Chap.2 Structure and properties of Atoms

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??? ????????
Chap.2 Structure and properties of Atoms
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2.0 ????????

• 19 ???-??????
• 1)????????????????????,??????????????,???
  ????????
• 2)?????????????????????????????????????,??
  ????????????????
• 3)???????,???????????
• Dalton, 1766-1844, ?????
• ?????????????

?????????????????
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1897-????????(J.J.Thomson,1856-1940)

• ?????????????,?1906??????????
• ??????? ???????
• ???????????,???????????,??????????,?????????????,
  ???????????

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???????(Ernest Rutherford)(1871-1937)
???????

• ?????????????,???????,??????????????,????
  ??,???????,????????????

??????????????????1908?????????
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?????
?????????????????????
????
n1, n2???, n2gtn1, R?Rydberg(???)??
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1913-??????

• 1) ??????????????,??????????????????,???????
  ??????????????????????????
• 2)????????????????,??????????,??????????????
  ?
• 3)?????????

(18851962)
??????,??????????, 1922?????????
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???
????
?????????
???????
a0 Bohr??
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????
???????
???????
?????????????
????????
?????
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??????
4
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??E1?E2
Rydberg?? R
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• ?????????
• ???H?He?Li2?Be3?????
• ?????????
• ???????(?X????)????
• ?????????
• ?????????
• ????????????????
• ??????????????
• ????????????

?Bohr??????????? ????????????????,?????????????
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2.1 ??????Schrödinger ?????

• -1-??????Schrödinger ?????
• ?????????,???????????Schrödinger ??

?????????
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?????????

• ?????????,??????????????,????????????Lap
  lace????????????
• ????????????, ??????????????.

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1.???????????
xrsin?cos? (1) yrsin?sin? (2) zrcos?
(3)
r2x2y2z2 (4) cos?z/(x2y2z2)1/2
(5) tg?y/x (6)
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xrsin?cos? (1) yrsin?sin? (2) zrcos?
(3)
r2x2y2z2 (4) cos?z/(x2y2z2)1/2
(5) tg?y/x (6)
???????
(4)??x???,??(1)???,
(5)?x???,?(3)(1)(4)??,
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??x???,
?(7)(8)(9)??(4),?
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??
?
?????????Schrödinger???
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2. ?????
??????r,?,?????,??????,???????,??-m2,??
?????l(l1),??
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?????

• ? ???????????????,??r?????????????????R??,?????
  ?????,Y(?,?) ?(?)?(?),???????????
• ?????????,?????????,????????,??Schrödinger???
  ??

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3. ?????
?????????????,????????????
A?????????
?m????????,?????, ?m?????,?, ?m(?)
?m(??2?) eim?eim(??2?) eim?eim2? ?
eim2?cosm2??isinm2?1,
m??????m0, ?1, ?2,
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?????
? ????????????z??????????,????????,??????????????
????,?????????????
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• ?????????z??????????,??????
• ?????????????????,?????????????

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4. ?????????
??????R??????,?????????????2?? ???n,l,m???,???nlm?
? ?nlmRnl(r)?lm(?)?m(?
)Rnl(r)Ylm(?,?) ????n1,2,3,,n
????l0,1,2,,n-1 ????m0,?1,?2,,?l ??,?,R,Y,???
???,????????d?r2sin?drd?d?
???????????????s,p,d,f,g,h,????l0,1,2,3,4,5,???
?????????????????????
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2.2 ????????

• ????n??????????
• ???????????n??????Hamilton????????????En???n,?
  ?n?????????En,???R???En????
• ? ??????????(??????????????)

1 2 3 4 5 K L M N O
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• ????n

?H??????E1-13.6eVlt0,?????,????? ?virial
theorem(????)?????rn?????,?????ltVgt?????ltTgt????ltT
gtnltVgt/2. ?H??????r-1??,??ltTgt-ltVgt/2 E1-13.6eV
ltTgtltVgtltVgt/2, ltVgt-27.2eV, ltTgt-ltVgt/213.6eV,??
????
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1. ????l????????????????

????????
?????????
?, ??????
?????????
??????????????

• l ??? 0,1,2,3n-1
• ??? s, p, d, f... (??)
• l ?????????????

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???? l
????????????
??,?????l???,??????????????
??Bohr??, ???????????
???????, l ??E ???l ??,?????

??,????n 2 ?,l ??? 0,1,????????2s, 2p ????,2p
???????2s?
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3. ???? m
????z????????
???????????????????
?, ??????
??
???????????z?????????

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???? m
???? m ????? ???????????z?????,??????????????????
. ??????????
????ml????????????,????????,???2l1???????
?l1,ml ??? 0,?1???????,?px, py, pz??? l2, ml
??? 0,?1 , ?2 ???????,?dxy, dyz, dxz, dx2-y2,
dz2???

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4.?????s???????ms
???????,??????????????s??
s ??????1/2. ????????????????????ms??
??????ms??????? ?1/2. ????????????????????
-??????
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?????
n l m ???????????? n l m mS ???????????????
? ???? n
n1, 2, 3,
? ????
? ???? m
? ?????? ms
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5. ???? j ??????mj
?????????,???????,??????????????,????????j???

?????????????????????mj??
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2.3 ??????????

• ? ???(?,????)????(?2??????)??????????,??????????,
  ????????????????,???????????,???????????????????
• ?-r??2-r?
• ? s???????r??,???????????s??????ns??????????,??r?
  ???????????,?????2???????
• ????????a01,me1,e1,4??01,h/2?1, e2/4??0a01
• H(Z1)???1s?2s??????????????

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??????????
???1s???????????????,?r??????? ???2s??r?2a0?,??
???1s????r2a0?,?0,???????(???n-1)?r?2a0?,????
,?r4a0?,????????r?4a0?,????0? ?1s????2s??????,?
???????????5.4,????94.63s??????,????????????1.5
,?????9.5,??????89.0?
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2. ?????

• ???????D???????????r?????,Ddr?????r?rdr?????????
  ??????

???2(r,?,?)d????????????,??????r,???dr????????????
???(r,?,?)R(r)?(?)?(?)?d?r2sin?drd?d???,??
?s??????r??,??(?)?(?)1/(4?)1/2,?
Dr2R24?r2?s2
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?????(??????r?????)
Dr2R24?r2?s2
?1s????D?0ra0?,D ??????ra0??,???dr????????????
???????????????????????????? ???n?l?????,?n-l?????
n-l-1?D??0??? ?n???l??,??????l??,????,?????????
?l???n??,????????n???????,??? ??????,?????????
,???????????????????
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3. ????????

• ?(????)?r,?,???,???????,??????,??????r,?,??????,??
  ?????????????,??????????????????????,?????????????
  ?
• 2pz????z????2a0?,xy?????(n-1)
• 3pz?2pz????,???6a0???????
• ????????s????????3?p?????????,????????5?d??????
  ??,??dz2?z?????,?2???????,??4?d???????????,???????
  ????

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??????????????????

• (1)????????2??????,??????????,??????
• (2)???????????????????????????????
• (3)??????????????????????,??????1nm??,??????????,
  ??????????(??),???????????(?90,99),?????????????
  ?????????
• (4)????????????????????????????,???????????????(?
  ?),??????????????????,????????,????9??????????-??
  ????

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