2.5.Vat Li Hat Nhan-nqhuy

8/2/2019 2.5.Vat Li Hat Nhan-nqhuy

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Chng 1

CAC AC TRNG VA TNH CHAT C BANCUA HAT NHAN

1.1. TOM TAT VE VAT L NGUYEN T

Nguyen t cau tao gan giong nh mo hnh he mat tri, gom mot cai loi lahat nhan va cac electron chuyen ong tren cac quy ao xung quanh hat nhan. Lthuyet nguyen t c xay dng tng oi hoan chnh, da tren s tng tacCoulomb gia hat nhan vi cac electron quy ao cung nh s tng tac gia cacelectron quy ao vi nhau. Hat nhan khong co cau truc cua hnh mau nguyen t,nhng khi xay dng l thuyet hat nhan, ngi ta cung ap dung mau nguyen t trong

trng hp mau vo hat nhan hay mau suy rong. Trong cac trng hp nay, cactrang thai va cac mc nang lng cua cac nucleon trong hat nhan c mieu tanh cac thong so tng ng cua cac electron trong nguyen t. Ngoai ra, khi xemxet s tng tac cua cac bc xa vi vat chat, phan ln cac bc xa nh alpha, beta,gamma eu tng tac vi cac electron cua nguyen t, gay nen hieu ng kch thchva ion hoa nguyen t. Nh vay, e thuan tien trong viec theo doi cac van e vevat l hat nhan, viec nhac lai mot so khai niem c ban ve vat l nguyen t la canthiet. Trong phan nay trnh bay tom tac ve cau truc nguyen t, phan loai cac trangthai va cac mc nang lng cua cac electron, quang pho nguyen t hydrogen vacac nguyen t kim loai kiem,

1.1.1. Nguyen t hydrogen

1.1.1.1. Chuyen ong cua electron trong nguyen t hydrogen

Cac nguyen t co cau truc rieng cua mnh phu thuoc vao loai nguyen to.Nhng ac iem chung cua chung la cau tao t hat nhan (nucleus) co ien tchdng +Ze, trong o e = 1,6.10-19 C, nam gia va cac electron ien tch am e =- 1,6.10-19 C chuyen ong tren cac quy ao xung quanh hat nhan. Mo hnh nguyen

t nh tren c goi la mo hnh nguyen t Bohr. ien tch dng cua hat nhanbang tong so cac ien tch am cua cac electron, do o nguyen t trung hoa ve ientch. So electron quy ao tang dan khi nguyen t cang nang. V du, nguyen thydrogen co 1 electron quy ao con uranium co 92 electron quy ao. Nguyen t cong knh khoang 10-10 m con hat nhan co ng knh khoang 10-15 m. Khoilng hat nhan chiem phan ln khoi lng nguyen t, con khoi lng cac electronkhong ang ke. V du, khoi lng proton bang mp = 1,67265.10-27 kg con khoilng electron bang me = 9,1091.10-31 kg.

Tng tac gia hat nhan va electron quy ao la tng tac Coulomb, co

dang sau:


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U = -r

kZe2(1.1)

Trong o k = 9.109 N.m2/C2 va r la khoang cach t electron en hat nhan.Phng trnh Schrdinger mieu ta s tng tac nay co dang:

+ 2em2

h(W + r

kZe2

) = 0 (1.2)

Trong o va W la ham trang thai va nang lng cua electron,h = 1,054.10-34 J.s la hang so Planck rut gon.

Do trng Coulomb oi xng tam nen phng trnh (1.2) c giai trong hetoa o cau vi goc toa o la hat nhan con r la khoang cach t electron en hatnhan. Nghiem phng trnh co dang tch so cua hai tha so:

nlm = Rnl(r) Ylm(,) (1.3)Trong o ham Rnl(r) ch phu thuoc vao ban knh r con ham Ylm(,) phu

thuoc vao cac goc cua he toa o cc. Cac ch so n, l, m la so lng t chnh, solng t quy ao va so lng t t, trong o:

n = 1, 2, 3, 4, . . . .l = 0, 1, 2, 3, 4, . . ., n 1 (nhan n gia tr) (1.4)m = 0, 1, 2, . . . , l (nhan 2l + 1 gia tr)Nh vay mot trang thai cua electron tren quy c mieu ta bi ham song

nlm ac trng bi 3 so lng t n, l, m. Ham ban knh Rnl(r) c ac trng bi 2so lng t n, l con ham goc Ylm(,) c ac trng bi 2 so lng t l, m. ailng Rnl(r)

2 la xac suat tm thay electron v tr r vi cap so lng t n va lcon ai lng Ylm(,)

2 la xac suat tm thay electron cac goc va vi cap so

lng t l va m.Nghiem th hai cua phng trnh Schrodinger la nang lng electron:

22

42

e

2n )2(4

eZm

n

1W

h= (1.5)

Bay gi ta hay xet trng hp n gian nhat la nguyen t hydrogen, gomhat nhan mang ien tch +e = +1,6.10-19 C, la mot hat proton, va mot electron quyao mang ien tch e = - 1,6.10-19 C. Khi o trong cac nghiem tren can thay Z = 1.Nang lng electron trong nguyen t hydrogen c mieu ta bi cong thc:

WRh

nn = 2 (1.6)

Trong o R = 3,27.1015 s-1 la hang so Rydberg con h = 6,625.10-34 J.s lahang so Planck. Cong thc (1.6) cho thay nang lng electron trong nguyen thydrogen ch phu thuoc vao mot so lng t chnh n va nhan cac gia tr gian oan.Hn na no con nhan cac gia tr am, trong o mc thap nhat W1 = - Rh, ng vin = 1, con mc cao nhat W = 0 ng vi n (hnh 1.1).

1.1.1.2. Quang pho cua hydrogen

T s o cac mc nang lng electron theo hnh 1.1 co the giai thch cautao vach quang pho hydrogen. Quang pho vach la cac vach mau nho net quan sat


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thay trong dung cu quang pho khi phan tch he phat sang cua kh hydrogen bangcach phong ien qua mot ong ng kh hydrogen ap suat thap. Hien tng nayc mieu ta nh sau. Khi khong co kch thch ben ngoai, electron bao gi cung trang thai c ban ng vi mc nang lng thap nhat W 1. Di tac dung cua kch

thch ben ngoai, v du dong ien, electron c tang nang lng. No chuyen disang trang thai kch thch vi nang lng Wn cao hn. Electron ch trang thai kchthch trong mot khoang thi gian ngan, khoang 10-8 s, sau o tr ve trang thai ngvi mc nang lng Wn thap hn. Trong qua trnh chuyen mc nang lng,electron se giai phong nang lng di dang bc xa ien t, ngha la phat ra motphoton mang nang lng h. Theo nh luat bao toan nang lng ta co:

Wn Wn = h (1.7)Thay Wn va Wn theo cong thc (1.6) vao (1.7) ta c tan so ng vi cac

vach quang pho:

= R

22 n

1

n'

1

(1.8)Tnh tan so theo cong thc (1.8) vi cac gia tr n =1, n = 2, n = 3, n = 4

va n = 5 ta c cac day quang pho Lyman (anh sang t ngoai), Balmer (anh sangnhn thay) va cac day anh sang hong ngoai nh Paschen, Brackett va Pfund, hoantoan phu hp vi thc nghiem (hnh 1.2).

1.1.2. Cac nguyen t kim loai kiem

1.1.2.1. Nang lng cua electron hoa tr trong nguyen t kim loai kiem

Hnh 1.1. Cac mc nang lng cua cacelectron quy ao trong nguyen t hydrogen.

Lp MLp N

Lp L

Lp K

W4 =16

Rh

W = 0

W3 = 9Rh

W2 =4

Rh

W1= -Rh

4

3

2

1Day Lyman (T ngoai)

Day Balmer(Nhn thay)

Paschen - Brackett - Pfund(Cac day hong ngoai)

Hnh 1.2. S o quang pho hydrogen.


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Cac nguyen t kim loai kiem (Li, Na, K, Rb, Cs, ) cau tao gan giong nhnguyen t hydrogen. Trong mau lp nguyen t, lp ngoai cung cua cac nguyen tnay ch co mot electron hoa tr (hnh 1.3).

Electron hoa tr lien ket yeu vi phan con lai cua nguyen t, c goi la loi

cua nguyen t, gom hat nhan va cac electron con lai. Co the xem chuyen ong cuaelectron hoa tr nh chuyen ong trong trng Coulomb gay bi loi nguyen t,giong nh chuyen ong cua electron trong nguyen t hydrogen. Cho nen, tnh chatquang hoc cua cac nguyen t kim loai kiem ve can ban giong tnh chat quang hoccua nguyen t hydrogen.

Trong nguyen t kim loai kiem, ngoai nang lng tng tac gia electronhoa tr vi hat nhan con co nang lng phu gay ra do s tng tac gia electron

hoa tr vi cac electron khac nen nang lng cua electron hoa tr trong nguyen tkim loai kiem khac chut t vi nang lng cua electron trong nguyen t hydrogen.Khi o nang lng electron hoa tr trong kim loai kiem, ngoai s phu thuoc vao solng t chnh n, con phu thuoc vao so lng t quy ao l theo cong thc sau ay:

( )2n

n

RhW

l

l

+= (1.9)

Trong o l la so hieu chnh phu thuoc vao so lng t quy ao l. Bang 1.1trnh bay cac gia tr l oi vi mot so nguyen t kim loai kiem cac trang thaivi l khac nhau. Ta k hieu trang thai s vi l = 0, trang thai p vi l = 1, trang thai dvi l = 2, trang thai f vi l = 3.

Bang 1.1. Cac gia tr l oi vi mot so nguyen t kim loai kiem cactrang thai khac nhau.

Z Nguyen to s p d f3 Li 0,412 0,041 0,002 0,000

11 Na 1,373 0,883 0,010 0,00119 K 2,230 1,776 0,146 0,00737 Rb 3,195 2,711 1,233 0,012

55 Cs 4,131 3,649 2,448 0,022

Hydrogen (H) Lithium (Li) Sodium (Na)

Hnh 1.3. Mau lp cua cac nguyen t kim loai kiem Li va Na.

LK

MLKK


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Theo cong thc (1.9), nang lng Wnl phu thuoc vao 2 so lng t n va lnen ngi ta k hieu cac mc nang lng bang nS khi l = 0, nP khi l = 1, nD khil = 2 va nF khi l = 3. Khi o ta co cac trang thai va nang lng tng ng neu trenbang 1.2.

Bang 1.2. Cac trang thai va nang lng cua electron hoa tr trong nguyen tkim loai kiem.

n l Trang thai Mc nanglng

Lp

1 0 1s 1S K2 0 2s 2S L

1 2p 2P0 3s 3S

3 1 3p 3P M2 3d 3D

1.1.2.2. Quang pho cua nguyen t kim loai kiem

Cung giong nh nguyen t hydrogen, khi co kch thch t ben ngoai,electron hoa tr chuyen t trang thai ng vi mc nang lng thap n0, l0 sang trangthai ng vi mc nang lng n, l cao hn. Sau o no tr ve trang thai vi mcnang lng n, l thap hn va giai phong nang lng di dang bc xa ien t,ngha la phat ra photon nang lng h. Viec chuyen mc nang lng nay tuan theo

quy tac la chon nh sau:n n va l = l - l = 1 (1.10)Theo quy tac la chon (1.10), quang pho cua lithium c the hien tren

hnh 1.4.

3P

3S

2P

2S

3D

Day 2S - nP

Cac day 2P - nS2P - nD

4F4D4P4S

Day 3S - nPHnh 1.4. S o quangpho cua lithium.Chu thch:K hieu 2S nP e chdch chuyennP 2S.


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1.1.2.3. Kch thch va ion hoa nguyen t

Cac electron cua nguyen t chiem ay cac trang thai thap nhat cac quyao thap nhat. V du nguyen t sodium (Na), hnh 1.3, co 11 electron, trong o 2electron nam lp K, 8 electron nam lp L va 1 electron con lai nam lp M.o la trang thai c ban (ground state) cua nguyen t. Cac electron nam lp cangthap th cang b lc tac dung hut manh vao hat nhan. e chuyen no len lp caohn phai co nang lng cung cap t ben ngoai. Khi mot electron nao o c cungcap nang lng chuyen t lp di len lp tren th e lai mot lo trong lp ma nova bo i. Khi o nguyen t trang thai kch thch. Neu c cung cap mot nanglng rat ln, electron co the thoat ra ngoai nguyen t, ngha la khong chu lc hutcua nguyen t, va e lai mot lo trong tai lp no va bo i. Khi o ta noi nguyen t

b ion hoa, tc la nguyen t vi ien tch dng co gia tr bang ien tch cacelectron bay ra ngoai.

Nang lng ion hoa nguyen t la nang lng can thiet e mot electronchuyen t mc c ban tr thanh electron t do. Chang han nang lng ion hoanguyen t hydrogen Eih, theo hnh 1.1, la nang lng can thiet e electron chuyent mc nang lng c ban K (n1 = 1) len mc nang lng cao nhat khi n2, tcla:

Eih = Wn2 Wn1 = 0 (-Rh) = Rh (1.11)Thay R = 3,27.1015 s-1 va h = 6,625.10-34 J.s vao cong thc (1.11) ta c

E = 13,6 eV.Khi nguyen t b kch thch hay b ion hoa, v tr cu cua electron tr thanh lotrong. Neu mot electron nao o lp cao n2 ri vao lo trong lp thap n1 thnguyen t giai phong mot nang lng bang hieu so gia hai mc nang lng tngng vi hai lp nay :

== 2

221

n1n2 n1

n1

RhWWE vi n2 > n1 (1.12)

Nang lng E c giai phong ra khoi nguyen t di dang mot bc xaien t, chang han la anh sang oi vi nguyen t hydrogen. oi vi cac nguyen t

nang, tc la co so nguyen t Z ln, nang lng bc xa co gia tr ln. Trong trnghp nay, khi electron chuyen gia cac mc thap, bc xa phat ra co nang lng khaln, goi la tia X (hnh 1.5), con oi vi cac lp cao hn, nang lng bc xa be, khio nguyen t phat ra cac tia anh sang t ngoai, anh sang nhn thay hoac anh sanghong ngoai. Tia X va cac bc xa anh sang eu la song ien t, chung ch khacnhau ve tan so song. Chung co tnh chat hat nen con goi la photon hay lng tanh sang.

Trong qua trnh tng tac cua bc xa vi vat chat, nang lng cua tia bcxa nh alpha, beta, gamma c truyen cho cac electron quy ao. Cac hieu ngchung khi tng tac cua bc xa vi vat chat la kch thch va ion hoa nguyen t moi

trng.


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Hnh 1.5. Nguyen t bc xa tia X.

1.1.3. Momen t cua electron va hieu ng Zeeman

Electron chuyen ong tren quy ao cua nguyen t nen no co momen ong

lng lr

vi cac gia tr gian oan: l

r = )1( +ll h (1.13)

va hnh chieu len phng z bat k:( l

r)z = mh (1.14)

trong o m la so lng t t. Electron chuyen ong quanh hat nhan tao nen dongien. Dong ien nay co momen t r ngc chieu va t le vi l

r:

r = -

em2

elr

(1.15)

Hnh chieu cua momen t len phng z bat k bang:z = - mB (1.16)

trong o B la magneton Bohr:

B =em2

e h = 10-23 A.m2 (1.17)

o ln cua momen t (1.15) c viet qua magneton Bohr nh sau: = r = )1( +ll B (1.18)Hien tng Zeeman la hien tng tach vach quang pho nguyen t thanh

nhieu vach st nhau khi nguyen t phat sang at trong t trng. V du, ta at motnguon kh hydrogen phat sang vao gia hai cc mot nam cham ien. Khi quan satcac bc xa phat ra theo phng vuong goc vi vector t trng th thay moi vachquang pho cua nguyen t hydrogen b tach thanh 3 vach st nhau.

Giai thch hien tng Zeeman nh sau. V electron co momen t r nen khi

at nguyen t hydrogen vao t trng Br

th electron co them nang lng phu:W = -(

r . Br

) (1.19a)

Gia s phng z la phng cua t trng Br

th:W = - z B = - mB B (1.19b)Nh vay khi nguyen t hydrogen at trong t trng, nang lng W cua

electron con phu thuoc vao so lng t m nh sau:W = W + mB B (1.20)

Electron lp L

Lo trong lp K Tia X

M L K


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Trong o W la nang lng cua electron khi nguyen t hydrogen khong attrong t trng.

Neu electron dch chuyen t trang thai ng vi nang lng W2 sang trangthai ng vi nang lng W1 thap hn th no se phat ra bc xa ien t. Tan so vach

quang pho bang: =

h

WW '1'

2 =h

WW 12 +h

B)m(m B12 (1.21)

Trong oh

WW 12 = la tan so cua vach quang pho hydrogen khi nguyen

t hydrogen khong at trong t trng. Do o:

= +h

B)m(m B12 (1.22)

Quy tac la chon oi vi so lng t t m nh sau:m = m m = 0, 1 (1.23)Nh vay co the nhan 3 gia tr:

+

=

Bh

Bh

'

B

B

(1.24)

ngha la mot vach quang pho khi khong co t trng c tach thanh 3 vach khi cot trng, trong o vach gia trung vi vach cu.

1.1.4. Spin electron va cau tao boi cua vach quang pho

1.1.4.1. Spin electron va cau truc tinh te cua mc nang lng

Electron co momen spin sr

vi o ln: s

r = h1)s(s+ (1.25)

Trong o s = 1/2 la so lng t spin, hay spin cua electron. Hnh chieu cuamomen spin len phng z bat k bang:

( sr

)z = 21

h

(1.26)Do electron co momen quy ao l

rva momen spin s

rnen no co momen toan

phan jr

:jr

= lr

+ sr

(1.27)

o ln cua momen toan phan jr

la:

jr

= h1)j(j+ (1.28)Trong o j la so lng t momen toan phan, c xac nh nh sau:j = l 1/2 (1.29)

Do co momen spin nen e xac nh trang thai cua electron, ngoai 3 solng t n, l, m con phai a vao so lng t ms ac trng cho s nh hng cua


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spin. Nh vay trang thai lng t cua mot electron trong nguyen t c xac nhbi 4 so lng t n, l, m, ms.

Electron co momen spin nen cung co momen t rieng, do o co s tngtac gia momen t rieng va momen t quy ao cung nh gia momen t rieng cua

cac electron trong nguyen t vi nhau. Nh vay co them nang lng bo sung vaobieu thc nang lng cua electron khi tnh ti spin. Nang lng phu nay phu thuocvao s nh hng cua momen spin, do o phu thuoc vao j. Noi khac i, nanglng toan phan cua electron trong nguyen t phu thuoc vao 3 so lng t n, l, j.

Khi a vao momen toan phan j th moi mc nang lng c tach thanh 2mc ng vi j = l - 1/2 va j = l + 1/2, trong o mc ng vi j = l - 1/2 cao hn mcng vi j = l + 1/2. Khoang cach gia hai mc nay khong ln lam nen cau truc nhvay goi la cau truc tinh te cua mc nang lng.

Ngi ta k hieu trang thai cua electron hoa tr bang nxj con mc nanglng cua no bang n2Xj , trong o:

n = 1, 2, 3, 4, . . . . . (so lng t chnh)X = S, P, D, F, . . . . ng vi l = 0, 1, 2, 3, . . . .j = l 1/2Ch so 2 pha trai va tren ch X ch cau tao boi kep cua mc nang lng.

Cac mc nang lng S (l = 0) khong co cau tao boi. Tren moi mc S co hai trangthai electron khac nhau ve s nh hng cua momen spin.

Bang 1.3 trnh bay cac trang thai va mc nang lng co the co cua electronhoa tr trong nguyen t hydrogen va cac nguyen t kim loai kiem.

Bang 1.3. Cac trang thai va mc nang lng co the co cua electron hoa trtrong nguyen t hydrogen va cac nguyen t kim loai kiem

n l j Trang thai cuaelectron hoa tr

Mc nang lng

1 0 1/2 1s1/2 12S1/20 1/2 2s1/2 22S1/2

2 1 1/2 2p1/2 22P1/23/2 2p3/2 22P3/2

0 1/2 3s1/2 32S1/23 1 1/2 3p1/2 32P1/2

3/2 3p3/2 32P3/22 3/2 3D3/2 32D3/2

5/2 3D5/2 32D5/2

1.1.4.2. Cau tao boi cua vach quang pho

Tren c s cau truc tinh te cua mc nang lng ta co the giai thch ccau tao boi cua vach quang pho hay tach tinh te cua vach quang pho. Do nang

lng electron phu thuoc vao so lng t j nen khi chuyen t mc nang lng cao


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xuong mc nang lng thap hn, ngoai quy tac la chon oi vi l theo cong thc(1.10), electron con phai tuan theo quy tac la chon oi vi j:

j = j j = 0, 1 (1.30)T quy tac la chon oi vi j co the suy ra cau tao boi cua cac vach quang

pho 2S 3P va 2P - 3D nh trnh bay tren cac hnh 1.6 va 1.7.

1.1.5. Quy luat phan bo cac electron quy ao va he thong tuan hoanMendeleev

Mot trang thai cua electron quy ao c ac trng bi 4 so lng t n, l,m va ms. Quy luat phan bo cac electron quy ao tuan theo nguyen l loai tr Pauli,phat bieu nh sau: moi trang thai lng t xac nh bi 4 so lng t n, l, m vams ch co the co toi a mot electron.

Cha ke ti spin electron, vi moi tr so cua n ta co so trang thai electronnh sau:

=

+1n

0

1)(2l

l = n2 (1.31)

Khi ke en spin th moi tr so cua l ta lai co hai tr so khac nhau cua ms lams = 1/2 va ms = -1/2. Nh vay vi moi tr so cua n ta co 2n2 trang thai lng t,ngha la co 2n2 electron. Tuy theo so lng t n ta chia thanh tng lp electronquanh hat nhan nh sau:

Lp K (n = 1) co toi a 2n2 = 2 electron.Lp L (n = 2) co toi a 2n2 = 8 electron.Lp M (n = 3) co toi a 2n2 = 18 electron.Lp N (n = 4) co toi a 2n2 = 32 electron.. . . . . . . . . . . . . . . . . . . . . . . . . . . . .Moi lp lai chia thanh cac lp con ng vi cac gia tr khac nhau cua l. Moi

lp con co 2(2l + 1) electron. Lp K (n = 1) co toi a 2 electron.

Hnh 1.6. S o vach kep khitnh ti spin electron.a) Vach quang pho khi chatnh en spin.b) Vach kep khi tnh ti spin.

32P3/2

32P1/2

22S1/2

a) b)

3P

2S

32D5/2

32D3/2

22P3/2

a) b)

Hnh 1.7. S o vach boi ba khitnh ti spin electron.a) Vach quang pho khi chatnh en spin.b) Vach boi ba khi tnh ti spin. 2

2P1/2

3D

2P


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Lp nay ch co mot lp S vi l = 0, cha 2(2l + 1) = 2 electron. Lp L (n = 2) co toi a 8 electron, gom 2 lp con: Lp con S (l = 0) cha 2(2l + 1) = 2 electron. Lp con P (l = 1) cha 2(2l + 1) = 6 electron.

Lp M (n = 3) co toi a 18 electron, gom 3 lp con: Lp con S (l = 0) cha 2(2l + 1) = 2 electron. Lp con P (l = 1) cha 2(2l + 1) = 6 electron. Lp con D (l = 2) cha 2(2l + 1) = 10 electron. Lp N (n = 4) co toi a 32 electron, gom 4 lp con: Lp con S (l = 0) cha 2(2l + 1) = 2 electron. Lp con P (l = 1) cha 2(2l + 1) = 6 electron. Lp con D (l = 2) cha 2(2l + 1) = 10 electron. Lp con D (l = 3) cha 2(2l + 1) = 14 electron.Quy luat phan bo cac electron quy ao nh tren cho phep sap xep cac

nguyen to theo th t tang dan so electron quy ao, nh c trnh bay tren bang1.4. Bang sap xep nay phu hp vi he thong tuan hoan Mendeleev, c xay dngt nam 1869, trc khi hnh thanh mon c hoc lng t.

Bang 1.4. Bang phan hang tuan hoan oi vi mot so nguyen to.

Nguyen Lp K L Mto Lp

con

1S 2S 2P 3S 3P 3D

H 1He 2Li 2 1Be 2 2B 2 2 1C 2 2 2N 2 2 3O 2 2 4F 2 2 5

Ne 2 2 6Na 2 2 6 1Mg 2 2 6 2Al 2 2 6 2 1Si 2 2 6 2 2P 2 2 6 2 3S 2 2 6 2 4Cl 2 2 6 2 5Ar 2 2 6 2 6


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T bang tuan hoan tren co the viet cong thc cau truc lp cua nguyen t.V du, oi vi Al cong thc la 1s22s22p63s23p1, co ngha la oi vi nguyen t nay trang thai 1s co 2 electron, trang thai 2s co 2 electron, trang thai 2p co 6 electron,trang thai 3s co 2 electron va trang thai 3p co 1 electron.

Cung t bang 1.4 thay rang cac kh tr la cac kh co cac lp b electronchoan ay, o la cac nguyen t ben ve mat hoa hoc. Tong so electron choan ay,theo bang 1.4, oi vi cac kh tr la 2 (He), 10 (Ne), 18 (Ar). oi vi cac kh trkhac ta co so electron choan ay la 36 (Kr), 54 (Xe), 86 (Rn).

1.2. CAC HAT NHAN ONG V, ONG KHOI VA ONG KHOIGNG

1.2.1. Cac thanh phan c ban cua hat nhan

Hat nhan cau tao t cacproton (k hieu la p) va cac neutron (k hieu la n).Khoi lng proton mp va neutron mn gan bang nhau va bang khoang 1840 lan khoilng electron me = 9,091.10-31 kg, trong o mp = 1836,15me = 1,67265.10-27 kg vamn = 1838,68me = 1,67495.10-27 kg. Proton co ien tch dng + e = +1,6.10-19 Ccon neutron la hat trung hoa.

Khac vi electron, proton va neutron chu tac dung cua lc hat nhan, o latrng hp rieng cua tng tac manh. Do lc hat nhan ma cac proton va neutronco the lien ket vi nhau tao nen cac hat nhan. oi vi tng tac manh th cacproton va neutron hoan toan giong nhau. V vay chung c goi chung la cac

nucleon. Co the noi proton va neutron la hai trang thai cua cung mot hat, o lanucleon.Nguyen t trung hoa ve ien nen so proton trong hat nhan bang so electron

trong vo nguyen t. Nh vay so proton bang so nguyen t Z. So nucleon trong hatnhan bang A, goi la so khoi lng. Neu goi so neutron trong hat nhan la N th ta coA = Z + N.

Ta k hieu hat nhan X co so khoi lng A va so nguyen t Z la ZAX . Chang

han hat nhan beryllium co 4 proton va 5 neutron, tc la Z = 4 va A = 9, nen c khieu la 4Be9. Ch so Z trong k hieu Z

AX oi khi co the bo qua v so nguyen t Z

c xac nh mot cach n tr bang ten goi cua nguyen to. V du, hat nhan 4Be9

co the viet la Be9. Vi k hieu cua hat nhan noi tren, co the k hieu proton la 1p1 vaneutron la on1.

1.2.2. Cac hat nhan ong v

Cac hat nhan vi so nguyen t Z giong nhau nhng vi so khoi lng Akhac nhau c goi la cac hat nhan ong v hay goi tat la ong v. Chang hanuranium vi Z = 92 co cac ong v 92U235 va 92U238 vi so neutron bang 143 va 146tng ng. Cac hat nhan cua cung mot ong v c goi la cac nuclide. a so cacnguyen to tao thanh t hon hp cac ong v khac nhau. oi vi moi nguyen to, t


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le gia cac ong v thanh phan goi la o pho bien. V du, o pho bien cua ong v3

7Li va 36Li cua nguyen to lithium la 92,5% va 7,5% tng ng. Nguyen to

oxygen co 3 ong v vi o pho bien nh sau: 8O16 (99,759%), 8O17 (0,037%) va8O18 (0,204%).

Moi nguyen to chiem mot v tr trong bang tuan hoan Mendeleev nen cacong v cua cung mot nguyen to co cung mot v tr trong bang tuan hoan. Do ocac nguyen t cua cac ong v khac nhau nhng cua cung mot nguyen to eu cotnh chat hoa hoc giong nhau. Viec tach mot ong v nao o ra khoi hon hp cuacung mot nguyen to la mot bai toan k thuat phc tap. e giai quyet van e naykhong the dung cac phan ng hoa hoc ma ch co cach phan biet cac ong v theos khac nhau khong ln cua van toc cua chung khi boc hi, khuech tan va cac quatrnh vat l khac.

Cac ong v co the ton tai trong t nhien, goi la cac ong v t nhien(natural radioisotope), hay co the tao nen trong cac lo phan ng hat nhan va cacmay gia toc hat tch ien, goi la cac ong v nhan tao. Mot so ong v t nhien vahau het cac ong v nhan tao eu khong ben va thng phat ra cac bc xa e trthanh cac ong v ben. Tnh chat phat bc xa nay goi la tnh phong xa va cac ongv phat bc xa goi la cac ong v phong xa. Cac ong v ben khong the t phat racac bc xa hoac phat bc xa vi mot lng rat be trong thi gian ton tai cua vu tru.Co khoang 70 ong v phong xa t nhien, trong o quan trong nhat la cac ong v92U235, 92U238, 90Th232 cung cac ong v con chau trong cac ho phan ra cua chung,va khoang 2000 ong v phong xa nhan tao, trong o cac ong v thng dung nh27Co60, 55Cs137, 77Ir192, 95Am241, . . .

Z

100

80

20

40

60

0 20 40 60 80 100 120 140 160 N

-

Z=N

S =0p

S =0n

Cac hat nhan phong xa

+Cac hat nhan

Cac hat nhan ben

phong xa

Hnh 1.8. Gian o Z-N phan biet cac hat nhan ben va khong ben. Mien giihan gia hai ng cong Sp = 0 va Sn = 0 gom cac hat nhan ben oi vi phan ranucleon. Dai hep gach ca ro gom cac hat nhan ben oi vi ca phan ra nucleon vabeta. Vung gach cheo pha tren gom cac hat nhan phan ra + con vung gach cheopha di gom cac hat nhan phan ra .


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e phan biet cac hat nhan ben va khong ben ngi ta thng dung gian oproton-neutron Z-N (hnh 1.8). Tren gian o nay hai ng gach noi co k hieuSp = 0 va Sn = 0 la gii han mien ton tai cua cac hat nhan ben oi vi phan raproton va neutron, trong o Sp va Sn la cac nang lng tach proton va neutron ra

khoi hat nhan. Mien gii han hep hn trong mien noi tren gom cac hat nhan benva cac hat nhan phong xa beta. Trong mien nay, cac hat nhan ben co so proton vaso neutron nam trong mot hanh lang hep mieu ta bi mien gach ca ro. Dai nay coso proton bang so neutron oi vi cac hat nhan t hydrogen en calcium va sau oso proton giam dan khi tang so neutron N, giam nhanh hn ng phan giac Z = N.Cac hat nhan phong xa beta nam ngoai hanh lang gii han cua dai nay, trong ocac hat nhan phong xa + nam mien gach cheo pha tren con cac hat nhan phongxa nam mien gach cheo pha di.

1.2.3. Cac hat nhan ong khoi

Cac hat nhan ong khoi la cac hat nhan co cung so A nhng so Z khacnhau. V du, cac hat nhan ong khoi la cac cap 16S36 va 18Ar36, 51Sb123 va 52Te123,. . . Ngi ta a tm c 60 cap hat nhan ong khoi lng ben co so A chan va soZ khac nhau hai n v bat au t A = 36 va hai cap ong v A le va Z khac nhaumot n v:

48Cd113 va 49In11351Sb123 va 52Te123Ngoai ra con tm c vai nhom ba hat nhan ong khoi lng nh:

22Ti50

, 23V50

, 24Cr50

54Xe136, 56Ba136, 58Ce136

1.2.4. Cac hat nhan ong khoi gng

Cac hat nhan ong khoi gng la cac hat nhan ong khoi ma so proton cuahat nhan nay bang so neutron cua hat nhan kia. Th du, cac hat nhan ong khoigng nh1H3 2He3; 3Li7 4Be7; 5B11 6C11; . . .

1.3. KICH THOUC VA HINH DANG CUUA HAT NHAAN

1.3.1. Kch thc hat nhan

Co the coi hat nhan nh mot qua cau ban knh R va xac nh ban knh hatnhan bang nhieu phng phap thc nghiem khac nhau. Sau ay trnh bay mot sophng phap.

1.3.1.1. Xac nh ban knh theo thi gian song cua cac hat nhan phan ra.


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Cac hat nhan phan ra co thi gian song T lien he vi ong nang cua hat theo quy luat Geiger-Nuttall:

lnT + AlnE = B (1.32)Trong o A va B la cac hang so, T bien thien t 10-7 s en 1010 nam con E

bien thien t 4 MeV en 7 MeV. Quy luat nay cua phan ra da tren hieu ng choc lng t khi hat i xuyen qua b the Coulomb. Bi v mot trong cac bien cuab the trung vi ban knh R cua hat nhan nen bieu thc l thuyet cua thi gian songT cha ai lng R. Do o co the xac nh R khi so sanh cac gia tr l thuyet vathc nghiem cua thi gian song T. Ket qua thc nghiem cho thay cac hat nhanphat co ban knh trong khoang t 8,4.10-13 cm en 9,8.10-13 cm va tuan theo bieuthc

R = roA1/3 (1.33)trong o

ro = (1,45-1,5).10-13 cm (1.34)

1.3.1.2. Xac nh ban knh theo s phan ra cua cac hat nhan oi xnggng

Nh se trnh bay trong muc 1.2.4, nang lng lien ket cua hat nhan cmieu ta theo cong thc ban thc nghiem sau ay:

Elk(A,Z) = A - A2/3 - 3/12

A

Z -A

1Z

2

A

2

+ Elk (1.35)

Trong cong thc nay, he soc bieu dien qua ban knh R theo cong thc

sau:=

o

2

r5

e3(1.36)

e xac nh ro qua he so, ngi ta dung s phan ra + cua cac hat nhan oixng gng. Khi phan ra + th hat nhan (A,Z) tr thanh hat nhan oi xng gng(A,Z-1). oi vi hat nhan oi xng gng th so neutron N = A Z bang so protonZ 1 cua hat nhan kia, do o A Z = Z 1, ngha la A = 2Z 1. Vi moi quan hegia A va Z nh vay th so hang Elk trong cong thc (1.35) bang khong con tat cacac so hang con lai eu bang nhau oi vi hai hat nhan oi xng gng, ngoai so

hang . Nh vay hieu nang lng lien ket cua hai hat nhan (A,Z) va (A,Z-1) la:Elk = Elk(A,Z-1) Elk(A,Z) = 3/1A

1)Z(2 = A2/3 =o

2

r5

e3A2/3 (1.37)

So sanh cac gia tr thc nghiem vi cong thc (1.36) ve hieu so nang lnglien ket oi vi cac hat nhan oi xng gng ta c:

ro = (1,2-1,3).10-13 cm (1.38)

1.3.1.3. Xac nh ban knh theo tan xa neutron nhanh len cac hat nhan

Khi mot chum hat neutron vi cng o No i qua bia vat chat coo day xth chum neutron sau bia o la:


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N(x) = Noe-nx (1.39)Trong o n la mat o hat nhan cua bia va la tiet dien vi phan tng tac

gia neutron va hat nhan bia. Qua trnh tng tac cua neutron nhanh vi hat nhanbia gom qua trnh tan xa khong an hoi va tan xa nhieu xa an hoi vi tiet dien vi

phan bang = 2R2 (1.40)Tren c s hai cong thc (1.39) va (1.40) co the xac nh ban knh hat nhan

khi cho chum neutron nhanh vi nang lng t 14 MeV en 25 MeV va nanglng 90 MeV i qua lp bia day d nh sau:

R2 = /2 = -ln[N(d)/No]/2nd. (1.41)Ket qua thc nghiem cho gia tr ban knh R = roA1/3 vi ro nh sau:ro = (1,3-1,4).10-13 cm. (1.42)

1.3.1.4. Xac nh ban knh theo tan xa electron nhanh len cac hat nhan

o dai bc song de Broigle cua electron vi ong nang Ee >> mec2 la:

e

10

e6

1027

e E1,24.10

E1,6.10.3.106,62.10

Ehc

ph

=== (1.43)

Trong o c tnh theo n v cm con Ee trong n v MeV. KhiEe = 100 Mev th vao c kch thc cua hat nhan. Bang thc nghiem tan xa anhoi cua electron len hat nhan va o phan bo goc cua cac neutron sau tan xa co thexac nh c ban knh hat nhan. So sanh ket qua tnh toan vi so lieu thcnghiem cho gia tr ban knh R = roA1/3 vi r0 nh sau:

ro = (1,2-1,5).10-13 cm. (1.44)

1.3.1.5. Xac nh ban knh theo nang lng bc xa tia X t nguyen t muon()

Hat co khoi lng m = 207me, mang ien tch dng, am hoac trung hoa,phan ra thanh mot electron va hai neutrino vi thi gian song 2.10-6 s.

Hat - co tnh chat giong nh electron va khi no b bat mot quy ao naoo cua nguyen t, ta co mot nguyen t . Ban knh cua nguyen t be hn banknh nguyen t thong thng 207 lan. Nguyen t giong nh nguyen t thongthng, trong o co hien tng phat bc xa tia X khi chuyen t quy ao caoxuong quy ao thap hn. Nang lng tia X phu thuoc rat manh vao ban knh hatnhan, co the o c bang thc nghiem va tnh bang l thuyet. T viec so sanh cacgia tr nang lng theo tnh toan l thuyet va cac gia tr thc nghiem co the xacnh c ban knh hat nhan. Thc nghiem tien hanh oi vi nguyen t ch cho ketqua

RPb = 1,17.10-13.2081/3

1.3.1.6. Tom tat cac ket qua xac nh ban knh hat nhan


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Cac phng phap thc nghiem khac nhau eu cho thay co the chap nhangia thuyet hat nhan co dang hnh cau vi ban knh

R = roA1/3trong o

ro = (1,2-1,5).10

-13

cm. (1.45)Tuy nhien hat nhan khong phai la mot khoi cau co bien gii ro rang mamat o cac nucleon, chnh xac hn la mat o cac proton, khong oi trong mien bentrong hat nhan va giam en 0 tai mien bien gii hat nhan, vi o rong d t o cao0,9/0 en 0,1/0 nh the hien tren hnh 1.9. Mat o phan bo ien tch trong hatnhan c mo ta bi cong thc sau ay:

+

=

Rrexp1

o

o (1.46)

trong o Ro = 1,08.10-13A1/3 cm va = 0,55.10-13 cm.

T cong thc (1.33) thay rang the tch hat nhan phu thuoc tuyen tnh vao so

khoi lng A :V = (4/3)ro3A (1.47)Mat o vat chat hat nhan bang:

14

453

27

453

p

3

10

.10(1,5)3

4

1,67.10

.10A(1,5)3

4

Am

R3

4

M ===

hatnhan tan/m3 (1.48)

Ta thay rang mat o hat nhan cc k ln va khong oi oi vi moi hat nhan.ay la gia tr trung bnh, con phan bo mat o vat chat hat nhan tuan theo congthc (1.46).

1.3.2. Hnh dang hat nhan

Trc nhng nam 1950 hat nhan c coi la co dang hnh cau. T nam1950 ngi ta chng minh c rang nhieu hat nhan co dang lech khoi oi xngcau. Bang chng trc tiep va thuyet phuc nhat ve s ton tai cac hat nhan khong codang hnh cau la s co mat cac dai quay trong pho cac hat nhan chan-chan. Daiquay la mot chuoi cac mc tuan theo he thc sau ay gia nang lng va spin:

2I1)J(J

E2

J+

=h

(1.49)

/o

R0

1,00,9

0,1r

Hnh 1.9. Phan bo mato ien tch trong hatnhan.


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Trong o I la momen quan tnh cua hat nhan oi vi truc oi xng va J laspin hat nhan. Neu hat nhan hoan toan oi xng cau th khong co phng u tien,do o spin bang 0. Con khi hat nhan mat oi xng cau nhng oi xng theo mottruc nao o th spin cua hat khac 0. Trong trng hp bat oi xng o nang lng

kch thch do s quay cua hat nhan c xac nh theo cong thc (1.49), co gia trkhac 0. oi vi hat nhan chan-chan, cac gia tr spin bang J = 0, 2, 4, 6, 8, . . . Trenhnh 1.10 trnh bay mot v du cua dai quay, o la pho cac mc thap nhat cua hatnhan 72Hf180.

Nh vay cac hat nhan co spin khac khong thng co dang khong oi xng

cau. Ngoai pho quay, tnh khong oi xng cau con the hien s co mat momen tcc ien Q, se c trnh bay trong muc 1.5. Thong thng cac hat nhan trangthai c ban co dang hnh cau hay ellipsoid tron xoay, con trang thai kch thch,chung co dang phc tap hn.

1.4. NANG LNG LIEN KET CUA HAT NHAN

1.4.1. n v o khoi lng va nang lng

e o khoi lng trong vat l hat nhan ngi ta dung n v khoi lng

nguyen t u, bang12

1 khoi lng nguyen t ong v C12:

1 u = 1,66056.10-27 kg (1.50)Do he thc Einstein E = mc2, n v khoi tnh theo kg tng ng vi n v

khoi lng tnh theo MeV la:1 u = 931,502 MeV (1.51)Bang 1.5 dan ra khoi lng cua mot so hat nh proton, neutron, deutron va

alpha.

12241090

714

660

340330

1020

8+

6

+

4+

2+0

Hnh 1.10. Pho quay cua hat nhan 72Hf180.Cac gach ngang am la cac mc nanglng thc nghiem con cac gach ngangkhong lien tuc c tnh theo cong thc(1.49). Cac so cot ben trai: Nang lngkeV. Cac so cot ben phai: Spin va chanle.


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Bang 1.5. Khoi lng cac hat proton, neutron, deutron va alpha

Hat Khoi lngn v khoi lng u kg MeV

Neutron 1,008665 1,67495.10-27

939,55Proton 1,007276 1,67265.10-27 938,26Deutron 2,01355 3,3325.10-27 1875,5Alpha 4,00047 6,6444.10-27 3726,2

1.4.2. o hut khoi va nang lng lien ket

Cac phep o chnh xac chng to rang khoi lng M cua hat nhan bao gicung nho hn tong khoi lng cua cac nucleon tao thanh hat nhan o mot lngM:

M = Zmp + Nmn M (1.52)Trong o mp va mn la khoi lng cua proton va neutron. M la mot ai

lng dng va c goi la o hut khoi cua hat nhan.S hut khoi o la do s tng tac cua cac nucleon gay ra. V vay o hut

khoi tng ng vi nang lng lien ket gia cac nucleon trong hat nhan. Nanglng lien ket cua hat nhan la nang lng can thiet e tach hat nhan thanh cacproton va cac neutron rieng biet. No ac trng cho s ben vng cua hat nhan.Theo he thc Einstein ta co nang lng lien ket Elk c bieu th qua o hut khoiM nh sau:

Elk = M.c2

= (Zmp + Nmn M).c2

(1.53)V trong cac bang thng ghi khoi lng nguyen t Mngt ma khong ghi khoilng hat nhan M nen cong thc (1.22) c viet lai nh sau:

Elk = M.c2 = (ZmH + Nmn Mngt).c2 (1.54)Trong o mH la khoi lng nguyen t hydrogen trung hoa, tc lamH = mp + me (1.55)

vi me la khoi lng electron.Sau ay la gia tr gan ung cua nang lng lien ket cua mot so hat nhan:

Elk (2He4) = 28 MeV; Elk (6C12) = 92 MeV; Elk (8O16) = 128 MeV; Elk (16S32) = 272MeV.

1.4.3. Nang lng lien ket rieng

e so sanh o ben vng cua cac hat nhan, ngi ta thng dung khai niemnang lng lien ket rieng , la nang lng lien ket ng vi mot nucleon:

=A

E lk (1.56)

Nang lng lien ket rieng cang ln th hat nhan cang ben vng. Hnh 1.11trnh bay s phu thuoc nang lng lien ket rieng theo so khoi lng A cua cac

hat nhan.T hnh 1.11 thay rang:


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oi vi cac hat nhan nhe nhat, nang lng lien ket rieng tang nhanh t1,1 Mev (1D2) en 2,8 MeV (1T3) va at en 7 MeV (2He4).

oi vi cac hat nhan nang co A t 140 en 240 th nang lng lien ketrieng giam dan nhng rat cham t 8 MeV en khoang 7 MeV.

oi vi cac hat nhan trung bnh vi A = 40 140 nang lng lien ketrieng co gia tr ln nhat nam trong khoang 8 8,6 MeV. ieu o giai thch tai saocac hat nhan trung bnh ben vng nhat.

Hnh 1.11. S phu thuoc nang lng lien ket rieng theo so khoi lng A cua cac

hat nhan. ng lien: Tnh toan theo cong thc (1.60). Cac iem: Cac gia tr thcnghiem.

1.4.4. Nang lng tach cac hat ra khoi hat nhan

T khai niem nang lng lien ket neu tren co the xac nh c s canbang nang lng oi vi mot qua trnh phan ra hay tng tac bat k. Chang han,nang lng tach mot proton ra khoi hat nhan la nang lng can thiet e tachproton ra khoi hat nhan ZXA, bang hieu so nang lng lien ket cua cac hat nhan

ZXA

va Z-1XA-1

:Ep = Elk(Z,A) Elk(Z-1,A-1) (1.57)

9,0

8,5

8,0

7,5

0 50 100 150 200 250 A

=A

E lk (MeV)

(MeV)6

4

8

2

00 10 20 30

A


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Cung tng t, nang lng tach neutron la:En = Elk(Z,A) Elk(Z,A-1) (1.58)Nang lng tach hat alpha ra khoi hat nhan bang:E = Elk(Z,A) Elk(Z-2,A-4) Elk() (1.59)

1.4.5. Cong thc ban thc nghiem ve nang lng lien ket

Tren c s cac so lieu thc nghiem ve nang lng lien ket nh trnh baytren hnh 1.11, Weizsacker a xac lap cong thc ban thc nghiem ve s phu thuocnang lng lien ket Elk vao so khoi lng A va so nguyen t Z nh sau:

Elk(A,Z) = A - A2/3 - 3/12

A

Z -A

1Z

2

A

2

+ Elk (1.60)

T cong thc (1.60) co the tnh c nang lng lien ket rieng theo cong

thc (1.56). Ket qua tnh toan c minh hoa tren hnh 1.11 vi cac gia tr = 15,75 MeV; = 17,8 MeV; = 0,710 MeV; = 23,7 MeV; Elk c tnh theocac cong thc (1.61) va (1.62). ng cong tnh toan rat phu hp vi cac gia trthc nghiem.

Cong thc (1.60) co the giai thch t quan iem mau giot chat long. Tuynhien cung co the giai thch nh sau.

So hang A: ay la so hang gan ung bac khong, noi rang nang lng

lien ket rieng =A

E lk la hang so, vao c 8 MeV, do o E lk~ A. So hang nay phan

anh tnh chat bao hoa cua lc hat nhan. That vay, cac hat nucleon trong hat nhan

ch tng tac vi mot so nucleon gii han ben trong hat nhan, do o Elk~ A, makhong phai tng tac vi tat ca cac nucleon trong hat nhan, khi o E lk~

2

1)A(A .

So hang -A2/3: So hang nay lien quan en hieu ng be mat. Cac nucleonnam tren be mat hat nhan ch tng tac vi mot so nucleon pha trong hat nhan, doo nang lng lien ket b giam i so vi cac nucleon nam trong hat nhan. Phannang lng lien ket b giam nay t le vi dien tch be mat, tc la vi A 2/3 do banknh hat nhan t le vi A1/3.

So hang -3/1

2

A

Z : So hang nay lien quan en hieu ng ay tnh ien gia

cac proton lam giam nang lng lien ket. Nang lng Coulomb t le vi bnhphng so proton Z2 va t le nghch vi kch thc hat nhan A1/3, ngha la t le vi

3/1

2

A

Z.

So hang -A

1Z

2

A

2

: Neu ta xet nang lng lien ket rieng nh mot

ham cua Z vi A co nh, hnh 1.12, th cac ng cong co cc ai nam tai gia trZ 0,5A oi vi cac hat nhe va dch chuyen ve pha Z < 0,5A oi vi cac hat nhan

nang, tc la ve pha N = A Z > 0,5A.


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Hieu ng neu tren chng to nang lng tng tac gia neutron vi protonln hn nang lng tng tac gia cac hat giong nhau. Khi o nang lng oi xng

co gia tr am va t le vi2

2

A

Z)(N .

So hang Elk: So hang nay lien quan en hieu ng bat cap cua cac loainucleon trong hat nhan, tc la cac nucleon tao nen tng cap mot. oi vi cac hatnhan chan-chan, tc la Z chan va N chan, tat ca cac hat nucleon eu bat cap; oivi cac hat nhan chan-le, tc la Z chan va N le hay ngc lai, th con lai motnucleon khong bat cap; oi vi cac hat nhan le-le, tc la Z le va N le, th con laihai nucleon khong bat cap. Nh vay cac hat nhan chan-chan ben vng nhat, sau oen cac hat nhan chan-le, con cac hat nhan le-le kem ben vng nhat. ieu o danti so hang hieu chnh trong nang lng lien ket nh sau:

=

chanchannhanhatvilechannhanhatvi0

lelenhanhatviE

lk

-

(1.61)

trong o

=3/1A

12MeV (1.62)

1.5. SPIN VA MOMEN T CUA HAT NHAN

1.5.1. Spin hat nhan

Hat nhan cau tao t cac nucleon. Cung nh electron, nucleon co spin

s =2

1. Ngoai ra nucleon con co momen quy ao khi no chuyen ong theo quy ao

ben trong hat nhan. Nh vay moi nucleon chuyen ong ben trong hat nhan comomen ong lng toan phan la:

iii sjr

lrr

+= (1.63)

Trong o ilr

va isr

la momen quy ao va spin cua nucleon th i. Do omomen ong lng toan phan cua hat nhan la:

= iijJ

rr

(1.64)

A=20

Z = 10 Z

Elk/A

A=146

Z = 60 Z

Elk/A

Hnh 1.12. S phu thuoc

nang lng lien ket riengvao Z vi A khong oi.


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Ngi ta goi Jr

la momen spin cua hat nhan, ac trng cho chuyen ong noitai cua hat nhan. Theo c hoc lng t, gia tr tuyet oi cua momen spin hat nhanla:

hr

1)J(JJ += (1.65)

Trong o J la lng t spin cua hat nhan, goi tat la spin hat nhan. No co giatr nguyen 0, 1, 2, 3, . . . neu A chan, va co gia tr ban nguyen

2

1,

2

3,

2

5, . . . neu A

le.Hnh chieu cua momen spin len phng z nhan 2J+1 gia tr:Jz = Jh, (J-1) h, . . . , -Jh (1.66)

1.5.2. Momen t cua hat nhan

1.5.2.1. Mo men t cua hat nhan

Hat nhan co spin khac khong se co momen t r c xac nh qua momen

spin Jr

nh sau:r = g J

r(1.67)

Trong o g c goi la he so t hoi chuyen. Do s song song gia cacvector r va J

rnen cac tnh chat t cua hat nhan c ac trng bi mot hang so ,

tng ng vi gia tr J nh sau: = gJ (1.68)

Bang 1.6. Gia tr spin va momen t mot so hat nhan.

Hat nhan Spin Momen t trong n vmagneton hat nhan o

p2

1 + 2,79

n2

1 - 1,91

H2 1 + 0,86He3

2

1 - 2,13

Al272

5 + 3,65

Si292

1 - 0,55

K40 4 - 1,30Zr91

2

5 - 1,29

Ag108

21 - 0,13


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Hang so goi la momen t. Momen t va he so t hoi chuyen g c otrong n v magneton hat nhan o:

o =p2m

eh= 5,05.10-27 J/T = 5,05.10-24 erg/G (T: Tesla; G: Gauss) (1.69)

Chang han momen t cua neutron bang n = -1,91 co ngha la n = -1,910= -0,95.10-26 J/T = -0,95.10-23 erg/G. Tren bang 1.6 dan ra mot so gia tr momen that nhan oi vi mot so hat nhan.

Khai niem momen t hat nhan do Pauli a ra e giai thch cau tao sieutinh te cua cac vach quang pho. Cac vach quang pho la he cac vach mau nho netquan sat thay trong dung cu quang pho khi phan tch he phat sang cua cac nguyent b kch thch. ay chnh la cac vach nang lng photon phat ra khi electronchuyen t mc nang lng cao xuong cac mc nang lng thap hn, phu thuoc vaoso lng t chnh n va so lng t quy ao l. Viec chuyen mc nay tuan theo quy

tac la chon l = 1 trong cong thc (1.10). Khi ke en spin s =2

1 cua electron

th cac mc nang lng electron c tach ra thanh cac mc con, phu thuoc vao

momen toan phan j = l2

1 . Khi o cac vach quang pho c tach thanh cac

vach con, goi la tach tinh te hay cau tao boi cua vach quang pho. Viec chuyenmc nay tuan theo quy tac la chon j = 0, 1 trong cong thc (1.30).

V momen t hat nhan tac dung vi t trng do chuyen ong cua cacelectron trong lp vo nguyen t nen electron co them nang lng phu va cac mc

nang lng tinh te cua cac electron c tach ra cac mc phu, goi la cau truc sieutinh te. Tr so nang lng nay phu thuoc vao tr so cua momen t hat nhan va snh hng cua no so vi phng cua t trng cua electron. Do momen t cua hatnhan ch co the nh hng theo mot so phng nhat nh so vi t trng cuaelectron hoa tr nen so mc them nay tuy thuoc tr so spin cua hat nhan conkhoang cach gia cac mc tuy thuoc vao tr so momen t hat nhan. Bay gi ta haydan ra cac tnh toan nh lng.

Gia s t trng cua lp vo electron la Hr

th nang lng tng tac cua novi momen t r cua hat nhan la:

E = - r

H

r

(1.70)Do t trng Hr

t le vi momen toan phan cua lp vo nguyen t Ir

conmomen t r t le vi momen spin hat nhan J

rnen:

E = C Ir

Jr

(1.71)Theo quy luat cua c hoc lng t th nang lng E theo cong thc (1.71)

nhan cac gia tr gian oan. Co the tnh cac gia tr o nh sau.a vao vector F

r= I

r+ J

rth:

( Fr

)2 = ( Ir

+ Jr

)2 = ( Ir

)2 + ( Jr

)2 + 2 Ir

Jr

= I(I + 1) + J(J + 1) + 2 I

rJr

= F(F + 1)

Vay:


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E = C Ir

Jr

=2

1 C[F(F + 1) - I(I + 1) - J(J + 1)] (1.72)

Trong o F nhan cac gia tr nh sau:F = I + J, I + J 1, . . . . . , |I - J| (1.73)

Nh vay nang lng E nhan 2I + 1 gia tr neu I J va 2J + 1 gia tr neuJ I.Co the anh gia ai lng nang lng tach sieu tinh te tren c s la nang

lng tng tac co bac

3

Bo

r

(1.74)

trong o r 10-8 cm la kch thc nguyen t, o la magneton hat nhan theo congthc (1.69), B la magneton Bohr electron:

B =e2m

eh = 10-23 A.m2 (1.75)

Thay cac gia tr o, B va r vao (1.74) ta c nang lng tach sieu tinh teco bac 10-7 eV.

1.5.2.2. Cau truc sieu boi cua vach quang pho

Tren hnh 1.13 trnh bay s o cau truc sieu tinh te cua cac mc nang lng2P3/2 , 2S1/2 va tach sieu tinh te, hay cau truc sieu boi, cua vach quang pho cuanguyen t 19K39 do chuyen mc t mc 2P3/2 xuong mc 2S1/2.

1.5.2.2.1. Cau truc sieu tinh te

mc nang lng 2P3/2 electron co momen quy ao l = 1 va momen toan

phan I =2

3. Cung nh vay, electron mc 2S1/2 co l = 0 va I =

2

1. Do spin hat

nhan J =2

3 nen mc nang lng 2P3/2 c tach thanh 2I + 1 = 2J + 1 = 2.2

3 + 1 =

4 mc con. oi vi mc nang lng 2S1/2 do I < J nen c tach thanh

2I + 1 = 2.2

1 + 1 = 2 mc con.

1.5.2.2.2. Tach sieu tinh te

Vach quang pho cua nguyen t 19K39 do chuyen mc t mc 2P3/2 xuongmc 2S1/2 c tach thanh mot so vach phu do s chuyen mc t 4 mc phu cuamc 2P3/2 xuong 2 mc phu cua mc 2S1/2. Khi o 4 mc phu cua mc 2P3/2 co 4 giatr F1 = 0, 1, 2, 3 va 2 mc phu cua mc 2S1/2 co 2 gia tr F2 = 1, 2, nh the hientren hnh 1.13. Viec chuyen mc t mot trong cac mc phu F1 xuong mot trong cacmc phu F2 tuan theo quy tac la chon sau:

F = F2 F1 = 0, 1 (1.76)Ket qua tach sieu tinh te c the hien tren hnh 1.13 vi 6 vach phu.


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1.5.2.3. Quy tac khoang cach

Theo cong thc (1.72) th khoang cach gia hai mc lien tiep nhau F vaF 1 bang:

EF EF-1 = CF (1.77)Bieu thc (1.77) la noi dung quy tac khoang cach, ngha la khoang cach

gia cac mc nang lng lien tiep nhau lien he vi nhau nh sau:(I + J) : (I + J 1) : . . . . : |I - J| (1.78)

1.5.3. Cac quy luat thc nghiem rut ra t nghien cu momen t hat

nhan Momen t cua cac hat nhan co spin J = 0 th bang 0. Momen t cua cac hat nhan co spin khac 0 vao c magneton hat nhan.

Gia tr be cua momen t hat nhan cho phep khang nh rang trong hat nhan khongco electron v moment t cua electron ln hn 2000 lan momen t cua hat nhan.

Tnh khong cong c cua cac momen t. Chang han deutron tao nen tproton va neutron nhng momen t cua deutron d = 0,86 trong luc o tong moment cua proton va neutron bang p + n = 2,79 1,91 = 0,88. Hai gia tr 0,86 va 0,88khac nhau ngoai pham vi sai so. Tnh khong cong c nay c giai thch bang

tnh khong oi xng tam cua lc hat nhan.

1.6. MOMEN T CC IEN CUA HAT NHAN

1.6.1. Momen t cc noi Qo va momen t cc ngoai Q

ien tch Z cua hat nhan la mot thong so quan trong, cho biet so protontrong hat nhan, o ln cua the Coulomb va cac tnh chat hoa hoc cua hat nhan.Tuy nhien Z ch la mot ai lng tch phan ve ien tch hat nhan ma khong cho

biet phan bo ien tch trong hat nhan the nao. S phan bo ien tch o dan ti viechieu biet ve hnh dang hat nhan va cac tnh chat quan trong khac.

F10123

F212

2P3/2

2S1/2

(I = 3/2; J = 3/2)

(I = 1/2; J = 3/2)

Hnh 1.13. S o tach sieu tinh te vach quang pho cua nguyen t 19K39


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S phan bo ien tch trong hat nhan co ba loai la phan bo oi xng cau,phan bo thanh lng cc va phan bo t cc.

Phan bo thanh lng cc khi cac proton va cac neutron phan bo lech ve haiau cua hat nhan vi khoang cach gia cac trong tam cua chung bang (hnh

1.14). ai lng ac trng cho phan bo lng cc la momen lng cc ien D mahnh chieu cua no theo truc z co dang:Dz = (r)dVz (1.79)Trong o (r) la mat o ien tch va dV la yeu to the tch tai iem r. Ngi

ta chng minh c rang momen lng cc ien bang 0 oi vi trang thai c banva cac trang thai kch thch khong suy bien cua hat nhan.

Phan bo thanh t cc khi cac ien tch trong hat nhan hnh thanh hai lngcc ien cach nhau mot khoang cach d bo tr nh tren hnh 1.15a. ai lng actrng cho phan bo t cc la momen t cc ien Q, phan anh mc o bat oi xng

cau co dang ellipsoid trong phan bo ien tch hat nhan. Khi Q = 0 th hat nhan codang hnh cau (hnh 1.15b), khi Q > 0 th hat nhan co dang ellipsoid cang (hnh1.15c) con khi Q < 0 th hat nhan co dang ellipsoid det (hnh 1.15d). Momen t ccc o trong n v cm2 hay barn = 10-24 cm2, chang han momen t cc cuadeutron Qd = 0,00282.10-24 cm2.

oi vi cac hat nhan bat oi xng cau, co hai khai niem ve momen t ccien la momen t cc ien noi Qo va momen t cc ien ngoai Q.

Momen t cc ien noi Qo c tnh trong he toa o cung quay vi hatnhan va bieu th bi cong thc sau ay:

Qo = )dVr-(r)(322 (1.80)

Trong o he toa o 3 chieu , , gan lien vi hat nhan vi at doc theotruc quay cua hat nhan. Nh vay r(, , ) la khoang cach t iem lay tch phan

en tam quan tnh cua hat nhan va dV la yeu to the tch tai r con la hnh chieucua r len truc , (r) la ham phan bo ien tch ben trong hat nhan. Do

p pp p p pp p p pn n n nn n n

+

-

+

-

-

+

d

z z

z

a) b) a) b) c) d)

Hnh 1.14. Lng cc ienhat nhan. a) Lng ccien; b) S lech cac trong

tam am proton va amneutron.

Hnh 1.15. T cc ien hat nhan.a) T cc ien; b) Hat nhan dang hnhcau; c) Hat nhan dang ellipsoid cang;

d) Hat nhan dang ellipsoid det.


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r2 = 2 + 2 + 2 nen 3 2 = 2r oi vi phan bo oi xng cau (hnh 1.15b),

3 2 > 2r oi vi phan bo keo cang (hnh 1.15c) con 3 2 < 2r oi vi phan bo detso vi truc (hnh 1.15d).

Momen t cc ien ngoai Q c tnh trong he toa o phong th nghiem

theo cong thc sau:Q = )dVr-(r)(3z

22 (1.81)

Trong o he toa o 3 chieu x, y, z trong phong th nghiem vi truc z cchon trong khong gian. o ln cua Q phu thuoc vao Qo va s nh hng cua hatnhan so vi truc z. S nh hng nay phu thuoc vao s nh hng cua spin J

rso

vi truc z va hnh chieu K cua no tren truc oi xng cua hat nhan.Phep tnh c hoc lng t oi vi hnh chieu cc ai J cua vector J

rlen truc

z cho quan he sau ay gia Q, Qo, J va K:

oQ3)1)(2J(J1)J(J3K

Q

2

+++

= (1.82)

Trong cong thc (1.82), he so3)1)(2J(J1)J(J3K 2

+++ goi la he so chieu va khi o Q

c xem nh hnh chieu cua Qo len truc z.oi vi trang thai c ban th J = K va

oQ3)1)(2J(J1)-J(2JQ++

= (1.83)

Theo cong thc (1.83), neu spin hat nhan J = 0 hay J =2

1 th momen t cc

ngoai Q bang 0 ngay ca khi momen t cc noi Qo khac khong. ieu nay c giaithch nh sau. Do cac thang giang lng t, truc oi xng cua hat nhan khi spin

bang 0 hay2

1nh hng ngau nhien, do o phan bo ien tch trong he toa o

phong th nghiem tr thanh oi xng cau.

1.6.2. Xac nh thc nghiem cac momen t cc

1.6.2.1. Momen t cc ngoai Q

Momen t cc ngoai Q c xac nh theo phng phap nghien cu cautruc sieu tinh te cua cac pho quang hoc giong nh a dung e o momen t. Tngtac cua momen t cc vi ien trng cua cac electron nguyen t lam xuat hiencac vach sieu tinh te bo sung khong tuan theo quy tac khoang cach (1.76) khi tachcau truc sieu tinh te do momen t. Chnh cac vach sieu tinh te mi nay cho phepxac nh momen t cc ien ngoai Q. oi vi deutron th Q = 0,00282.10-24 cm2.S ton tai momen t cc ien hat nhan n gian nhat nay, ch co mot proton, chothay rang ham so mieu ta s chuyen ong cua cac hat trong deutron khong hoantoan oi xng cau. Gia tr Q = 0,00282.10-24 cm2 tng ng vi o pha tron 4%trang thai d, tc la deutron nam trang thai s (l = 0) 96% thi gian va trang thai


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d (l = 2) 4% thi gian. Tren bang 1.7 dan ra ket qua o ac momen t cc ngoaicua mot so hat nhan.

Bang 1.7. Momen t cc ngoai Q cua mot so hat nhan.

Hatnhan

Q10-24 cm2

Hatnhan

Q10-24 cm2

Hatnhan

Q10-24 cm2

Hatnhan

Q10-24 cm2

1H2 0,00273 16S33 -0,064 37Rb85 0,29 72Hf179 35B11 0,0355 16S35 0,045 41Nb93 -0,3 73Ta181 67N14 0,0071 27Co59 0,404 56Ba135 0,25 81Bi204 -0,198O17 -0,027 29Cu63 0,16 59Pr141 -0,054 92U233 3,4

13Al27 0,149 35Br81 0,28 71Lu175 5,9 93Am241 4,9

1.6.2.2. Momen t cc noi Qo

Momen t cc noi Qo khong anh hng en cau truc tinh te cua cac vachquang pho nen c xac nh bang cach khac. e o Q 0 ta dung hien tng kchthch Coulomb cua hat nhan. Khi hat nhan va cham vi hat tch ien, chang hanhat alpha, co the chuyen len trang thai kch thch do tng tac Coulomb. Neu mckch thch la mc quay th so sanh tnh toan l thuyet vi thc nghiem co the suy raQo.

Momen t cc ien la mot thong so quan trong cho them thong tin ve cautruc va cac tnh chat cua hat nhan. Noi rieng, neu gia thuyet rang hat nhan vi

Qo 0 la mot ellipsoid tron xoay vi ien tch phan bo eu th co the bieu th Q oqua cac truc a doc theo z va b vuong goc vi z nh sau:

Qo =5

2(a2 b2)eZ =

5

4 2R eZ (1.84)

Trong o =22

22

ba

ba

+

la o lech tam, 2R =2

ba 22 + la ban knh bnh phng

trung bnh cua hat nhan, eZ la ien tch tong cong cua hat nhan. Thay bnh phngban knh hat nhan R2 vao (1.84), ta nhan c o lech tam cua hat nhan khi bietai lng Qo. Gia tr thong thng kha be, vao c 0,01 0,02. Tuy nhien oi vicac hat nhan nang vi A 150 180 va A > 220 th chung b bien dang ro ret. Cachat nhan nay co gia tr Qo ln c Qo = 0,1 va o lech tam = 0,1 02.

Hnh 1.16 la ng cong thc nghiem trung bnh ve s phu thuoc momen tcc noi cua hat nhan vao so proton Z hay so neutron N = A Z. Hnh nay cho thayxu hng chung ve s tang Qo theo Z hay N, cung nh vai tro ac biet cua cac giatr magic 2, 8, 20, (28), 50, 82, 126 cua Z va N (gia tr 126 ch dung oi vineutron), tai o momen t cc noi Qo = 0. Dang ng cong cung cho thay a socac hat nhan nang co dang cang rat manh trong luc cac hat nhan magic co dangoi xng cau.

T hnh 1.16 thay rang momen t cc noi co gia tr ln c 10 20 lan bnh

phng ban knh hat nhan. Nh vay chung c gay ra bi chuyen ong tap thecua nhieu nucleon trong hat nhan.


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1.7. O CHAN LE

Tnh chan le ac trng cho tnh oi xng cua hat nhan oi vi phep phan xaqua gng. Quy luat bao toan tnh chan le la mot trong cac quy luat bao toan oivi mot he vat l. Quy luat nay ung oi vi tng tac ien t, xac nh cau truccua nguyen t va phan t, lan tng tac hat nhan, xac nh cau truc cua hat nhan.

Trong c hoc lng t, trang thai mot he vi mo c mieu ta bi ham song( rr ) phu thuoc vao toa o cua he nay. Trong phep phan chieu qua gng th

vector toa o bien oi thanh:rr rr = - rr (1.85)Ta goi P la toan t phan xa gng va la gia tr rieng cua no. Khi o phep

bien oi toa o (1.85) dan ti phep bien oi ham so:P ( rr ) = (- rr ) = ( rr ) (1.86)Neu thc hien hai lan phan xa gng lien tiep th he vi mo tr ve trang thai

ban au, ngha laP P ( rr ) = ( rr ) (1.87)T o ta co:P P ( rr ) = P (- rr ) = P ( rr ) = 2( rr ) (1.88)So sanh (1.86) vi (1.87) ta c2 = 1, do o = 1 (1.89)Ta goi la o chan le cua he vi mo.ng vi gia tr = 1 th ham song ( r

r ) mieu ta trang thai vi mo khong oidau trong phep phan xa qua gng. Trang thai cua he la trang thai chan, hoactrang thai cua he co o chan le dng.

ng vi gia tr = -1 th ham song ( rr ) mieu ta trang thai vi mo oi dautrong phep phan xa qua gng. Trang thai cua he la trang thai le, hoac trang thaicua he co o chan le am.

Hnh 1.16. S phu thuoccua momen t cc ien noiQ0 vao so N (Z).

Q0/eR2

20

1510

5

0

-5

0 10 20 30 40 50 60 70 80 90 100 120 140 N(Z)

2 8 20 50 82 126


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lng khac nhau chut t, do o tng ng vi hai mc nang lng gan nhau. Ta cothe so sanh tnh chat nay vi tnh chat cua electron trong nguyen t. Neu khong ey en spin th moi trang thai electron trong nguyen t tng ng vi cung mot mcnang lng, con neu e y en spin th mc nang lng o tach thanh hai mc gan

nhau, tng ng vi hai trang thai cua electron khac nhau ve s nh hng cuaspin la sz = + h

2

1 va sz = h2

1 . oi vi nucleon, e tien tnh toan, ngi ta a ra

mot ai lng goi la spin ong v T. Neu he co spin ong v T th he se co 2T + 1trang thai ng vi cac gia tr khac nhau cua hnh chieu spin ong v tren mot truc znao o.

Nh vay khai niem spin ong v cho phep mo ta cac trang thai ien khac

nhau cua cung mot hat. Nucleon co hai trang thai ien, do o 2T + 1 = 2 va T =2

1 .

Proton va neutron la hai trang thai khac nhau cua nucleon ve hnh chieu Tz cua

spin ong v, cu the la proton co Tz = +21 va neutron co Tz =

21 .

Cung tng t, cac hat meson +, o, - co the coi la ba trang thai cuacung mot hat, ngha la 2T + 1 = 3. Do o meson co spin ong v T = 1. Cac hat+, o, - ng vi ba gia tr khac nhau cua hnh chieu spin ong v la 1, 0 va 1.

Ngi ta noi (p,n) tao nen mot bo oi ong v con (+, o, -) tao nen motbo ba ong v.

1.9. CAC LOAI TNG TAC VA LC HAT NHAN

1.9.1. Tong quan ve cac loai tng tac

Vat chat trong t nhien van ong va bien oi eu do chung tng tac vinhau. Co 4 loai tng tac sap xep theo cng o tang dan la tng tac hap dan,tng tac yeu, tng tac ien t va tng tac manh. Chung ta hay lan lt xem xettom tat cac loai tng tac nay.

1.9.1.1. Tng tac hap dan

Tng tac hap dan la tng tac gia hai vat co khoi lng khac khong vatuan theo nh luat hap dan Newton. Theo nh luat nay, hai chat iem khoi lngm1 va m2 cach nhau mot khoang r se hut nhau bi lc hap dan co phng la ngthang noi hai chat iem o va co cng o t le thuan vi hai khoi lng m1 va m2va t le nghch vi khoang cach r:

FG = G 221

rmm

(1.93)

Trong o G = 6,67.10-11 Nm2/kg2 la hang so hap dan vu tru.

1.9.1.2. Tng tac yeu


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Tng tac yeu bao gom cac qua trnh phan ra cac hat c ban hadron, hapthu meson bi cac chat va qua trnh co s tham gia cua hat neutrino. Cac hathadron gom cac nucleon, va K meson va cac hat , , . V du, cac qua trnhtng tac yeu la:

p n + e

+

+e (Phan ra +

)n p + e + e (Phan ra -) (1.94)Tng tac yeu co cng o ln hn tng tac hap dan nhng be hn tng

tac ien t. Ban knh tac dung cua tng tac yeu c xem la bang khong. Thigian ac trng la 10-10 s, tr phan ra neutron vi thi gian ac trng c 11,7 phut.Di tac dung cua tng tac yeu khong tao c cac trang thai lien ket cua cachat, do o no ch bieu hien chu yeu cac qua trnh phan ra hat nh a neu trong(1.94).

1.9.1.3. Tng tac ien t

Tng tac ien t la tng tac gia photon va cac hat mang ien. Mot trongcac hnh thc pho bien cua tng tac ien t la tng tac gia hai ien tch iemtuan theo nh luat Coulomb. Theo nh luat nay, hai ien tch iem vi ien tchq1 va q2 nam cach nhau mot khoang r trong chan khong tng tac vi nhau bi lcco phng nam tren ng thang noi hai ien tch, co chieu ay ra xa nhau khi cacien tch cung dau hoac hut lai gan nhau khi cac ien tch khac dau, co o ln t levi tch so q1 va q2 va t le nghch vi bnh phng khoang cach r:

FC = k 221

r

qq(1.95)

Trong o k = 9.109 Nm2/C2.Ban knh tac dung cua tng tac Coulomb la vo cung. Ve mat hnh thc th

tng tac ien t va tng tac hap dan giong nhau. S khac nhau gia chung chotng tac ien t co the hut nhau hoac ay nhau con tng tac hap dan luon luonhut nhau. Ve cng o tng tac th tng tac ien t co cng o ln hn nhieu sovi tng tac hap dan.

Nh a nh ngha, tng tac ien t la cac tng tac co s tham gia cuaphoton. Trong tng tac gia hai ien tch noi tren, phng tien truyen tng tac laphoton. Cac qua trnh khac co photon tham gia cung eu la tng tac ien t, nh

qua trnh nguyen t phat xa va hap thu anh sanh hay tia Roenghen, hay cac quatrnh:

e+ + e- 2 (Qua trnh huy cap)+ hat nhan e+ + e- (Qua trnh sinh cap) (1.96)

1.9.1.4. Tng tac manh

Tng tac manh co cng o ln nhat trong bon loai tng tac. Tng tacmanh la tng tac gia cac hat c ban hadron vi nhau, tr qua trnh phan ra

chung. Cac hat hadron gom cac nucleon, va K meson va cac hat , , . Noirieng, tng tac gia cac nucleon e gan chung lai vi nhau trong hat nhan thuoc


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loai tng tac manh. Thi gian ac trng cua tng tac nay vao c 10-23 s va banknh tac dung vao c 10-13 cm. Phng tien truyen tng tac manh la cac meson.V du, cac qua trnh tng tac manh sau ay:

p + n n + + + n n + p

n + p p + -

+ p p + nn + n n + o + n n + n (1.97)p + p p + o + p p + pSo sanh cng o gia bon loai tng tac c the hien tren bang 1.8.

Bang 1.8. So sanh cng o gia bon loai tng tac.

Loai tng tac Manh ien t Yeu Hap danCng o

(tng oi)1

137

1 10-14 10-39

1.9.2. Cac tnh chat cua lc hat nhan

Tng tac hat nhan thong qua lc hat nhan. Sau ay la tom tat cac tnh chatcua lc hat nhan.

a) Lc hat nhan co cng o rat ln. Tng tac hat nhan la tng tac manh.V du, nang lng lien ket do lc hat nhan gay ra oi vi hat nhan deutron bang2,23 MeV, trong khi nang lng lien ket do lc ien t gay ra oi vi hydrogen

bang 13,6 eV.b) Lc hat nhan co tam tac dung ngan c fermi, tc la c 10-13 cm. ieunay suy ra t th nghiem cua Rutherford ve tan xa cua hat alpha tren hat nhan.

c) Lc hat nhan co tnh boa hoa, moi nucleon trong hat nhan ch tng tacvi mot so nucleon quanh no ma thoi. ieu nay the hien nang lng lien kettrung bnh tren nucleon hau nh giong nhau oi vi cac hat nhan khac nhau.

d) Lc hat nhan co tnh oc lap ien tch. Trong cac th nghiem ve tan xanucleon-nucleon, bao gom tan xa n-n, n-p, p-p, sau khi loai bo phan tng tacCoulomb trong tan xa p-p, ngi ta thay co s ong nhat ve dang ieu tan xa cuaba qua trnh tren. Do do ve phng dien lc hat nhan th ba qua trnh tng tac (n-n), (n-p) va (p-p) la nh nhau.

e) Lc hat nhan phu thuoc vao spin hat nhan, tc la phu thuoc vao s nhhng tng oi gia spin cua cac nucleon. ieu nay the hien trong tan xaneutron-proton nang lng thap.

f) Lc hat nhan khong oi xng tam, tc la co tnh chat tensor. ieu o congha la phng cua lc tac dung tng ho gia hai nucleon khong trung viphng noi hai nucleon o. Khi o lc hat nhan khong bao toan momen quy ao.Tnh khong xuyen tam cua lc hat nhan suy t s co mat cua momen t cc iencua deutron.


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g) Lc hat nhan co tnh trao oi. Khi va cham nhau, cac nucleon trao oivi nhau ien tch, hnh chieu spin, . . . Tnh chat trao oi nay suy ra t cac thnghiem tan xa neutron nang lng cao len proton.

h) Lc hat nhan co loi ay manh, tc la khi at en khoang cach u nho,

lc hat nhan khong hut cac nucleon lai na ma tr thanh ay chung vi cng oln. Loi ay bat au xuat hien khoang cach c 0,5 fermi, tc la c 0,5.10-13 cm.i) Lc hat nhan co the phu thuoc manh vao van toc cac hat va cham.j) Co the ton tai trong lc hat nhan loai lc nhieu hat, trong o chu yeu la

loai lc ba hat. Loai lc nay ch ton tai khi ba hat gan nhau va se triet tieu khimot trong ba hat o chuyen ra xa vo han.

1.10. BAI TAP

1.10.1. Cac bai tap v du

V du 1.1. Tnh nang lng, tan so va bc song cua bc xa anh sang dayLyman khi nguyen t hydrogen chuyen t mc kch thch L xuong mc c ban K.

Bai giai. Mc L va mc K ng vi n2 = 2 va n1 = 1. Theo cong thc (1.8),nang lng anh sang bang:

E = h = Wn2 Wn1 = Rh

22 2

1

1

1 =4

3 Rh

Thay R = 3,27.1015 s-1 va h = 6,625.10-34 J.s vao cong thc tren ta cnang lng E = 16,25.10-19 J. Do 1 eV = 1,6.10-19 J nen E = 10,2 eV.

Tan so anh sang bang =43 R = 2,4525.1015 s-1.

Bc song anh sang tng ng la =

c =R3

c4 = 0,1223 m.

V du 1.2. Xac nh so trang thai electron trong nguyen t thuoc lpn (n = 3 va n = 4) co cung nhng so lng t sau ay:

a. Cung msb. Cung ml = 1c. Cung ml = -1 va ms = - 1/2

Bai giai.a) Cung ms : Do ms co nh nen cac trang thai electron khac nhau bi ba so

n, l va ml. Vi n xac nh th l = 0, 1, 2, . . . , n -1 va vi l xac nh th ml = 0, 1, 2, . . . ., l. Vay vi n xac nh va ms co nh th so trang thai electron la:

=

+1

0

)12(n

l

l = n2

Khi n = 3 th n2 = 9 va khi n = 4 th n2 = 16.b) Cung m1 = 1: Khi n va ml xac nh th l = ml, ml + 1, . . . , n 1.

Nh vay ta co n - ml trang thai cua electron khac nhau bi cac gia tr cua l va

ket qua co 2(n - ml) trang thai electron khac nhau bi cac gia tr l va ms.Vi ml = 1 va n = 3 th ta co 2(n - ml) = 2(3 1) = 4


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Vi ml = 1 va n = 4 th ta co 2(n - ml) = 2(4 1) = 6c) Cung ml = -1 va ms = - 1/2: Vi n, ml va ms xac nh ta co n - ml trang

thai electron khac nhau bi cac gia tr cua l. Do oVi n = 3 va ml = -1 th n - ml = 3 1 = 2

Vi n = 4 va ml = -1 th n - ml = 4 1 = 3.V du 1.3. Tm so bo chnh Rydberg oi vi so hang 3P cua nguyen t Na

biet rang the kch thch oi vi trang thai th nhat bang 2,10 V va nang lng lienket cua electron hoa tr trang thai 3S bang 5,14 V.

Bai giai.oi vi nguyen t Na th electron hoa tr thuoc lp M vi n = 3. Trang thai

c ban la 3s ng vi mc nang lng 3S. Trang thai kch thch th nhat la 3p ngvi mc nang lng 3P.

Mc nang lng trang thai

nl theo cong thc (1.9) la:

( )2n

n

RhW

l

l

+=

Do o cac mc nang lng

3S va 3P la( )2s

s33

RhW

+= va

( )2pp3 3Rh

W += . T hnh 1.18 ta co hai phng trnh:

h = W3p - W3s =( )2s3

Rh

+-

( )2p3Rh

+= 2,10 eV

( )2ss3

3

RhW

+= = - 5,14 eV

T o ta co:( )2p3

Rh

+= 3,04 eV hay p =

3,04

Rh - 3

Thay so: R = 3,27.1015 s-1 ; h = 6,625.10-34 J.s va 1 eV = 1,6.10-19 J ta cp = 2,109 3 = - 0,891.

V du 1.4. Chng minh rang nang lng lien ket cua hat nhan vi so khoilng A va ien tch Z c xac nh bi cong thc:

Elk = ZH + (A Z) n - Trong o H, n, la phan d khoi lng (M A) cua nguyen t hydrogen,

neutron va nguyen t tng ng. S dung cong thc nay e tnh nang lng lienket tren mot nucleon trong cac hat nhan Li6, Ar40, Ag107 va Pb208 (xem bang cac

gia tr = M A trong Phu luc 2).

3D

3P

3S

h = 2,10 eV

W3p

W3s = 5,14 eV

Hnh 1.18


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Bai giai.Theo nh ngha nang lng lien ket ta co:Elk = ZmH + (A Z)mn MTrong o mH, mn va M la khoi lng nguyen t hydrogen, neutron va

nguyen t tng ng. Do H = mp 1, n = mn 1 va = M A nen:Elk = Z(1 + H)+ (A Z)(1 + n) MElk = ZH + (A Z) n (A M) = ZH + (A Z) n - Nang lng lien ket cua hat nhan 3Li6: Z = 3 ; A = 6T Phu luc 2 ta co: H = 0,007825 u ; n = 0,008665 u ; Li6 = 0,015126 u;

u = 931,44 MeVElk = 3 0,007825 u + 3 0,008665 u - 0,015126 u = 0,034344 u

= 0,034344 931,44 MeV = 31,99 MeVNang lng lien ket tren mot nucleon la: = Elk/A = 5,33 MeV

Nang lng lien ket cua hat nhan 18Ar40:Z = 18 ; A = 40 ; Ar 40 = - 0,037615 uCung tnh tng t nh oi vi Li6, ta co: Elk = 346,79 MeV; = 8,60 MeV Nang lng lien ket cua hat nhan 47Ag107:Z = 47 ; A = 107; Ag107 = - 0,09303 uCung tnh tng t nh oi vi Li6, ta co: Elk = 913,47 MeV; = 8,55 MeV Nang lng lien ket cua hat nhan 82Pb208:Z = 82 ; A = 208; Pb208 = - 0,02336 uCung tnh tng t nh oi vi Li6, ta co: Elk = 1636,35 MeV; = 7,87 MeV

V du 1.5. Cac mc c ban cua cac nguyen t sau ay co bao nhieu thanhphan cau truc sieu tinh te: H3(2S1/2); Li6(2S1/2); Be9(1So); N15(4S3/2); Cl35(2P3/2).Trong dau ngoac la mc c ban cua lp vo electron cua nguyen t.

Bai giai.

H3(2S1/2): Momen toan phan cua lp vo nguyen t la I =2

1 ; spin hat nhan

H3, theo Phu luc 2, la J =2

1. Do I = J nen so thanh phan cau truc sieu tinh te la

2I + 1 = 2J + 1 = 2 21 + 1 = 2.

Li6(2S1/2): Momen toan phan cua lp vo nguyen t la I =2

1 ; spin hat nhan

Li6, theo Phu luc 2, la J = 1. Do I < J nen so thanh phan cau truc sieu tinh te la

2I + 1 = 2 2

1+ 1 = 2.

Be9(1So): Momen toan phan cua lp vo nguyen t la I = 0; spin hat nhan

Be9, theo Phu luc 2, la J =

2

3 . Do I < J nen so thanh phan cau truc sieu tinh te la

2I + 1 = 2 0 + 1 = 1.


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N15(4S3/2): Momen toan phan cua lp vo nguyen t la I =2

3 ; spin hat nhan

N15, theo Phu luc 2, la J =2

1. Do J < I nen so thanh phan cau truc sieu tinh te la

2J + 1 = 2 21

+ 1 = 2.

Cl35(2P3/2): Momen toan phan cua lp vo nguyen t la I =2

3 ; spin hat nhan

Cl35, theo Phu luc 2, la J =2

3. Do I = J nen so thanh phan cau truc sieu tinh te la

2I + 1 = 2J + 1 = 2 2

3 + 1 = 4.

V du 1.6. T so cng o cac thanh phan tach sieu tinh te cua vach pho

2P1/22S1/2 cua sodium gan bang6

10 . Chu y rang cau truc sieu tinh te gay nen do

viec tach mc 2S1/2 (co the bo qua viec tach mc 2P1/2). Hay tnh spin hat nhanNa23.

Bai giai. Hnh 1.19minh hoa s o tach vach pho thanh hai vach pho 1 va 2.Mc 2P1/2 coi nh khong tachcon mc 2S1/2 tach thanh haimc con vi:

F1 = J I = J 2

1

F2 = J + I = J +2

1

Vay ta co hai vach pho mi 1 va 2. Cng o cac vach pho nay t le vitrong so thong ke cua cac mc tng ng, ngha la vach 1 ng vi trong so thongke 2F1 + 1 va 2 ng vi trong so thong ke 2F2 + 1. Nh vay:

6

10

1F2

1F2

1

2 =+

+hay

6

10

J2

2J2

12)/12(J

12)/12(J=

+=

+++ . T o ta co J =

2

3 .

V du 1.7. Cac mc nang lng F11/2 va F9/2 cua nguyen t 27Co59 eu tachthanh 8 mc phu. Hay xac nh spin hat nhan 27Co59 va s o tach vach quang phovi bc song = 4234 Ao cua chuyen mc F11/2 F9/2.

Bai giai.a. Xac nh spin hat nhan: mc nang lng F11/2 electron co momen quy

ao l = 3 va momen toan phan I =2

11 . Cung nh vay, electron mc F9/2 co

l = 3 va I =2

9 . Moi mc nang lng F11/2 va F9/2 eu tach thanh 8 mc phu. Do oi

2P1/2

2S1/2

21 F1 = J 1/2

F2 = J + 1/2

Hnh 1.19


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vi hai mc o, 2I + 1 bang 12 va 10, tc la ln hn 8, nen 8 mc phu la do spin

hat nhan quyet nh. Nh vay 2J + 1 = 8 va spin cua hat nhan 27Co59 J =2

7 .

b. Tach sieu tinh te: Vach quang pho vi bc song = 4234 Ao c tach

thanh mot so vach phu do s chuyen mc t 8 mc phu cua mc F11/2 xuong 8 mcphu cua mc F9/2. Khi o 8 mc phu cua mc F11/2 co 8 gia tr F1 = I1 J, I1 J + 1,

I1 J + 2, . . ., I1 + J (2, 3, 4, 5, 6, 7, 8, 9) trong o I 1 =2

11 va J =2

7 va 8 mc phu

cua mc F9/2 co 8 gia tr F2 = I2 J, I2 J + 1, I2 J + 2, . . ., I2 + J (1, 2, 3, 4, 5, 6,

7, 8) trong o I2 =2

9 va J =2

7 , nh the hien tren hnh 1.20. Viec chuyen mc t

mot trong cac mc phu F1 xuong mot trong cac mc phu F2 tuan theo quy tac lachon sau F = F2 F1 = 0, 1. Ket qua tach sieu tinh te cho 21 vach phu c thehien tren hnh 1.20.

1.10.2. Cac bai tap t giai

1.1. Nang lng lien ket cua electron hoa tr trong nguyen t lithium trang thai 2s bang 5,59 eV; trang thai 2p bang 3,54 eV. Tnh cac so bo chnhRydberg oi vi cac mc nang lng s va p cua lithium.

1.2. Tm bc song cua cac bc xa phat ra khi nguyen t lithium chuyentrang thai t 3s xuong 2s. Cho biet cac so bo chnh Rydberg oi vi nguyen tlithium la s = - 0,41 ; p = - 0,04.

F123456789

F212345678

=4234

F11/2

F9/2

Hnh 1.20


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1.3. Hay xac nh nhng trang thai nang lng co the chuyen ve trang thaing vi n = 3 oi vi electron hoa tr trong nguyen t Na. Khi xet co chu y en caspin.

1.4. Lp ng vi n = 3 cha ay electron, trong so o co bao nhieu electron:

a) Co cung ms = 21 b) Co cung m = 1c) Co cung m = -2

d) Co cung ms = -2

1va m = 0

e) Co cung ms =2

1 va l = 2

1.5. Hay anh gia mat o vat chat hat nhan, nong o cac nucleon va mat oien tch trong hat nhan.

1.6. Tm nang lng lien ket cua neutron va alpha trong hat nhan Ne 21.1.7. Xac nh nang lng can thiet e tach hat nhan O16 thanh bon hat nhan

giong nhau.1.8. Tm nang lng kch thch cua hat nhan Pb207 khi hat nhan Pb206 bat

neutron nhiet.1.9. Dung cong thc Weizsacker ve nang lng lien ket e tnh:a) Nang lng lien ket cua cac hat nhan Ca40 va Ag107.b) Nang lng lien ket cua mot nucleon trong cac hat nhan V50 va Hg200.c) Khoi lng cac hat nhan Sc45 va Zn70.

1.10. Hay xac nh spin hat nhan Co59

vi mc c ban cua nguyen t4

F9/2cha 8 thanh phan cau truc sieu tinh te.1.11. Hay xac nh so thanh phan tach sieu tinh te cua vach quang pho

2P1/22S1/2 oi vi nguyen t K39. Cho biet spin hat nhan K39 la J =2

3 .

1.12. Mc 2D3/2 cua hat nhan Bi209 co 4 mc con, ong thi t so cac khoangcach gia cac mc canh nhau bang 4:5:6. Nh quy tac khoang cach hay tm spinhat nhan Bi209 va so cac thanh phan tach sieu tinh te cua vach quang pho2P1/22D3/2.


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Chng 2

CAC MAU HAT NHAN

2.1. S CAN THIET CUA CAC MAU HAT NHAN

2.1.1. L do xuat hien cac mau hat nhan

Cac van e lien quan en l thuyet hat nhan co the phan thanh hai loai lacau truc hat nhan va phan ng hat nhan. Tuy nhien, khi xay dng l thuyet hatnhan ta vap phai 3 kho khan chnh la:

a). Khong biet chnh xac ve lc tng tac gia cac nucleon trong hat nhan.e xay dng l thuyet hat nhan chung ta thng ap dung mo hnh cau truc nguyen

t cho cau truc hat nhan. Tuy nhien viec ap dung nay thieu chnh xac v lc tngtac cua cac electron trong nguyen t c xac nh la tng tac tnh ien, cac ketqua tnh toan kha phu hp vi thc nghiem. Trong luc o l thuyet nh lng velc tng tac gia cac nucleon van cha xay dng c, ac biet la lc hat nhan lalc tac dung ngan. Do o viec mieu ta s tng tac gia hai nucleon gap rat nhieukho khan, ma trong thc te hat nhan la mot he lng t nhieu hat va ta phai mieuta qua trnh tng tac nhieu hat o cua hat nhan.

b) So lng cac phng trnh mieu ta s chuyen ong cua cac nucleon tronghat nhan rat ln. Gia s ta biet c chnh xac lc tng tac gia cac nucleon thcung con mot van e kho khan la viec giai bai toan lng t ve he nhieu hat. That

vay, mot he thong gom A nucleon c mieu ta bi ham song )r,...r,r( A21...mmm A21 rrr phu thuoc vao 3A toa o khong gian A21 r,...r,r

rrrva A ch so spin m1, m2, . . . mA, ma

moi ch so co hai gia tr theo hai nh hng spin cua nucleon. Nh vay phngtrnh Schrdinger oi vi hat nhan gom A = 100 nucleon th se la he phng trnhvi phan oi vi 2100 1030 ham so cua 300 bien so. Mot bai toan nh vay khongthe giai c trong thc te.

c) Khong the quan niem hat nhan nh mot moi trng v mo lien tuc. Tronghe thong vi mot so be cac hat, chung ta can nghien cu tat ca cac bac t do khad. Trong he thong rat nhieu hat ta khong lam nh vay ma phai lay trung bnh

thong ke bang cach mieu ta he bang mot so khong ln cac thong so v mo nh apsuat, nhiet o, mat o, . . . Hat nhan khong thuoc ve hai he thong noi tren ma nam trung gian gia hai thai cc o. So hat nucleon trong hat nhan qua ln khi nghiencu tat ca cac bac t do kha d, nhng lai khong u ln e coi nh mot moi trnglien tuc. That vay, khai niem ve moi trng lien tuc khong nhng coi toan bo vatcha mot lng rat ln cac hat ma mot yeu to the tch vo cung nho cua no cungphai cha mot lng rat ln cac hat. Yeu cau nay ro rang khong ap ng c oivi hat nhan v no ch cha cao lam la vai tram nucleon. Tuy nhien ngi ta sdung mo hnh moi trng lien tuc trong mot vai trng hp coi hat nhan nh giot

chat long hay mot vat ran, khi o can phai than trong.


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e tranh cac kho khan tren ngi ta phai xay dng cac mau hat nhan, trongo hat nhan c thay bang mot he vat l nao o co kha nang mieu ta cac tnh chatcua hat nhan vi cach giai thch toan hoc n gian co the chap nhan c. Mauhat nhan can giai thch c cac tnh chat c ban cua cac trang thai hat nhan nh

spin, o chan le, momen t, momen t cc ien, cac tnh chat cua cac trang thaikch thch , ma trc tien la pho kch thch cua hat nhan, va cac tnh chat ong lchoc cua hat nhan nh xac suat phong gamma cua cac mc kch thch cua hat nhan.Moi mau hat nhan ch giai thch c mot so tnh chat cua hat nhan, do o conhieu mau hat nhan khac nhau.

2.1.2. Phan loai cac mau hat nhan

C s e xay dng mau hat nhan la gia thuyet ve s oc lap cua mot taphp nao o cac bac t do cua hat nhan. Cac bac t do cua hat nhan c chia

thanh hai loai la bac t do mot hat, mieu ta s chuyen ong cua cac hat rieng biet,va bac t do tap the, mieu ta s chuyen ong cua mot so ln hat. Mot cach tngng, mau hat nhan cung c phan thanh hai loai la mau tap the va mau mot hat,ngoai ra con co mau suy rong, la tong hp cua hai mau noi tren.

2.1.2.1. Mau tap the

Mau tap the la mau da tren cac bac t do tap the cua nhieu hat va conc goi la mau tng tac manh gia cac hat. Mau nay the hien cac hieu ng tap

the trong hat nhan khi quang ng t do cua cac hat trong hat nhan rat be so vikch thc hat nhan. ieu o cung tng ng vi khai niem cho rang cac hatben trong hat nhan tng tac manh vi nhau va vi mot so t cac hat ben canh. Viy ngha o mau tap the coi hat nhan nh mot giot chat long hay mot vat ran. Mautap the gom mau giot chat long va mau hat nhan khong co dang hnh cau.

2.1.2.2. Mau mot hat

Mau mot hat da tren cac bac t do cua mot hat va c goi la mau cac hatoc lap. Trong mau nay quang ng t do cua cac hat ln hn kch thc hat

nhan, tc la mot hat chuyen ong oc lap trong mot trng the trung bnh nao o.Mau mot hat gom mau vo khong co tng tac dva mau vo co tnh en hieu ngcap.

2.1.2.3. Mau suy rong

Mau suy rong tnh en cac tnh chat chuyen ong oc lap lan tnh chatchuyen ong tap the cua cac hat trong hat nhan. Mau nay gom mau suy rong vilien ket yeu va mau suy rong vi lien ket manh.

2.2. MAU GIOT CHAT LONG


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2.2.1. C s xay dng mau giot chat long

Mau giot chat long cua hat nhan c xay dng tren c s giong nhau gia

hat nhan va giot chat long. o la:a) Tnh khong chu nen cua hat nhan va giot chat long. Theo cong thc(1.48) th mat o hat nhan khong phu thuoc so khoi lng A, tc la khong phuthuoc vao kch thc hat nhan, va bang c 1014 g/cm3. Giot chat long tuy co mat obe hn nhng cung khong phu thuoc vao kch thc cua no. o la tnh khong chunen cua hat nhan va giot chat long.

b) Tnh bao hoa cua cac lc tng tac. Nang lng lien ket trung bnh trenmot nucleon tuy co thay oi theo so khoi lng A nhng dao ong trong khoang t7,4 MeV en 8,6 MeV, vi gia tr trung bnh khoang 7,6 MeV. ieu o cho thaymot nucleon trong hat nhan khong tng tac vi tat ca cac nucleon con lai ma ch

tng tac vi mot so hu han cac nucleon gan no. Hien tng nay xuat phat ttnh bao hoa cua lc hat nhan. Giot chat long cung co tnh chat tng t. Trongmot giot chat long cac phan t tng tac vi nhau bang cac lc tac dung gan, nghala moi phan t ch tac dung vi mot so phan t gan no. Cac phan t nam tren bemat cua giot chat long ch lien ket mot pha vi cac phan t khac. V vay pha conlai se tao nen mot sc cang be mat.

Da vao cac ac tnh giong nhau o ma N. Bohr va J. Frenkel a xay dngmau giot chat long. Mau giot chat long coi hat nhan la mot giot chat long mangien tch va khong nen c. Cac phan t tao nen hat nhan la cac nucleon, chung

tng tac vi cac nucleon ben canh. Nang lng lien ket cua hat nhan gom nanglng the tch, nang lng be mat va nang lng Coulomb, tng ng vi 3 sohang au trong cong thc ban thc nghiem Weizsacker (1.60). Pham vi ng dungcua mau giot chat long la mieu ta nang lng lien ket trung bnh cua hat nhan laham cua A va Z, khao sat cac dao ong be mat cua cac hat nhan hnh cau va giaithch nh tnh qua trnh phan hach hat nhan.

Trong muc nay trnh bay viec ng dung cua mau giot chat long e mieu tanang lng lien ket cua hat nhan, khoi lng hat nhan, cac dao ong be mat cuahat nhan, con viec giai thch nh tnh c che phan ng phan hach hat nhan sec e cap trong chng 3, muc 3.5.

2.2.2. Nang lng lien ket cua hat nhan

Trong chng 1 chung ta a xem xet nang lng lien ket cua hat nhan, thehien trong cong thc ban thc nghiem Weizsacker. Cong thc nay c viet lainh sau:

Elk(A,Z) = A - A2/3 - 3/12

A

Z -A

1Z

2

A

2

+ Elk (2.1)

Nh a noi tren, ba so hang au cua cong thc (2.1) co the giai thch tren

c s mau giot chat long.


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cua parabole co khoi lng ln hn M(Zo) nen phan ra + e chuyen ve hat nhannay. Hat nhan ong khoi vi Z = Zo 1 nhanh ben trai cua parabole cung cokhoi lng ln hn M(Zo) va phan ra - e chuyen ve hat nhan ben. Cung tngt nh vay, hat nhan (A, Zo + 2) phan ra + e chuyen ve hat nhan (A, Zo + 1) va

hat nhan (A, Zo 2) phan ra -

e chuyen ve hat nhan (A, Zo 1). V du vi A =25 th Zo = 12, o la hat nhan ben 12Mg25; vi A = 43 th Zo = 20, o la hat nhanben 20Ca43, . . .

oi vi hat nhan ong khoi vi A chan, khoi lng M(Z) la ham lng trv so hang Elk trong cong thc (1.61) nhan hai gia tr khac nhau oi vi cac hatnhan chan-chan va le-le. Khi o khoi lng M khi A khong oi c mieu ta bihai ng parabole the hien tren hnh 2.2.

Tren hnh 2.2a, ng parabole di ng vi cac hat nhan ben hn, o lacac hat nhan vi Z chan, con ng parabole tren ng vi cac hat nhan kem benhn, o la cac hat nhan vi Z le. T hnh 2.2a thay rang cac hat nhan canh nhau

tren cung mot parabole khac nhau ve Z en 2 n v va ton tai mot vai hat nhanben oi vi cac hat nhan ong khoi chan-chan. o la do s chuyen oi hat nhan

e-

e-

e+

e+

A = const

(Le)

Zo-3 Zo-2 Zo-1 Zo Zo+1 Zo+2

M

Hnh 2.1. Cac hat nhanong khoi vi A le. Cac hatnhan phan ra va + echuyen ve hat nhan bennhat co khoi lng be nhatng vi ien tch Zo.

e-

e+

e+

e+

Zo-4 Zo-2 Zo Zo+2 Zo+4

M

e-

e-

A = const(Chan)

Hnh 2.2. Cac hat nhan ong khoi vi A chan. Hnh 2.2a ng vi cachat nhan le-le khong ben con cac hat nhan chan-chan ben. Hnh 2.2bng vi cac hat nhan le-le ben con cac hat nhan chan-chan khong ben.

Z le

Z chan

e- e+

Zo-2 Zo-1 Zo Zo+1 Zo+2

M

A = const(Chan)

Z le

Z chan


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vi ien tch Zo + 2 hay Zo 2 thanh hat nhan vi ien tch Zo +1 hay Zo 1 b camve mat nang lng con s chuyen oi trc tiep bang phan ra kep t hat nhanZo + 2 hay Zo 2 sang hat nhan Z0 co xac suat rat be, coi nh khong the xay ra.Mat khac moi hat nhan tren parabole tren co hai hat nhan nhe hn vi ien tch

cach 1 nam parabole di nen tat ca hat nhan ong khoi le-le eu khong ben,tr bon hat nhan 1H2, 3Li6, 5B10 va 7N14.Bon hat nhan nay thuoc trng hp c minh hoa tren hnh 2.2b, khi o

hat nhan le-le ben con hat nhan chan-chan khong ben. V du vi hat nhan le-le7N14 do cac hat nhan chan-chan 6C14va 8O14 chuyen thanh.

2.2.4. Cac dao ong be mat cua hat nhan hnh cau

Ta hay xem xet s kch thch cac bac t do kha d cua giot chat long hatnhan. Trong trang thai t do, ngha la khong b kch thch, giot chat long co dang

hnh cau. trang thai kch thch, giot chat long khong b nen nhng co the thay oidang hnh hoc, do o cac bac t do b kch thch se tng ng vi cac dao ong bemat.

L thuyet phi lng t cua cac dao ong be be mat cua giot chat long t doa phat trien trc khi co l thuyet lng t. Theo l thuyet nay th tan so thap nhatquad ng vi cac dao ong rieng t cc, khi o giot chat long co dang hnhellipsoid cang hay det (hnh 2.3b). Tan so cao hn oct ng vi cac dao ong batcc, khi o giot chat long co dang hnh qua le (hnh 2.3c). Cac dao ong riengkhac tng ng vi cac bien dang phc tap hn va co tan so cao hn.

Khi chuyen sang l thuyet lng t th cac dao ong rieng cua hat nhan

c lng t hoa. Viec lng t hoa khong lam thay oi cac tan so rieng nhngcac pho nang lng va momen ong lng cua cac trang thai dao ong kch thchtr thanh gian oan. Khi o cac nang lng dao ong t cc va bat cc nhan cacgia tr sau:

Equad = hquadnquad ; Eoct = hoctnoct (2.4)Trong o nquad va noct la so cac lng t t cc va bat cc, ong thi nquad,

noct = 1, 2, . . . Moi lng t t cc co spin J = 2 va o chan le dng, con moilng t bat cc co spin J = 3 va o chan le am. S dung cong thc Weizsacker(1.60) co the tnh c nang lng cua lng t t cc bang:

hquad 30A-1/2

MeV (2.5)

Hnh 2.3. Giot chat longco dang hnh cau (hnha). Dao ong t cc(hnh b) va dao ongbat cc (hnh c) cuagiot chat long. a) b) c)


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Lng t bat cc co nang lng c hai lan nang lng lng t t cc vicung mot gia tr A. Cac cong thc (2.4) va (2.5) phu hp vi thc nghiem oi vicac mc thap nhat khi nquad = 1, 2 va noct = 1.

Bay gi ta hay xem xet mau giot chat long mieu ta cac mc nang lng

thap nhat nh the nao. Neu mc c ban co ac trng 0

+

th mc kch thch th nhatla mc 2+ co nang lng tnh theo cong thc (2.5). Mc 3- tiep theo se co nanglng gap oi. Gan mc 3- la ba mc nam rat gan nhau tng ng vi trang thaikch thch cua hai lng t t cc vi cac ac trng 0+, 2+ va 4+. Chu y rang khicong hai vector 2

rvi 2

rta c vector tong cong vi cac o ln 0, 1, 2, 3, 4,

nhng cac trang thai 1+ va 3+ b cam do cac lng t kch thch (2.4) tuan theothong ke Bose.

Tien oan ve viec mc kch thch au tien co ac trng 2+ c thc hienhau nh oi vi tat ca cac hat nhan chan-chan. Tuy nhien nang lng cua mc naythap hn gia tr tnh theo cong thc (2.5). Chang han mc 2+ oi vi hat nhan28Ni60 co nang lng 1,3 MeV trong khi tnh toan cho nang lng 3 MeV. ratnhieu hat nhan chan-chan cung thay co bo ba 0+, 2+ va 4+ nam mc nang lngcao hn hai lan so vi mc kch thch au tien (hnh 2.4). Va cuoi cung hau nh tat ca cac hat nhan chan-chan eu co mc 3- c giai thch do kch thch bat cc.

Trong mau giot chat long con co bac t do rieng do dao ong cua toan bokhoi lng cac neutron oi vi toan bo khoi lng cac proton. Vi gia thuyet nayta coi hat nhan gom hai giot chat long neutron va proton tron vi nhau. Khi kchthch bac t do nay, hat nhan tr thanh mot t cc ien, ngha la b phan cc. Kch

thch phan cc ng vi s thay oi cau truc ben trong hat nhan. Do o nang lngkch thch kha ln, c 15-20 MeV oi vi cac hat nhan nang va 20-25 MeV oi vicac hat nhan nhe.

Nh vay mau giot chat long cho phep giai thch nh tnh s phu thuoc nanglng lien ket vao A va Z, dang hnh cau cua a so cac hat nhan cung nh spin vao chan le cua mot so mc kch thch thap cua hat nhan chan-chan. Thieu sotchnh cua mau giot chat long la so pho kch thch t, khong tnh en cac tnh chatrieng biet cua tng hat nhan cung nh khong the giai thch cac momen t cc cuacac trang thai kch thch au tien.

2.2.5. Cac dao ong be mat cua hat nhan khong hnh cau

2+0+4+

2+

0

2,882,542,29

1,33

0

Hnh 2.4. Pho cac mc thap nhatcua hat nhan 28Ni60. Cot so ben

trai: Nang lng (MeV). Cot benphai: Spin va o chan le.


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Nhieu hat nhan co dang khong hnh cau va cac tch chat cua chung cgiai thch tren c s mau khong hnh cau. Nh mau nay co the xac nh c cacmc quay thap va cac mc dao ong cua cac hat nhan chan-chan.

Dang n gian nhat cua hat nhan khong hnh cau la dang ellipsoid vi haithong so va lien he vi cac ban truc R1, R2 va R3 cua ellipsoid nh sau:

R1 = R1 Ro =4

5Rocos(+

3

)

R2 = R2 Ro =4

5Rocos(+

3

2 ) (2.6)

R3 = R3 Ro = -4

5Rocos

Trong o Ro la ban knh trung bnh cua hat nhan. T (2.5) thay rang khi

= 0 th R1 = R2 = R3 = 0, tc la hat nhan co dang hnh cau. Khi = 0 thR1 = R2 < R3, hat nhan co dang ellipsoid cang. Khi =

3

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2.5.Vat Li Hat Nhan-nqhuy