x ca sng DBri ca electron. y l mt kt qu bt nght sc th v. iu ny mt ln na khng nh tnh cht sng DBri ca electron.


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6. H THC BT NH HAISENBC (HEISENBERG)

i vi electron khi chuyn ng v nguyn tc th chng ta c tho c c v tr(ta ) ln xung lng (p = mv) ca n ti bt c thi im no vi ta chnh xc khnghn ch. Nhng iu khng th lm c. khng phi l do nhng kh khn no trong khi tin hnh o m do mt nguyn nhn g ? iu m chng ta gp phi, l mthn ch c tnh cht cbn i vi khi nim ht vi m. H thc bt nh Haisenbc to cho

chng ta mt o nh lng ca s hn ch. Gi s chng ta o c v tr ln xung lngca mt electron b gii hn khi chuyn ng qua khe c b rng l d hng theo trc x. Gis (x l bt nh trong php o v tr v (px l bt nh trong php o xung lng caelectron. Haisenbc pht biu h thc bt nh (cn gi l nguyn l bt nh):

x.px hTng t nh vy i vi hai trc y v z:

z.pz h

tm hiu ngha ca h thcbt nh ta xt trng hp:

x.px h

(nu cn n s chnh xc hn ngita cn biu din h thc bt nh

di dng: .2

hx px

hoc

x.px h

4 thay cho h, tm thi

chng ta khng quan tm n skhc bit nh ny).

iu c ngha l, nu ta dn dng mt th nghim xc nh v tr ta caelectron mt cch chnh xc nht (c thc) bng cch lm cho x nh ty , th s khng

o c tht chnh xc xung lng ca n (v px s trnn ln hn). Ngc li nu dndng mt th nghim lm tng chnh xc ca php o xung lng th chnh xc caphp o ta s km i. Tch ca hai bt nh lun ln hn hoc bng hng s Planck(h). Ta v xung lng l hai vc t, nn h thc trn cng ng cho hai ta v xunglng theo y v z.

Gi s mt electron c biu din bng mt sng DBri p vp mt khe c rng x trn mn chn L. Ta s th xc nh chnh xc v tr theo phng thng ng x vcc thnh phn xung lng ca electron ti thi im i qua khe.

Nu electron i qua khe, th ta s bit v tr ca n ng thi im vi bt nh (x.Bng cch thu nh rng d ca khe, chng ta c th xc nh v tr theo phng thng ngca electron vi bt k chnh xc no m ta mong mun.

Tuy nhin, cc sng DBri ca ht vt cht, cng ging nh cc sng khc s b loera do nhiu x khi chng i qua khe. Hn th na, khe cng hp th chng b loe cng nhiu.Theo quan im ht, s loe c ngha l electron s c c thnh phn thng ng ca xunglng khi n i qua khe.

C mt gi trc bit ca thnh phn thng ng ca xung lng sa electron ncc tiu u tin ca bc tranh nhiu x, im N trn mn hng nh nhiu x electron quakhe (Mn M). Chng ta ly gi tr ny lm so bt nh px ca xung lng chiu ln

phng trc x.

X

L

e

d

p

M

N

N

p


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Cc tiu u tin ca bc tranh nhiu xc xc nh theo biu thc:

d.sin = n. vi n = 1, 2, 3,

y l quy lut xc nh cc v tr cc vn ti ca sng nhiu x qua khe hp. Cc tiu utin ng vi n = 1 nn ta c:

d.sin =

b rng ca khe d c xc nh chnh xc n x nn c th xem nhx = d, vy ta c:

sin =

x

Nu gc nh ta c th thay th sin = vh

= , do ta c:

=h

p.x

Trong : p l thnh phn xung lng theo phng nm ngang. t ti cc tiuu tin th gc cng cn phi tha mn iu kin:

=pxp

T ta suy ra: x.px h

Mt pht biu khc ca h thc bt nh Haisenbc l pht biu qua nng lng vthi gian, c hai u l nhng i lng v hng:

E.t h

Nh vy, nu chng ta tho nng lng ca ht trong mt khong thi gian no .

Php o ny s chu mt lng bt nh l E lin h bi E h

t

. hon thin chnh

xc E ta phi tin hnh php o nng lng ko di trong thi gian lu hn. iu ny pdng cho nguyn t th b rng mc nng lng kch thch E cng ln th thi gian tn tica n cng ngn. i vi mc nng lng cbn tn ti lu bn, c th xem nht ,do vy bt nh v nng lng ca n xem nhE 0.

V d: Xt electron chuyn ng trong nguyn t c kch thc xp x bng 10-10 m.Vn tc chuyn ng trung bnh ca electron trong nguyn t l 106 m/s.

Theo h thc bt nh:

s

m10.2,7

10.10.1,9

10.6,6

x.m

hv 6

1031

34

x ===

c ngha l sai s v vn tc vx c gi tr tng ng vi gi tr vn tc ca electron.Sdc nghch l ny l do chng ta bt electron chuyn ng theo quo trn

quanh ht nhn. Khi vn dng h thc bt nh cho thy s p buc l v l. Vy khngth xem electron ging nh vt vm. Nh vy h thc bt nh Haisenbc c xem nhmt gii hn cho bit khi no vt l cin cn hiu lc. khng xut hin nghch l trnch c cch l khng xem electron chuyn ng theo quo khp kn quanh ht nhn trongnguyn t m mang c tnh sng, khng chuyn ng theo quo no ht.

V d: Cng l electron nhng chuyn ng trong bung bt Winsn th li c quor rt.


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i vi electron chuyn ng trong bung bt Winxn c quo r rt v quo lmt chui ca nhng git nc nhnh du v tr ca electron trn ng i. Kch thcca cc git nc khong chng 10 - 6 m cho nn c th ly x = 10 - 6 m. Khi lng cami git nc c chng m = 10 - 3 g do vy sai s v vn tc theo h thc bt nh:

s

m10.6,6

10.10.

10.6,6

x.m

hv 22

66

34

x ===

Sai s ny v cng nh do vy trong trng hp ny c th p dng vt l cin choelectron chuyn ng trong bung bt Winxn.

7. HM SNG V PHNG TRNH SRODING.1. Phng trnh Srding.

Nm 1926 Srding xut phng trnh vi phn m nhng tnh cht ca n png cc qui lut vn ng ca cc ht trong th gii vi m. Phng trnh Srdingc xeml mt trong nhng csquan trng ca l thuyt lng t. Chng ta quan tm n phngtrnh dng l phng trnh cp n cc hin tng v cc qu trnh khng ph thuc vothi gian, c dng:

+ 2m2 [E - U] = 0

Trong : U = U(x,y,z) l hm th tng tc ca ht vi m trong trng th. E l nng lng ton phn ca ht. m l khi lng ca ht vi m. l hm sng m t trng thi ca ht vi m. l ton t Laplace c dng:

=2

x2 +

2

y2 +

2

z2

Khi gii phng trnh Srdingi vi hm th U v cc iu kin bin cho trc, tas xc nh c nghim (x,y,z). Tuy nhin khng phi mi nghim (x,y,z) u lnghim vt l. Trong nhng nghim (x,y,z) ch c nhng gi tr no tha mn cc iu kin:n tr, hu hn v lin tc th mi c xem l nghim vt l. Ngoi ba iu kin trn hm sng (x,y,z) c xem l nghm vt l, cn i hi thm iu kin o hm bc nhtca n cng phi n tr, hu hn v lin tc.

Vn ngha ca hm sng c tranh lun trong mt thi gian kh di v cuicng i n s tha nhn rng ri l: Hm sng m t trng thi ca ht vi m v n mang ngha xc sut i vi th gii cc ht vi m.

Theo gi thuyt DBri, chuyn ng ca ht t do c m t bi hm sng tngt nh sng phng n sc:

- = 0.e-

i [Et -

p

.r

]


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hoc c dng:.

0.

Eti k r

e

=

Trong :

k l vctsng c tr s bng k = 2

0 gi l bin ca hm sng c xc nh bi biu thc:20 =

2 = .*

Biu thc trn gi l hm sng DBri. Ni chung, i vi cc ht vi m chuynng trong trng th, hm sng ca n l mt hm phc tp ca ta v thi gian:

(r

,t) = (x,y,z,t)


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2. ngha ca hm sng.

hiu r ngha ca hm sng ta i chiu vi ngha sng ht ca photon nhsng truyn trong khng gian.

Gi s ti im M trong khng gian c mt chm sng di vo. Ta vy quanh im Mbi mt yu t th tch V. Theo quan im sng th cng sng ti M s t l vi bnhphng bin dao ng sng ti M.

I = 0. c. E2

Trong : Cng sng I l nng lng trn mt n v din tch trong mt n v thi

gian 0 l hng sin. c l vn tc nh sng. E l cng in trng.

Trong trng hp ny nu bnh phng bin dao ng sng 20 ti M cng ln thim M cng sng.

Theo quan im ht th cng sng ti M bng:I = N. h

Trong :

h l nng lng ca mt photon. N l thng lng photon (s photon ti trn mt n v din tch trong mt

n v thi gian) ti im M.Nh vy, theo quan im ht, sng ti M t l vi nng lng ca cc ht trong n

v th tch bao quanh M, ngha l t l vi s ht c mt trong n v th tch .

Do s ht trong n v th tch bao quanh M t l vi bnh phng bin dao

ng sng 20 ti M.Nu s ht trong n v th tch cng nhiu th kh nng tm thy ht trong cng

ln. V th ngi ta ni rng bnh phng bin sng 2 ti M c trng cho kh nng tm

thy ht trong n v th tch bao quanh M.V vy, ngi ta gi 2 l mt xc sut tm thy ht ti M (xc sut tm thy ht

trong mt n v th tch). T cho thy xc sut tm thy ht trong th tch bt k dV l: (2

.dV) Nu i tm trong ton b khng gian chc chn phi thy ht, tc l:

-

+

2.dv

= 1

iu kin ny c p dng chun ha hm sng gi l iu kin chun ha.Hm sng khng m t mt sng thc no trong khng gian nh sng chay sng

in t m ch cho php ta tnh xc sut tm thy ht ti mt trng thi no . Hay ni cchkhc hm sng mang tnh xc sut.


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8. HT TRONG HP TH NNG.Vn dng phng trnh Srdingcho trng hp mt ht vi m trong hp th nng.

Ta xt trng hp n gin l ht chuyn ng theo phng x trong vng c th nng cxc nh theo iu kin sau:

U =0 trong vung 0 < x < a trong vung x 0 va x 0

Min nh vy, c gi l hpth nng hay h th nng c b rng la.

Nh vy ta ch xt trng hpht vi m ch chuyn ng trong phmvi trong lng h p th v khng thvt ra ngoi gii hn ca h p th.(Trng hp ny c th tng ng vielectron trong kim loi ch khng

th t thot ra ngoi c).

Gii phng trnh Srdingcho ht trong hp th c khi lng m:

+2m2 [E - U] = 0

Bn trong hp th, th nng tng tc U = 0, nn phng trnh c dng:

+2m 2 E = 0

V ch xt hp th mt chiu, nn hm ( ch ph thuc vo mt ta x:d2dx2 +

2m 2 E(x) = 0

t 22

2mK E=

phng trnh c dng:

d2dx2 + k

2(x) = 0

Phng trnh ny thuc loi chnh tc, c nghim c xc nh di dng:(x) = A sinkx + B coskx

A, B l nhng hng sc xc nh da vo cc iu kin c th ban u ca bi ton vtl.

V ht ch tn ti bn trong lng h p th, nn trn thnh tr ra ngoi h p th htkhng c mt, do ta c:

(0) = (a) = 0Th vo: (0) = Asin k.0 + Bcosk.0 = 0 + B = 0

Vy ta c (x) = A sin kxThiu kin (a) = Asin k.a = 0V A 0 nn:

a.k = n vi n = 1, 2, 3, 4 . . .

U

U = U =

U = 0

a x0

Hnh 2.10


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Suy ra: k =na

Vy: (x) = A sinn

a

x

xc nh A ta da vo iu kin chun ha hm sng:

0

a

2.dx

= 1

th vo: 2 2

0

sin . 1a

nA x dx

a

=

Ly tch phn ta c: A =2

a

Vy hm sng c xc nh hon ton:

...,4,3,2,1nxa

nsin

a

2)x(n =

= vi

Kt qu nng lng:2 2

22 2

2mE nk

a

= =

Suy ra: En = n2

22

2ma2 vi n = 1, 2, 3,

Kt lun chung:

1)Mi trng thi ca ht ngvi mt hm sng n(x).

2)Nng lng ca ht trongh p th nng ph thucvo s nguyn n = 1, 2,3, 4, tc l nhn nhnggi tr gin on, khnglin tc gi l b lng tha.

3)Mt xc sut tm thyht trong hp th bng:

n(x)2 =2a sin

2

n

a x

Hnh 2.11 minh ha cc mc nng lng v mt xc sut tm thy ht vi m tronghp th, tng ng vi cc trng thi khc nhau.

n = 4

n = 3

n = 2

n = 1

n = 4

n = 3

n = 2

n = 1

E4

E3

E2

E1

0 a x

En2

0 a x

Hnh 2.11


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Chng III

CU TRC NGUYN YTHEO L THUYT LNG T

1. CU TRC NGUYN THYDR V CC ION TNG THYDR (He+,

Li++, Be+++, )

Theo quan nim lng t thnguyn t Hydr v cc in tng tHydr nh He+ (Z=2), Liti Li++ (Z= 3), Berili Be+++ (Z=4), ccu to t ht nhn mang in tchdng (+Ze) v mt electron mangin tch m (-e).

tin kho st cc tnh cht

ca nguyn t ta xem nh ht nhnng yn, ch c electron chuynng quanh ht nhn. Chn ht nhnlm gc ta v r l khong ccht ht nhn n electron.

Phng trnh Srdingi vi nguyn t c dng:

+2m2 [E U] = 0

Trong :

m l khi lng ca electron chuyn ng quanh ht nhn. (Trong trng hpxem electron v ht nhn khng ng yn ta thay th khi lng ca electron

m bng khi lng rt gn ca c h electron ht nhn.m M

m M =

+vi M l

khi lng ht nhn).

U(r) l th tng tc gia ht nhn (+Ze) v electron mang in tch m (-e) ctnh cht i xng cu, do vy bi ton s gii trong h ta cu (r,,) thtin li hn. Gia h ta cu v h ta (Oxyz) c quan h:

x = r sin.siny = r sin.cos

z = r cosTh nng tng tc gia ht nhn v electron c dng:

U = - kze2

r

k l h s t l (trong hn vo lng SI: k =0

1

4

= , trong hn vo lng CGS:

k = 1).

Th K vo phng trnh ta c:

y

x

e

0

z

Hnh 3.1. Nguyen t trong he toa o cau


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+2m2

E + kZe2

r = 0

Trong :

E l vo nng lng lin kt ca electron vi ht nhn. l ton t Laplace trong h ta (Oxyz) c dng:

=2.x2 +

2. y2 +

2. z 2

Th ton t vo phng trnh ta c:

2x2 +

2y2 +

2z 2 +

2m2

E + kZe2

r = 0

Chuyn sang h ta cu (r,,) phng trnh c dng:

1r2

r

r2r +

1r2sin

sin +

1r2sin2

22

+2m2

E + k

Ze2r = 0

y l phng trnh vi phn o hm ring cp hai, c th gii theo cch phn ly binc, bng cch t:

(r,,) = R(r). Y(,)Trong :

R(r) gi l hm bn knh Y(,) gi l hm cu.

Ring hm cu c th tip tc phn ly bin s:

Y(,) = ().()Vy nghim tng qut ca phng trnh c dng:

(r,,) = R(r).().()Trong v s nghim ca phng trnh, ch c nhng nghim no hi iu kin n

tr, hu hn v lin tcmi l nghim vt l ch thc.

Nghim ca hm c dng: = A.ei.m., trong A l hng s chun ha.

cho (r,,) tha mn iu kin n tr, hu hn v lin tc th m = 0. 1, 2, 3, , .

Nghim ca hm c dng:

() = c(1 x2)|m|2

d+|m|

d+|m| (x2 - 1)

vi x = cos ; c l hng s. cho () tha mn iu kin n tr, hu hn v lin tc th = 0, 1, 2, 3, (n

1) vi n = 1, 2, 3, 4, v m = 0, 1, 2, 3, , ?

Nghim ca hm c dng:


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R = c.e

ra0

Trong :- c l hng s.-

2

0 2a kme=

gi l bn knh quo N. Bohr.

Kt qu gii phng trnh Srding thu c hm sng(r,, ) v biu thc nnglng:

En = k2me4Z2

2n2 2

Vi n = 1, 2, 3, 4, gi l lng t s chnh, c trng cho s lng t ha nnglng lin kt ca electron trong nguyn t.

Thng qua hng s Ritbe R =2 4

0 34

k mea

c=

biu thc nng lng c dng:

En = Rhcn2 Z

2

i vi nguyn t Hydr (Z = 1) cn cc in tng t Hydr th Z > 1 (V d: ivi He+ th Z = 2,vi Liti (Li++) th Z = 3, vi Berili (Be+++) th Z = 4, ).

Hm sng m t trng thi lng t ca electron trong nguyn t, li ph thuc vo hlng t s n, ?, m. Mi lng t sc trng cho mt i lng vt l. Mi trng thi nnglng ph thuc vo ba lng t sc k hiu nh sau:

(r,,)n,,m =

R (r)n,

(),m

()m

Trong qu trnh gii phng trnh Srdingcn nhn c nhng kt qu v momenng lng quo L, gi tr hnh chiu ca momen ng lng Lz ln phng u tin Ozc xc nh:

( 1)L = + vi = 0,1, 2, 3 (n-1)

gi l lng t s momen ng lng quo.

Lz = m vi m = 0 1, 2, 3,

m gi l lng t s t xc nh gi tr hnh chiu ca vctmomen ng lng L ln trcOz, gm c thy (2 + 1) tr s khc nhau.


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2. MU NGUYN TTHEO L THUYT LNG T.

Theo l thuyt lng t th nguyn t l mt h thng gm c ht nhn l trung tm vcc electron phn b quanh ht theo cc qui lut xc sut thng k lng t, ch chngkhng chuyn ng theo quo c th no c. C th l mi trng thi lng t xc nhvi mt xc sut tm thy electron trong nguyn t, c c trng bi 2 th xc sut

tm thy electron bng:

dr.d.dsinr.m,,n

,,r(dv. 2

22

=

vi dV l yu t th tch, trong electron tn ti quanh ht nhn:

dV = r2.sin.d.d.dr

Biu thc xc sut c th tch lm hai phn: mt phn ph thuc vo bn knh v mtphn ph thuc vo gc.

Nu gi mt xc sut tm thy electron quanh ht nhn trong yu t th tch dV phthuc vo bn knh l

( )

,

W r

n v ph thuc vo gc l

( , )

,

W

m

th xc sut tm thy electron:

Xc sut theo bn knh r: 2 2( ). ( ). ., ,

W r dr R r r dr

n n=

Theo cc gc , : 2( , ).sin . . ( , ) .sin . ., ,

W d d Y d d

m m

=

minh ha ta ch xt ngcong biu din mt xc sut tmthay electron quanh ht nhn nguynt bn knh r:

Trc tung l mt xc sut tmthy electron quanh ht nhn R2.r2 = R.R*.r2 , trc honh l bn knh tnht tm O ht nhn, r ly theo n v a0l bn knh quo N. Bohr : a0 =0,53A0 .

Hnh 3.2

T th cho thy bt k khong cch no ca r (ngoi tr trong ht nhn r = 0) uc kh nng tm thy electron: mi trng thi ng c tng ng xc sut ln nht; ngha lti kh nng tm thy electron l ln nht.

V dtrng thi cbn (n = 1 th = 0) hm bn knh c dng:

n = 1, l = 0

R.R*.r2

n = 1l = 0

n = 1, l = 0

r0 1 32 4 5 76 8 9 1110 12


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R1,0 = 2

Z

a0

32 .e

zra0

Xc sut tng ng: 03 2

2 2 21,0

0

4 . .zr

azR r e r

a

=

tm gi tr ca bn knh rng vi xc sut cc i ta i tm gi tr cc tr ca hmbng cch cho o hm bc mt ca hm bng khng:

dW1,0dr = 4

z

a0

2.e

zra0 .2r

1 zra0

= 0

o hm trit tiu ti r = 0 v r = 0a

Z. Nghim r = 0 b loi v khng ph hp

ngha vt l, v electron khng tn ti trong ht nhn.

Vy xc sut cc i ng vi bn knh r =0a

Z , i vi Hydr Z = 1 nn r = a0 =0,53 A0 . Khong cch ny ng bng bn knh quo N. Bohr. Nh vy hai kt qu ca hail thuyt ph hp vi nhau l thuyt ca N. Bohr v l thuyt lng t cho cng mt tr sca bn knh rquo gn ht nhn nht.

T kt qu trn cho thy electron trong nguyn t khng chuyn ng theo quonht nh nh quan nim cin. V mt hnh thc ta c th hnh dung electron bao quanhht nhn nh mt m my xc sut ni no s c mt ca electron thng xuyn hn thni xc sut tm thy electron ln hn cc ni khc. Ni no khng c electron th xcsut tm thy n phi bng khng. Kt qu ny khng nh lng tnh sng ht ca ht vim.


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3. MOMEN TCA ELECTRON CHUYN NG QUANH HT NHN.

Electron chuyn ng quanh ht nhn nn c momen ng lng L. Nhng v electronchuyn ng quanh ht nhn khng theo quo xc nh do mi trng thi vc tmomen ng lng khng c hng xc nh. Tuy nhin vc tmomen ng lng li c trs xc nh bng:

( 1)L = +

vi

= 0,1, 2, 3 (n-1)v gi tr hnh chiu ca vc tmomen ng lng ln phng u tin z c xc nh:

Lz = m vi m = 0 1, 2, 3, Nh vy, hnh chiu ca momen ng lng cng nhn nhng gi tr gin on (khng

lin tc) tng t nh tr s ca vc tmomen ng lng. Nhng i lng ch nhn nhnggi tr gin on gi l b lng t ha.

Electron mang in tch (-e) nn khi chuyn ng quanh ht nhn s tng ng nhmt dng in kn, do vy n c momen t. Gia momen ng lng v momen t c milin h:

=

e2me

L

trong me l khi lng electron, du try biu hin snh hng ngc chiu camomen t v momen ng lng.

Hnh chiu ca momen t ln phng u tin z c xc nh:

z = e

2meLz

Mt khc zL m= , nn ta c:

z = e

2me

m

t: 240 9,273.102 e

e J

m T = =

gi l Magnheton Bohr v c coi l n vo

momen t trong vt l nguyn t v ht nhn.

Ta c: 0z m = vi m = 0 1, 2, 3,

Nh vy, momen t v hnh chiu zu b lng t ha.

4. SPIN CA ELECTRON.

Electron chuyn ng quanh ht nhn c momen ng lng, ngoi ra cn thc hinchuyn ng t quay xung quanh trc ca n. c trng cho chuyn ng ring ny ngita a vo khi nim spin. Momen spin hay gi tt l spin v mt hnh thc ng vai tr nhmomen ng lng ring c gi tr xc nh:

S = s (s + 1)

vi s =1

2 gi l lng t s spin, i lng ny trong vt l hc cin cha c bit

n, n l i lng thun ty mang sc thi lng t.


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Gi tr hnh chiu ca spin ln phng u tin z bng:

sz = ms vi ms = 12

trong ms =1

2 gi l lng t s hnh chiu spin.

Tng ng vi momen spin, electron c momen t ring hay cn gi l spin t:

s

= e

me

S

Gi tr hnh chiu: 02sz e

e

m = =

Nh vy, vc tspin t lun hng ngc chiu vi vc tspin v nh hng dc theophng z. Tr s hnh chiu ca momen t ring ln phng trc z, c gi trng bngMagnheton N. Bohr.

Nu tnh n spin th momen ton phn ca electron trong nguyn t bng:

J

= L

+ S

Vi tr s: J = ( 1)j j + trong j =1

2

j gi l lng t s momen ton phn.Trng thi ca electron trong nguyn tc m t bi hm sng . Hm sng c

c trng bi bn lng t s (n, , m, ms) hhoc c c trng bi ba lng t s (n, , j).V s tn ti spin ca electron, cho nn nhng trng thi ca nguyn tng vi cc mc

nng lng t n = 2 tri u nhn nhng gi tr ca 0. iu ny ng vi j = 1

2

,

tc l mi mc nng lng chnh u b tch thnh hai mc ng vi j =1

2+ v J =

1

2

(ngoi tr trng hp ? th mc nng lng khng b tch thnh hai mc).

Mc nng lng th n no ng vi J =1

2 scao hn mc nng lng ng vi j

=1

2+ . Khong cch gia hai mc con ny rt nh, cu trc nh vy gi l cu trc tinh vi

ca mc nng lng.Nh vy nhc khi nim spin ngi ta l gii c cu to tinh vi ca cc mc

nng lng m trc vt l cin khng gii thch c.S tn ti ca spin v hin tng nh hng ca n trong khng gian c khng nhbng nhng kt qu ca th nghim Stern Gerlc vo nm 1929.


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5. TH NGHIM STERN GERLC.Nguyn tc ca th nghim Stern Gerlc c minh ha hnh (3.3). Ton b th

nghim c b tr trong chn khng p sut c10- 5 mm Hg. Th nghim gm mt ngunnguyn t bc Ag, c nung nng n nhit va cho nguyn t bc bc hi cho

bay qua khe h p L vi vn tc trung bnh 100 m/s (tng ng nhit bc hi ca bc).Chm nguyn t bc bay qua vng t trng khng u do nam chm in t to ra vi gi

tr vc tcm ng tB

hng theo phng trc z.Sau khi qua t trng B

, chm nguyn t bc sp ln mn quan st M (dng knh

nh hng chm nguyn t bc ghi nhn li nhng du vt ca n). tng ca th nghim l: Khi chm nguyn t bc bay qua t trng khng u , s

chu tc dng ca lc t ln momen ca cc nguyn t bc c gi tr bng:

F = zdBdZ

Trong :z l hnh chiu

ca momen t lnphng trc z

dBdZ

l phn b t

trng theo trc z.

Theo quan nim cin th trn mn M s xut hin mt dy du vt lin tc ca ccnguyn t bc p ln mn . Dy du vt ny m nt khu vc trung tm v mnht dnv hai pha ca vng trung tm. Nhng kt qu th nghim nhn c khng theo nh dkin ca l thuyt cin. Trn mn M ch nhn thy hai vch m nt b tr i xng nhautheo phng trc z. iu ny khng l gii c theo quan nim ca vt l cin.

Nh ta bit nguyn t bc trng thi bnh thng (trng thi cbn n = 0 tc l = 0). Nguyn t bc c Z = 47, tc l cha 47 electron, trong 46 electron to thnhcc lp in t khp kn y xung quanh ht nhn ch v ch cn li 1 electron ha trlp ngoi cng.

Nguyn t bc trng thi cbn n = 1, = 0 th momen t ca n bng khng. S

kin chm nguyn t bc b lch khi bay qua t trng B

, chng t trong chm nguyn ttn ti mt loi momen t ring no khc vi momen t nguyn t . Vy ch c th lmomen t ring ca in t ha tr lp ngoi cng, v cc lp in t trong cng c tngmomen t bng khng. (V 46 in tcc lp trong cng hp thnh cc vnh kn momen tca chng trit tiu ln nhau).

Theo kt qu tnh ton, cn c vo nhng s liu thu thp c t th nghim SternGerlc, nhn c kt qu sz = 0 . Nh vy l spin v momen t ring c xc nhn.Th nghim Stern Gerlc khng nh c hai ni dung mi ca l thuyt lng t l:S tn ti ca spin v snh hng khng gian ca spin. Spin ch c hai kh nng nh

Z

S

N

M

L

A

Nguon

Hnh 3.3. S o th nghiem Stern Gerlac


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hng song song hoc phn song song vi t trng ngoi. Mt khc momen t v moment ring ch nhn nhng gi tr gin on (khng lin tc) tc l b lng t ha th hin 2 gi tr ca 2 vt trn mn quan st M.

6. CU TRC NGUYN TPHC TP NGUYN TKIM LOI KIM.

Nhng nguyn t c t 2 electron trln gi l nguyn t phc t p (Z > 2).

Trong nguyn t Hydr ch c mt electron tng tc vi ht nhn, trong nguyn tphc tp electron tng tc vi ht nhn cn phi tng tc U cc electron khc, do hmth tng tc U s trnn phc tp hn.

gii quyt bi ton cu trc nguyn t phc tp, ch c th s dng phng php gnng x l dng tng tc ca hm th U ca cc electron trong nguyn t.

Do tnh cht quyt nh ca lc ht ht nhn i vi tng electron trong nguyn t nnta vn c th xem trng lc trong nguyn t phc tp vn l trng lc xuyn tm gia ccelectron vi tm l ht nhn. Tuy nhin tc dng thc s ca trng lc ny i vi tngelectron khng ng nht. Electron gn ht nhn chu tc dng lc ht ht nhn mnh hn sovi cc electron b tr xa ht nhn. Do vy in tch thc t ca ht nhn khng phi bng(Ze) m ch bng gi tr trung bnh hiu dng (Z*e) nh hn gi tr thc s (Ze). V rng ccelectron gn ht nhn ng vai tr nh mn chn in tch m lm gim lc ht ht nhni vi cc electron pha ngoi.

Nh vy c th xem mt cch gn ng l in tch hiu dng ca nguyn t (Z*e)bng in tch thc s ca ht nhn khu tri tng in tch m ca cc electron nm gnht nhn hn so vi cc electron c xt xa ht nhn hn. Trng lc nh vy gi ltrng t hp do Hatri Fok xut vo nm 1930.

Da vo phng php trng lc t hp Hatri Fok, vic gii quyt bi ton cu trcnguyn t phc tp trnn n gin hn. Mi electron trong nguyn t phc tp, by gic xem nh chuyn ng trong trng lc xuyn tm hiu dng do ht nhn v (Z - 1)electron cn li to ra, tc dng ln electron ang xt. Nh vy electron ang xt lin kt yuvi phn cn li ca nguyn t gm ht nhn v cc electron cn li cn to ra, phn ny gi, l li nguyn t hay khung nguyn t.

Trong s cc nguyn t phc tp, cc nguyn t kim loi kim (Li, Na, K, Rb, Cs v.v ) c cu trc tng t nh cu trc ca nguyn t Hydr v lp ngoi cng ca kim loikim ch cha mt in t ha tr. Ta c th xem chuyn ng ca electron ha tr nhchuyn ng trong trng lc Culon hiu dng, gy ra bi li nguyn t ging nh electrontrong nguyn t Hydr chuyn ng quanh ht nhn.

1. Nng lng ca electron ha tr trong nguyn tkim loi kim.

Nng lng ca electron ha tr trong nguyn t kim loi kim s khc vi nng lngca electron trong nguyn t Hydr, nhng s khc bit ny khng ln lm. Sdnh vy lv ngoi nng lng tng tc gia ht nhn v electron ha tr, cn c nng lng ph gyra bi tng tc gia electron ha tr vi cc electron khc cn li.

Nh vy mi electron trong nguyn t kim loi kim cng tn ti nhng trng thilng t xc nh bi h lng t s (n, , m, ms). Tuy nhin, khc vi nguyn t Hydr,nng lng ca electron ha tr trong kim loi kim trng thi y, ph thuc vo hai lngt s n v , do vy nng lng ca electron ha trc xc nh:


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E n, = Rhcn2 Z

*

trong Z* c trng cho in tch hiu dng ca li nguyn t thay th cho Z c trngcho in tch ca ht nhn trong nguyn t Hydr, tc l:

Z* e = (Z a) e

trong a l h s b chnh, cho nn biu thc nng lng c dng:E n, =

Rhcn2 (Z a)

2

Ni chung nng lng ,nE tng khi cc lng t s n v tng. Nhng nhng trng

thi thp, ng vi n nh, th s ph thuc ca ,nE vo lng t s khng mnh lm, tuy

nhin cc mc nng lng ,nE ng vi lng t s n ln (cc mc nng lng cao) th n

ph thuc vo rt mnh; thm ch lm o ln trt t sp xp cc mc nng lng trongnguyn t, c ngha l:

En + 1,

> En,

i vn n nh th ng vi cng mt tr s ca n v th mc nng lng ng vi (n +1) s nm cao hn mc nng lng ng vi n.

Ngc li i vi n ln th:

E n, > E n + 1,

tc l ng vi n ln vi lng t s > th mc nng lng ng vi (n + 1) snm thp hn mc nng lng ng vi n.

th hn c tnh ni trn ta c th biu din nng lng thng qua h s b chnh

phn nh s ph thuc ca nng lng vo momen ng lng :

E n, = Rhc

(n + )2 Z2

2. Cc lp in ttrong nguyn t.Cc lp in t trong nguyn t c sp xp tun theo hai nguyn l Paoly v nguyn

l cc tiu nng lng.a) Sin t trong nguyn t cng chung lng t s n v khng th qu sin t

do nguyn l Paoly quy nh.b) Trong tt c cc trng thi kh dvi n v cho trc, in t phi trng thi no

c nng lng nh nht.Nguyn l Paoly cho rng trong nguyn t khng th c qu 1 in t cng c trngbi 4 lng t s: n, , m, ms ; c ngha l trng thi c trng bi 4 lng t s ni trn chc th cha 1 electron duy nht.

T nguyn l Paoly suy ra cc h qu sau:- Trng thi ca electron trong nguyn tc m t bi hm sng , mi trng thi

c c trng bi 4 lng t s (n, , m, ms) v c k hiu , , , sn m m .

- Trong n = 1, 2, 3, 4, 5, l lng t s chnh.


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- ng vi mt tr s ca n th nhn cc gi tr sau: = 0, 1, 2, 3, , (n - 1), tc lnhn n n gi tr khc nhau.

- ng vi mi tr s ca th m nhn cc gi tr sau: m = 0, 1, 2, 3, , ,tc l nhn (2 + 1) tr s khc nhau.

- Mi in t c spin bng1

2v lng t s spin ms ch nhn 2 gi tr (hoc song song

hoc phn song song); cho nn momen ton phn ca in t trong nguyn t j = +1

2 , vdo ng vi mi tr s ca c thm 2 tr s na, v vy s c 2(2 + 1) tr s.

S electron ti a c th chim mt lp v bng:

=

=++++=+1n

0

2n2)]1n(2...531[2)2(2

T cho thy s trng thi ng vi sin t, c ngha l ng vi n xc nh s ckhng qu 2n2 in t. Nhng in t cng lng t s n lp thnh mt lp vi k hiu: n =1 gi l lp K ; n = 2 gi l lp L ; n = 3 gi l l p M ; n = 4 gi l l p N ; n = 5 gi llp O Nhng in t c chung lng t s n v li c chung lng t s ? na c xpthnh lp con (hay phn lp) vi k hiu: = 0 gi l phn lp s ; = 1 gi l phn lp

p ; = 2 gi l phn l p d ; = 3 gi l phn lp f ; = 4 gi l phn l p g v.vmi phn lp cha ti a: 2(2 + 1) in t. (Xem bng lit k sau).

0(s)

1(p)

2(d)

3(f)

4(g) = 2n2

2 (2 + 1)1 (K) 2 22 (L) 2 6 83 (M) 2 6 10 184 (N) 2 6 10 14 325 (O) 2 6 10 14 18 50

T bng thng k cho thy:- L p K ch gm 1 phn l p 1s cha ti a 2 lectrn- L p L cha 2 phn lp 2 s v 2p c ti a 2+6= 8 lectrn.- L p M cha 3 phn l p 3s , 3p v 3d c ti a 2 + 6 + 10 = 18 lectrn v

cho cc lp khc, nh lp N, l p O

phn nh cu trc lp in t trong nguyn t ngi ta dng cng thc cu hnh nhsau:

1s, 2s2p, 3s3p4s3d, 4p5s4d5p6s4f, 5d6p7s5f.

V d: Cu hnh in t ca ngyn t Na (Z = 11) l 1s22s2 2p6 3s1 (nhng s nh, ghipha trn k hiu ca phn lp l s electron m phn lp c).

P. lp

Lp n


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3. Quang ph kim loi kim.

Khi nguyn t kimloi kim b kch thch thin t ha tr s chuynln cc trng thi kchthch vi nng lng caohn v tm tr ti mt thi gian ngn c 10-8 s). Sau li chuyn vtrng thi c nng lngthp hn v bc x photon(h).

Qu trnh thc hincc bc chuyn phi tuntheo iu kin lc la sau:

= 1

tc l cc bc chuyn ca in t ha tr trong nguyn t ch c th din ra gia cc trngthi c lng t s momen ng lng chnh lch nhau 1 n v (quy tc lc la ny thhin nh lut bo ton momen ng lng trong nguyn t).

Chnh do s chuyn trng thi nng lng, m hnh thnh nn quanh ph kim loikim c minh ha trn hnh 3.4. Trn hnh v trnh by s to thnh quang ph canguyn t Liti (Z= 3), lp trong cng lp y 2 in t (phn lp 2s), in t ha tr th 3nu b kch thch s chuyn ln cc mc cao hn l p, d, f, Khi trv trng thi c nnglng thp hn s bc x photon h v cho quang ph. Trng thi thp nht ca nguyn tLiti ng vi 2s (n = 2, = 0), so vi quang ph nguyn t Hydr th trng thi thp nht

ca n l 1s (n = 1, = 0).Do tng tc ca in t vi nhau lm cho cc trng thi c cng lng t s n tch

thnh cc trng thi con s, p, d, f v v.v trong khi nguyn t Hydr vn gi nguynkhng b tch ra. Hin tng chng chp cc trng thi con s, p, d, f, trong quang phnguyn t Hydr gi l hin tng suy bin nng lng. Bc suy bin nng lng k hiu lg v c gi tr bng g = 2n2 v rng in tng vi lng t s n c th tn ti 2n2 trngthi khc nhau. T cho thy s vch ph trong quang ph kim loi kim trnn phong

ph hn v phc tp hn. Nh vy trong quang ph nguyn t Hydr c s suy bin nnglng, tc l mt mc nng lng c th tn ti nhiu trng thi khc nhau, cc trng thiny b chng chp li vi nhau. Cn trong quang ph kim loi kim cc trng thi con ngvi mc nng lng n b tch ra ring bit, hin tng ny gi l s kh suy bin. Do b kh

suy bin nng lng m quang ph nguyn t kim loi kim c nhiu dy:- Dy chnh gm nhng vch phng vi cc bc chuyn t np v mc 2s vi n = 2,

3, 4, . v = 1.

- Cc dy phng vi cc bc chuyn ns (vi n = 3, 4, 5, v = 0) v mc 2p vcc bc chuyn nd (vi n = 3, 4, 5, v = 2) v mc 2p.

- Dy cbn ng vi cc bc chuyn nf (vi n = 4, 5, 6, v = 3) v mc 3d.


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7. BNG PHN HNG TUN HON MENDELEP.

Nm 1869 Mendelep xy dng bng phn hng tun hon cc nguyn t ha hc,da trn csnguyn t lng ca cc nguyn t ha hc, tc l cc tnh cht ha hc v lhc ca chng lp li tun hon theo chiu hng tng dn nguyn t lng. Theo quan nimca l thuyt lng t do N. Bohr xng th tnh cht tun hon ca cc nguyn t hahc do in trng ca nguyn t quyt nh, tc l s tun hon ca cc tnh cht ha hcv l hc ph thuc vo cch sp xp mt cch tun hon ca cc electron theo cc lp trongnguyn t quyt nh.

Mi chu k trong bng Mendelep tng ng vi mt lp in t. u mi chu k lmt nguyn t hot ng ha hc mnh v kt thc mi chu k l mt kh tr l nguyn tha hc bn vng, hot ng ha hc km. Theo quan im lp in t th nguyn t ha hcu mi chu k c cu trc cha hon chnh, lun c xu hng thu thm in t v vy hottnh ha hc mnh. Cn nguyn t ha hc cui mi chu k c cu trc lp in t honchnh, kh thu thm v kh bt i sin t cho nn rt bn vng. Nguyn tc ny th hin cc chu k sau:

V d nh chu k I bt u t Hydr (H) c mt in t thn nhpc xp vo lp thnht (lp K), lp ny c mt phn lp 1s cha ti a 2 in t, song vi Hydr ch c 1 int cho nn n c xu hng phi thu thm mt in t na. n nguyn t th hai trong chuk ny l Heli (He) c 2 in t, 2 in t ny xp y phn lp 1s, to thnh mt cu trclp hon chnh. iu ny l gii ti sao Heli l kh tr.

in t th 3 khng th thm nhp vo lp th nht c na, buc phi chuyn lnlp cao hn l lp L (tng ng vi chu k II trong bng Mendelep). Nguyn t mu chochu k II l Liti (Z = 3). Liti c 3 in t th in t th 3 phi xp vo phn lp 2s. Phnlp 2s cn 2 in t mi lp y, i vi Liti ch c mt in tc xp vo phn lp 2scho nn n cn phi thu thm 1 in t na, do vy hot tnh ha hc mnh. Lp th hai cn8 in tc phn b cng vi 2 in tphn lp 2s mi to nn cu trc in t hon

chnh. Nguyn t Neon (Ne) c 10 in tp ng yu cu ny. Vy Neon l kh trcuichu k II, c cu hnh in t hon chnh. Tng t nh vy chu k III bt u t Natri (Nac Z = 11) v kt thc Argon (Ar c Z = 18) l mt kh tr, chu k IV bt u t Kali (Kc Z = 19) v kt thc Kripton (Kr c Z = 36) cng l mt kh tr. T nguyn tc ny lgii to sao u mi chu ku bt u t nguyn t kim loi kim c cu trc lp in tcha hon chnh v cui mi chu k kt thc bng mt kh tr c cu trc lp in thon chnh.

Nh vy tt c cc tnh cht tun hon phc tp do Mendelep tm ra c gii thchy bi s phn b cc electron thnh lp v phn lp da theo cc lng t s n v .

iu lu y l Mendelep khng th l gii nhiu trng hp ngoi l v tnh cht

quang ph nguyn t phc t p theo quan im nguyn t lng. Nhng iu ckhc phc nhvo l thuyt tng tc ca cc in t vi in trng ca ht nhn nguynt. Nhng kt qu ca l thuyt lng t gp phn lm chnh xc ha nhng don trong

bng tun hon Mendelep. T kt qu ny tn vinh thm cho nhng d on caMendelep v khng nh tnh ng n ca bng tun hon Momen nhng theo quan imlp in t ch khng theo quan im nguyn t lng.


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8. TIA X V PH TIA X.1. Tia X (hay tia Ronghen).

Nm 1895 Ronghen khm ph ra mt loi bc x do cc chm tia in t pht ra tKatt, c tng tc trong in trng vi hiu in th cao p vo Ant v c gi l tiaX. Tia X c bn cht l sng in t vi bc sng ngn = 0,01 A0 800A0.

Mun thu c tia X ngi ta dngmt chm in t c vn tc rt ln p voAnt (cn gi l i m cc), c lm

bng vt liu cn nghin cu. Trong ng pht tia X c ht ht khng kh n chn khng c 10 - 6 mm Hg, gia Katt(K) v Ant (A) b tr hiu in th c(103 ( 10 6) V. i m cc A s bc x tia Xc nhiu bc song khc nhau. Tp hpcc tia X to thnh ph tia X.

Trong nhng my gia tc hin i (nh Btatron hay Xyclotron) c th tng tc chmelectron ln n 102 MeV hoc cao hn cho p vo i m cc nhn nhng chm tia Xc pha dng.

2. Ph tia X.

Ph tia X gm hai loi: phlin tc v ph vch (cn gi l

ph c trng). Trn th minhha s ph thuc ca cng bcx tia X vo bc sng . T ccng cong thc nghim cho thycng v bc sng ca tia X

ph thuc vo hiu in th u tvo K v i m cc A. Trn hnh3.6 minh ha ba ng cong ngvi cc hiu in th: 50 kV ; 30kV v 20 kV.

Ph lin tc ca bc x tia X xut hin l do hin tng bc x hm ca cc electrontrn b mt ca i m cc. Trong qu trnh b hm electron chuyn ton bng nngthnh dng nng lng in t di dng cc photon (h). Mt khc ng nng electron c

c l nhcng ca lc in trng (2

2

mv= e.u). Ton bng nng chuyn thnh nng

lng in t pht ra di dng cc photon vi tn s tng ng:max

h max = e.u

K Ae

Tia X

- +u

Hnh 3.5. S o ve cach phat ra tia X


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hay: hc

min= e.u

tin o c trong thc nghim, thay th cc tr s ca c, h, e, biu th bc sngbng A0 v hiu in th u bng kV ta c:

min =12,35u(kV) A

0

Mi ng cong trn thu bt u t mt tr s ca bc sng cc tiu. Gi trbc sng cc tiu ng vi u = 50 kV l nh nht, gi tr cc tiu ca bc sng ng vi u= 30 kV th ln hn v gi tr cc tiu ca bc sng ng vi u = 20 kV l ln hn c.

Ngoi ph lin tc, ph vch ca bc x tia X c trng cho cu trc cc lp in ttrong nguyn t, nn c gi l phc trng.

Cch to ra ph tia Xc trng, c th hnh dungnh sau: Trong s cc in tp vp i m cc b hm li,c nhng electron nng lng

ln xuyn su vo lng nguynt, va chm vi electron lptrong cng ca nguyn t. Khiin t t ngoi vo va chmvi in t l p trong cngca nguyn t lm cho n btra khi nguyn t.

Ch trng m in t va b ri khi nguyn tlp vin t trong cng b cc int t lp cao hn xung chim ch. Qu trnh chim ch din ra lin tip nhau. Km theo

bc x photon h. Trng hp lp K bnh bt i 1 in t li mt ch trng, lp tc t

cc lp bn ngoi L, M, N electron s chuyn xung chim ch trng lp K s lm xuthin cc vch ph K,K , K , Tng t nh vy nu lp L bnh bt i 1 electron li mt ch trng, th t cc lp v ngoi M, N, O, in t chuyn xung chim chkm theo pht x cc vch ph L,L , L , v tng t nh vy khi in t lp ngoichuyn xung ch trng lp M cho cc vch ph M ,M , M,

xc nh bc sng tia X phc trng, ta vn dng biu thc nng lng lin ktca in t trong nguyn t phc t p (Z > 1). V ch c nguyn t phc tp mi cho ph tiaX (tc l ch c cc nguyn t vi Z ln).

E

n,

= Rhc

n

2 (Z* )2

vi Z*e = (Z - a) e gi l in tch trung bnh hiu dng, a l h s mn chn in tch mi vi ht nhn. H s a ny thay i ty theo tng lp in t. i vi lp K th h s a =1, vy khi in t chuyn t lp L vo ch trng lp K s cho vch ph K tng ng vitn s:

2222

KL )1Z(C.R4

3)1Z(

2

1

1

1C.R

h

EEv =

=

=


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Trong :

R l hng s Ritbe. c l vn tc nh sng Z l nguyn t s ca

nguyn t ha hc ch to

nn m cc.Biu thc trn c gi l

nh lut Moseley, cng thc nyng vi cc nguyn t c nguynt s Z > 30 (tc l nhng nguynt t trung bnh n cc nguyn tnng).

Mi dy phu c vch uv vch cui gi l vch ranh gii.Vch u l K , L , M vch

cui l K, L , M.


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Chng IV

LIN KT NGUYN TTRONG PHN T

Trong cc chng trc chng ta ch xt nguyn t thun ty trng thi c lp.

Trong thc t cc nguyn t thng khng tn ti c lp m lun lin kt vi nhau to thnhphn t. Cc phn t lin kt vi nhau to thnh cc cht. Nu kch thc ht nhn nguyn tc10 -13 cm, kch thc nguyn t c10 -8 cm th kch thc phn t vo khong 10 -6 10 -7 cm.

Phn t l mt h thng phc tp, y ch cp n nhng tnh cht lin kt cacc nguyn t thnh phn t, ch khng cp ton b nhng vn v cu trc phn t.

Nh chng ta bit, nng lng lin kt ca cc in t vi ht nhn trong nguyn tchng chc eV th nng lng lin kt ca cc nguyn t to thnh phn t nh hn10eV. Chng hn, nng lng lin kt ca phn t Cl2 l 2,5 eV, ca phn t H2 l 4,8 eV).Cc gi tr nng lng lin kt cc nguyn t trong phn t khng ln lm, chng cng bc

vi nng lng cc trng thi ngoi cng ca nguyn t. iu ny chng t qu trnh tothnh cc phn t cng nh cc phn ng ha hc ch lin hn cc electron lp ngoicng ca nguyn t (l nhng electron ha tr).

Chng ta quan tm n hai loi lin kt c trng ca phn t l lin kt in (hay linkt d cc) v lin kt ng ha tr (hay lin kt ng cc). Vic phn loi lin kt ny chmang tnh c l, v c nhiu phn t khng th xp vo loi no cho tha ng.

1. LIN KT ION.

Phn t mui n NaCl c th xp vo loi lin kt in tiu biu. Theo qui lut sp xp

cc lp in t trong nguyn t, nguyn t Na (Z = 11) c cu hnh: Na: 1s2, 2s2, 2p6, 3s1

Nguyn t Cl (Z = 17) c cu hnh:

Cl: 1s2, 2s2, 2p6, 3s2, 3p5

Nu a nguyn t Na v Cl li gn nhau chng s lin kt to thnh phn t NaClbng cch in t lp 3s1 ca Na chuyn sang lp 3p5 ca Cl v kt qu Na nhng 1in t bin thnh in Na+ v Cl thu thm 1 in t bin thnh in Cl-. Hai in ny nhlc ht tnh in Culon to thnh phn t. Tuy nhin nng lng lin kt phn t NaCl khng

bng nng lng tnh in Culon gia hai in dng v m. trn chng ta mi xt mtcch hnh thc, thc ra qu trnh lin kt ny phc tp hn. Tht vy, khi y thc vy khiin t chuyn t trng thi 3s1 sang 3p5 km theo nhng hiu ng nng lng sau:

- Trc ht phi kn nng lng in ha Natri trng thi 3s1.- Kn phi kn nng lng i lc ha hc ca Clo dng vo mc ch thu nhn

thm 1 in t t Na chuyn sang bin thnh in m Cl-.

- Cui cng l nng lng lin kt Culon.Nh vy to thnh phn t NaCl cn n 3 dng nng lng:


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E = E ion + E ai + E Cu

Nhng phn t c lin kt in in hnh l nhng phn t cha cc nguyn t kim loikim v h Halogen.

2. LIN KT NG HA TR - PHN THYDRO H2

Xt phn tn gin nht l Hydr (H2). Nu dng mu lin kt in th khng thgii thch s tn ti ca phn t Hydr.

Lin kt trong phn t H2 cng nh nhiu phn t khc gi l lin kt ng ha tr -mt hiu ng c bit ca l thuyt lng t.

Nm 1927 Hailer v London vn dng l thuyt lng t gii quyt thnh cng lthuyt v lin kt ca cc phn tng ha tr, tiu biu l phn t Hydr.

i vi phn t Hydr, phng trnh Srdingc dng sau:

i = 1

2

2

x2i

+ 2

y2i

+ 2

z2i

+2m2 [E U] = 0

trong th tng tc:

U =e2

r12+

e2

r e2

i = 12

1

rai

+1

rbi

Trong :

r l khong cch gia hai htnhn a v b.

r12 l khong cch gia haiin t (1) v (2).

r1a l khong cch t ht nhna n in t (1).r2a l khong cch t ht nhna n in t (2).

Hnh 4.1

r1b l khong cch t ht nhn b n in t (1).r2b l khong cch t ht nhn b n in t (2).

Kt qu ca vic gii phng trnh Srdingnhn c biu thc nng lng lin ktca h 2 nguyn t Hydr to thnh phn t H2 c dng tng qut:


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E p(r) =C(r) A(r)

1 S(r)

Trong :

S(r) l thnh phn c trng cho s che ph ln nhau ca mt xc sut tm thyelectron trong phn t.

C(r) l thnh phn c trng cho tng tc tnh in Culon gia ht nhn vi ccelectron trong phn t H2.

A(r) l thnh phn c trng cho tng tc trao i v tr ca cc electron trong phnt H2.

Cc kt qu tnh toncho thy vi nhng khongcch trung bnh ca r (vo ccng bc vi bn knh quo

N. Bohr r0 = 0,53 A0 ) ththnh phn C(r) v A(r) uc gi tr m v ( )A r >

( )C r do hai gi tr nng

lng tng tc ca 2 nguynt trong phn t Hydr cdng:

Trng hp E(r) < 0 ng vi trng thi lin kt bn vng ca phn t H2. Trng hpE(r) > 0 tng ng vi nng lng y nhau lm cho h phn t Hydr khng bn vng.

Kt qu tnh ton nng lng tng tc ph thuc vo khong cch r, c biu dintrn hnh 4.2. Trc tung E vi n v nng lng tnh bng eV, trc honh l khong cch rtnh bng n v a0 (bn knh quo N. Bohr)

Nng lng cc tiu ca ng cong tng tc ht (E < 0) ng vi khong cch r =1,6 a0 (tc l r = 0,83 A

0). H phn t H2 bn vng, cc electron trong phn t lun lun cspin nh hng ngc chiu nhau E v h phn t H2 khng lin kt (tng ng vi

ng cong nng lng tng tc y), cc electron trong phn t Hydr lun lun cng

chiu E

.Nhng kt qu tnh ton ca Hailer v London ph hp vi kt qu thc nghim.


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3. TRNG THI NNG LNG CA PHN T.Khi cc nguyn t lin kt to thnh phn t, th trng thi nng lng ca phn t

tng i phc t p, v phi tnh n mi kh nng tng tc ca cc electron vi cc htnhn v gia electron vi nhau. n gin ha vic tnh ton, thng thng ngi ta tinhnh theo cch phn tch chuyn ng ca phn t thnh nhng chuyn ng thnh phn vnghin cu cc chuyn ng thnh phn ring r. C 3 dng chuyn ng ph bin trong

phn t l: chuyn ng ca electron, chuyn ng dao ng ca phn t v chuyn ngquay ca phn t.

Vn nghin cu cu to phn t v l thuyt, cng nh thc nghim, cho n nayvn cn l vn nan gii, sdnh vy l v phn t l mt h gm nhiu nguyn t linkt vi nhau bng nhng lc m bn cht ca chng, thc ra cha c xc nh mt cch cth. Chng ta ch cp n phn t gm 2 nguyn t l phn tn gin nht.

Lc lin kt gia cc nguyn t to thnh phn t l lc tng tc gia cc in tvnh ngoi cng ca cc nguyn t. Cc in tvnh trong khng tham gia vo lin kt

phn t.V tnh cht phc tp ca lin kt phn t, mt cch gn ng c th xem nng lng

ton phn ca h phn t bao gm nng lng in t Et , nng lng dao ng ca htnhn nguyn t Ed v nng lng quay ca phn t Eq:

E = E

t + E

d + Eq

Bc x do phn t pht ra l do s bin thin nng lng ton phn E. Bc xpht ra photon (h) c tn s xc nh:

=Eh =

E

th +

E

dh +

Eq

h

Thc nghim cho thy bin thin nng lng in tEt l ln nht cn bin

thin nng lng quay Eq l nh nht:E

q E

d E

t

Ph phn t thng nm vng hng ngoi, vng nhn thy v vng t ngoi. hnh dung s khc bit gia cc trng thi nng lng Et , Edv Eq cc mc

nng lng ca in t trong phn tc minh ha trn hnh v. Khong cch gia cc mc nng lng in t chnh lch nhau khong vi eV. Khong cch gia cc mc nng lng dao ng chnh lch nhau trong khong (10-

2 101) eV

Khong cch gia cc mc nng lng quay chnh lch nhau trong khong (10 - 5 10 3) eV.

Nng lng in t trong nguyn tc xc nh:

En = Rhcn2 . Z

2 vi n = 1, 2, 3


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Nng lng dao ng ca h phn t quanh v tr cn bng c xc nh:

E

d = h0

N +12 vi N = 0, 1, 2, 3,

Trong : 0 l tn s dao ng ring ca h phn t (0 ph thuc vo khi lng cc ht

nhn v cu hnh in t ca phn t).

N = 0, 1, 2, 3, gi l lng t s dao ng. phn t tn ti bn vng th hmth tng tc U=U(r), ph thuc vokhong cch gia cc ht nhn cacc nguyn t trong phn t. Ti r =r0, phn t c nng lng cc tiu v

phn t trng thi bn vng. Khikhong cch gia cc nguyn ttrong phn t bin i r < r0 hay r> r0, s lm xut hin nhng lc gin hi c xu hng khi phc li

trng thi cn bng bn ca phn t.Nhng lc ny lm cho cc nguynt dao ng quanh v tr cn bng.S cc mc nng lng dao ngc minh ha trn hnh 4.3.

Phn t cn c kh nng quay i vi phn t gm 2 nguyn t th h phn t quayquanh khi tm vi nng lng c xc nh:

Eq =

L2

2I Q(Q + 1)

Mc ien t Mc dao ongMc dao ong Mc quay

hd

ht

hd

hq

Hnh 4.3


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vi L l momen ng lng v I l momen qun tnh ca h phn t. Thay tr s ca momenng lng ta c:

Eq =

2

2I( + 1) vi = 0, 1, 2, 3 (n - 1)

V momen qun tnh I ca phn t ln, do vy nng lng Eq nh hn rt nhiu so vinng lng dao ng Ed v nng lng in t Et.

4. QUANG PH PHN T.Nghin cu quang ph phn t chng ta thy chng c nhng c im rt khc so vi

quang ph nguyn t. Nh bit ph ca nguyn t gm nhiu vch ring bit hp thnhtng dy.

Ngc li ph phn t gm rt nhiu vch nm st nhau to thnh tng m, m ngayc khi dng nhng my quang ph c nng sut phn gii cao cng khng th tch cc mny thnh nhng vch ring bit. V th ph phn t gi l phm.

Cc m quang ph phn t gm cc vch ph sp xp theo qui lut sau:

-Tp hp cc vch ring bit tothnh m.

-Tp hp mt sm to thnhnhm.

-Tp hp mt s nhm to thnhph phn t Hnh 4.5. Phm

S xut hin cc vch phm lin quan n cc bc chuyn trng thi ca electrontrong phn t. Tp hp cc photon pht ra do nguyn t chuyn t trng thi ny sang trngthi khc trong tp hp cc dng nng lng in t, nng lng dao ng v nng lngquay, to nn hnh nh phc tp ca phm.


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Chng V

NHNG NH HNG BN NGOILN NGUYN TBC X

Khi nghin cu ph bc x ca nguyn t Hydr v l thuyt N. Bohr chng ta nhn

thy s bc x ca nguyn t lin h mt thit vi cu trc nguyn t.Thi gian u, vn bc x ca nguyn t cha phi c gii quyt mt cch

thu o; m ch sau khi khm ph ra electron l thnh phn cu to nn nguyn t th vai trca n trong cch bc x ca nguyn t mi c khng nh.

Theo l thuyt cin, nhiu hin tng bc x ca nguyn t c th gii thch datrn m hnh lin kt gia electron v ht nhn nguyn t to thnh h nguyn t. Trongnhiu trng hp h nguyn tc xem tng ng nh mt lng cc. S bc x canguyn t l bc x ca h lng cc khi dao ng.

Song song vi l thuyt cin, l thuyt lng t m rng v b sung cho lthuyt cin. Chng hn, khi gii thch ngun gc gin on cc vch quang ph th lthuyt cin t ra bt lc, nn phi dng n l thuyt lng t. Mc d vy l thuytlng t vn c hn ch nh: khng th gii thch v tnh ton chnh xc cng bc x,

phn cc hoc s phn b cng bc x trong khng gian.

Trong khi , bng cch ng nht s bc x ca nguyn t vi bc x ca h lngcc, l thuyt cin c th tnh ton chnh xc cc i lng trn. T, dng nguyn ltng ng, c th dn n nhng kt qu ph hp vi thc nghim.

Chnh v th m cn xc nh ranh gii p dng cho c l thuyt cin ln l thuytlng t.

1. RNG CA MC NNG LNG V VCH QUANG PH.

Trong thc t cc vch quang ph nguyn t bao gicng c rng nht nh, iu chng t nng lng cc trng thi dng khng th ch c mt tr s chnh xc n mctuyt i, m c bao trong mt khong xc nh vi mt sai s no v thng c gil bt nh v nng lng.

Nh bit khi nguyn t chuyn t mc nng lng cao hn Eksang mc nng lngthp hn Ei s bc x photon h:

h = Ek

Ei

Nu gi Ek l rng ca mc nng lng, th nng lng trng thi k s bng:k

k

EE

2

v nng lng trng thi i bng: ii

EE

2

.

Do mc nng lng c rng nn tn s bc x ca nguyn tc xc nh:


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+ =

Ek Ek

2

Ei Ei2

h

Suy ra:

Gi s:

E k = E i = E

ta c: 20

E chnh l rng camc nng lng.

Khi nim rngmc nng lng, hon ton

ph hp vi h thc btnh Haisenbc:

E.t h

C ngha l vi trng thi cbn n = 1, mc nng lng E1 tn ti lu bn vi thigian t ty v c th xem nht , nn b rng mc nng lng E 0. Cc mcnng lng ng vi n = 2, 3, 4, 5, u c b rng E 0. Nu thi gian tn ti ca mcnng lng t (gi l thi gian kch thch) cng nh th b rng mc nng lng cng ln.

Ngoi ra rng cc vch ph ph thuc vo b rng hai mc nng lng tng ng vi ccbc chuyn ca electron trong nguyn t.

2. BC X TPHT V BC X CNG BC (HAY BC X CM NG).

Khi nguyn t nhn cc tc ng t bn ngoi n s b kch thch. Nu khng c tcng lm cho nguyn t b kch thch th n khng th tng chuyn t trng thi nnglng th p ln trng thi nng lng cao hn (nh lut bo ton nng lng khng cho

php). Do vy nguyn t ch c th thc hin cc bc chuyn cng bc t trng thi nnglng thp ln trng thi nng lng cao hn.

Ngc li khi nguyn t trng thi nng lng kch thch ln hn s c hai conng chuyn sang trng thi c nng lng thp hn: l chuyn mc nng lng bngcch t pht v bng cch cng bc.

1. Shp th photon.

Nu nguyn t nhn photon h chuyn t trngthi E1 ln trng thi E2 th

photon bin mt lm chonguyn t b kch thch:

Hnh 5.1. o rong mc nang lng va vach pho

E1

E2

E3

En En > 0

0

Ei

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