원자물리학 원서 38장 무엇을 배우는가 36.1 스펙트럼선 36.2 보어의 원자모형 보기문제 36.1 스펙트럼선 궤도각운동량의 양자화 36.3 보어 모형의 스펙트럼선 수소 전자의 파동함수 구형대칭 해 보기문제 36.2 수소 파동함수의 규격화 각운동량 36.4 완전해 다른 원자들 보기문제 36.3 헬륨 원자의 이온화에너지 36.5 엑스선 생성 레이저 유도방출과 밀도반전 보기문제 36.4 펄스 루비레이저의 광자수 첨단 레이저 연구 무엇을 배웠는가/주요내용 문제풀이 능력 키우기 풀이문제36.1 이가리튬이온의파셴계열 객관식 문제 설명문제 연습문제 그림 36.1 나트륨레이저(거의 수직인 노란색 선)가 하와이 마우나케아 켁 천문대에 있는 망원경의 적응광학계에 필요한 레이저 안내별을 제공하기 위해 밤하늘로 발사되고 있다. 사 진기를 오래 노출시켜 별들이 (극미한) 곡선들로 보인다. 545
546.. n1, 2, 3,..., 0, 1,...,. n1, m,...,......... (). 50,. CD, DVD, BD,,.. ( 36.1 ).....,. 37.,,. 36 37,.. 32. 36.2 ( ). (spectrometer).. 36.3
547...... 19..( 36.3.). 36.2,.,,.... 4, ( 656 nm, H- ), ( 486 nm, H-), (434 nm, H- ), (410 nm, H-)..,19. 36.4. 4,. 4,,,,.( 2000 nm.) 1885... (36.1) 3 (,, ). (Rydberg formula)
548. (36.2) n 1, n 2, R H (Rydberg constant). R H. n 1 1, n 2 2, 3, 4,...,, n 1 2, n 2 3, 4, 5...,. 36.4.? 36.2. n 1 < n 2 1/n 1 2 1/n 2 2. n 1 n 2 1/n 1 2 1/n 2 2 1/. n 2.,, n 2 n 2.. n 2., n 2. n 1 < n 2 n 2, n 1 1.. : : : : H-,
549... 1875 nm, 1458 nm.,, 36.4,...,. 36 37,... () (line spectra)..,......,. d 10 10 m, 10,000... 20,... 1909,. 39 40...9. (21)..
550 (36.3) k8.9875510 9 Nm 2 /C 2. 2... m.,. (reduced mass). (36.4) m9.10938215(45)10 31 kg, M1.672621637(83)10 27 kg, 9.1044210 31 kg. 1836, M/(Mm) 1 1/2000 m. m.. m. (), m.,..... 1913. 1913.10 " L r " p ". ( 2 ). (36.5)? kg m 2 s 1 Js...,.,. (Bohr model of the hydrogen atom), 36.3 r 3
551. 2 v 2 r 2, ( 36.5) n 2 2. r. (36.6) (). n, a 0 (Bohr radius). Å nm. 1Å10 10 m0.1 nm. 36.3, v. n1 0.73%,... (36.7) ( ) (12). E 0. E(n1)13.6 ev, E(n2)-3.40 ev, E(n3)1.51 ev, n 0. 36.6 36.7 EE 0 a 0 /r. 36.5 E r. 36.6 36.7 n E r. m e.
552 a 0,me 5.29210 11 m.... n 2 n 1,. Ehf: E n2 E n1 hf. fc/, c. (36.8) 36.7. 36.2.... a 0 2 /ke 2..,, m( ), e, h(2), c, k.,,. 36.6 (energy-level diagram).
553.. 1923 (36 ) 1926 (37 )., 0 1.,.,37. E n. 36.7, E n 13.6/n 2 ev......,..., U(r " )ke 2 /r. ( ) ( ). 3.37 3. 2 2 " " 2 /x 2 2 /y 2 2 /z 2. 37. 1 2 d 2 /dx 2.. U r. 36.7 r,,. (36.9).. U..
554 (36.10)?.....,. r.. (36.11).,. 1 E 0 k 2 e 4 /2 2 13.6 ev. n. (36.12) n. A 1, A 2, A 3 1. 36.8a, 36.8b r 2.3 na 0. n. n >1, n1.
555 3. (a). (b). (b). n1 36.12 1 (r)a 1 e r/a0. 1 A 1. 1.,. c2/a 0, A 1. n1.
556 37. id/dx,3.. ( ), "... (36.13).( " L r " p ".). (36.14), r.. (36.15) 36.15.,, 0. tr " r rtr. 36.15. 0. trtr0 0.
557., 0. n (r) 0., n...,. 0?...,.... 1. (36.16). 36.9. (, 36.10).
558, 2r 2 / 2 f(r)g()h()., r r,. r,. (36.17). (1). (1) ( 36.17). ( f.) f(r) 2 /2r 2. (36.18) 36.11 (1) 2 /2r 2 (0 ).?. v 2 U(r)E.(.), v 2 v r 2 v t 2 v r 2 (r) 2. Lrv t r 2.,. 1 2 1 2 L 2 /r 2. (r) 2 v r 2 U(r) L 2 /2r 2 E. L 2 (1) 2 (1) 2 /2r 2. (1) 2 L 2.. (1) 1 2 1 2 1 2 1 2 1 2 1 2 1 2
559. (1) 2 /2r 2,. r. 36.9 36.18. 36.18?. r. 2. n.,.(.),. 0, 1, 2, 3, 4( ). (36.19) n, n > 0. n. 36.19 L 21 n1 (2r/na 0 )..,.(2r/na 0 ) L 21 n1 (2r/na 0 ) n1. r0 n1. 36.10 n3,. 36.19 n,. n3. ( 36.12), n 0
560 (a) n,. (b).. n,. n,. 36.11a 6. n n1, r 0. >0 r0 0. 0 r0 0. ( 0 r0. r0 1,.) 36.11b r n,. n1 f 10, n2 (f 20 f 21 ). n3 f 30, f 31, f 32. b n. (shell).,.. : f n,n1 n r. 36.17. (1). (36.20),.,.,. m 2.( m.). (36.21)
561 (36.22) 36.21 14. 36.21. sin(m) cos(m).. (36.23) A. 2, xy 360,. m. 36.22,. (36.24) B. A. P m, P., 36.12. 1, 2, 3, 4, 5. P l. n >, n 0. m. 21 m..
562 36.24 m m. g()h() (spherical harmonics) Y m. (36.25). e im. 36.13. z, m 0.? (1) 2 L 2 m z L z.. (36.26) (36.27),, m z. L 2 L z. 36.20 36.21 36.26 36.27..., ( 36.19) ( 36.25). (36.28)
563. 1 1. (radial quantum number) n1, 2, 3,..., (orbital angular momentum quantum number) 0, 1,..., n1, (magnetic quantum number) m,...,.. (36.29) n, r n n 2 a 0 n 2 2 /ke 2,.( n1.) n. ( ). K, n..
564.,,. s() p(), 2() d.(?.) 4d 4 2. 36.14... m0,,. 36.15, y0 xz m0 n, nm.,, 0 y0 xz nm (x,0,z). xz a 0. nm.
565,. x, z 30a 0. s (0 ).0.. n, ( ). p. d, f.,. n1, s. (36.30), E 1 13.6 ev.., 36.30. 36.30 36.2. n2 s 1 3 p 4. E 2 3.40 ev. n3 s 1, p 3, d 5 1359. E 3 1.51 ev.
566 2, 1,1 (r,,) 2,1,1 (r,,) m 21. nn1, n N(n). n5 n2 (36.31)?.....,.,.. 36.15...,,.? Z. Z1 Z. Z Z... 1s. 36.29. (36.32) e 2 Ze 2., 36.32
567.( 36.32 M 36.4.)? Z,....,.. 0... 36.16. 36.14. Z 2.,.. 36.16 36.14? 36.16 n,.. 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 5d, 4f, 6p, 7s, 6d, 5f. 1/2. 2(1/2)12,.. 36.16 2,. C.. (Z9) [He]2s 2 2p 5, 1s 2 [He]. 1s, 2s 2, 5 2p. (Z13) [Ne]3s 2 3p. 1s, 2s 2p Ne ( ), 3s 2,3p 1.,. Z n n s.( Z19, 37 55.) n..... [Xe] 4f 14 5d 10 6s 2 6p 2 [Rn] 4f 14 5d 10 6s 2 6p 2 [Rn] 5f 14 6d 9 7s 2 [Xe] 5f 14 6d 9 7s 2
568. (ionization), (ionization energy). 0 0. 36.17.( Z85.)?.. 1s. 13.6 ev 13.6 ev. : 2, 1s. Z2 2... 24.6 ev.?. n1. n1 2. n2., (noble gas). : Z3 3. 2 1s n1. 2s. 36.11b 2s., 5.39 ev.. : 4 4. 2s 2s. n2 0 1.. 9.32 ev. : 2(21)2(211)6 2p
569.. 2p. 36.11b 2s 2p. (Z5).2p.,,. 2p. n2. (Z10) n2 2p.. n2 n1, n2. (24.6 ev) (21.6 ev).. 36.17. (periodic table of chemical elements) ( 36.18 ). n1, n2.....,. 3d.3d 4s 4s 3d.4s 3d.
570 Z104... (valence electrons),.. 36.18. 92().,.. 113, 115, 116 118 21 10, ms s. (40.), Z104 3 ( 36.19 ). n.,,.... 24.6 ev. n1 2 (Z2)... 36.32. 4..
571.... 36.6 e 2 Ze 2. d 23 Uke 2 /d... 27.2 ev, 24.6 ev..... 1895.., 25 kev 60 kev,25kev 140 kev. 160 kev. ( 36.20 ).?... ( ).... 36.21.
572...,., hf hc/ E e V....,. 36.2. Z >1,. 36.21,.. (n1 K, n2 L,...) (,,...). K n2 n1.. 36.32 E 1 k 2 Z 2 e 4 /2 2 (13.6 ev)z 2. Z 2., (ZZ ) 2. Z Z.. 1. 1913,. 36.22 K. NIST. Z (ZZ ) 2.( K 1 Z 1.). (laser) (Light Amplification by Stimulated Emission of Radiation).
573. 1960 CD, DVD, BD,,,,.,,.., (,, )..,.,. -(He-Ne). 36.23., 1s. 10 1s, 2s 2p. 36.23 (, ). 2s, 20.61 ev. 1,1s 2s 0. 1s 2s 2s 1s. 36.23b.( 9 (1s 2s 2,2p 5). (3s, 4s, 4p, ) (2p, 3p, 5s, ). 2p 5s 2s 1s 20.61 ev 20.66 ev. 0.05 ev, ( 19.4 ). 3p 18.70 ev.3p( 1) 5s ( 0) ( 36.8 ). (a) (b). 5s 3p 633 nm.. 5s 4p., 3390 nm. 4s 3p, 1150 nm. - 10, 5s 3p.. 36.24.
574 ( ) (, ). (a). (b). (c).. 36.24a. 36.24b... 36.24 c (stimulated emission).,.. ( )...... 19 T E e E/kBT.. E.. 5s 3p E1.96 ev. (T300 K) 3p 5s e 1.96/(3008.617105) 1.210 33.( k B 8.61710 5 ev/k
575.) E e E/kBT <1,.,. 36.23 2s...., 5s.,3p 5s 5s 3p.. 36.25 -... 99%..,.. (Al 2 O 3 ). 10.0 ns3.00 kw (685 nm).?.. E t..
576 N. 10 23.. 5mW,. 100 kw 9.6 m 10.6 m..,,. 1 ps(10 12 s)...,. mm.,.. 2009, NIF( 36.26 36.27 ). 192 NIF.. NIF 2, 8 6 48 3. 2006 10,6 2006 12. 1000 ft.
577, 4 ns, 1.8 MJ.. NIF.... nm (r,, )f n (r)y m (, ). n1, 2, 3,..., 0, 1, 2,..., n1, m, R H 1.09737310 7 m 1....,...... a 0 5.29510 11 m0.05295 nm0.5295 Å.. (r,,)f(r)g()h().. L 2 Y m (, )(1) 2 Y m (, ), z L z Y m (, )my m (, ). n... 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 5d, 4f, 6p, 7s, 6d, 5f...
578 (spherical harmonics) (orbital angular momentum quantum number) (shell) (laser) (Rydberg formula) (Rydberg constant) (Bohr radius) (spectrometer) (line spectra) (Bohr model of the hydrogen atom) (energy-level diagram) (noble gas) (valence electrons) (stimulated emission) (ionization) (ionization energy) (magnetic quantum number) (metastable states) (radial quantum number) (periodic table of chemical elements) (reduced mass) R H 1.09737310 7 m 1, a 0 5.29510 11 m0.05295 nm0.5295 Å, Y m (, ), nm (r,, )f n (r)y m (, ), 36.1 n 2,,2. R H 1.09737310 7 m 1, (n 1 1), (2), (3), (4) 91.1 nm, 365 nm, 820 nm, 1458 nm... 36.2 n 1 2, n 2 n: 36.3 211 (x,0,z) 210 (x,0,z) xz 90. 36.4 100 (r,,). 100 (r,,)..1
579,,,,... ()...? Z3.,. kze 2 /r3ke 2 /r..., ( 36.28 ). (). 36.2...( 1/2000 ). ke 2 3ke 2 R H 1.09737310 7 m 1 9[(3ke 2 ) 2 9(ke 2 ) 2 9k 2 e 4 ]. 36.28 n 1 3, n 2 5. R H 9R H n 1 3, n 2 5
580... 1/2000, 3 4.. 36.4 820 nm. 820 nm. 9.. 36.1? a) 80.0 nm b) 85.0 nm c) 90.2 nm d) 94.9 nm 36.2 n5., m? a) 5, 3 b) 4, 5 c) 3, 2 d) 4, 6 36.3 207.. E B E Be? a) E B E Be b) E B 100 E Be c) E B E Be /100 d) E B 200 E Be e) E B E Be /200 36.4? a) b) c) d) e). 36.5 n6? a) 12 b) 6 c) 3 d) 5 36.6 d.? a) 2 b) 6 c) 10 d) 14 36.7 (He )?
581 a) 0.00 nm b) 23.0 nm c) 46.0 nm d) 91.0 nm e) 365 nm 36.8. ()? a) h b) e c) c d) - 36.9.? 36.10? 36.11,, n. 36.12 2?? 36.13? 36.14 <4 xy, m? 36.15...? 36.16. ( ). 36.17 200 r2a 0 0. 2a 0, r2a 0?? 36.18 10 ev ( ).,... 36.1 36.19? 36.20. 36.21 ( ) n5 ( ) ( ).? 36.22.? 36.2 36.23. 36.24 13.1 ev.. 36.25 R R H /(1m/M), m M..a) b) ( ) 36.26. 1.8810 28 kg. a). b). 36.27 1.133 ev.? 36.28 n2 8.00 ev
582.. 36.29. 36.6.. 36.30 n Tn 3 /(2cR H )(n1, 2, 3,...). 36.3 36.31 n5 L L? 36.32 n K, L, M, N.. a) K b) L c) M 36.33 (3,2,1) z? 36.34 n6. 410 nm.. 36.35 1s R 1s A 1 e r/a 0. a) A 1. b) ra 0 /2. c) 1s r0,1s ra 0.. 36.36 36.30 100 (r) P(r)4r 2 100 (r) 2 r. 36.37 2s. (a 0 0.05295 nm).. Mathcad Mathematica http://integrals.wolfram.com/index.jsp. 36.4 36.38 ( He He 2 )... 36.39 He ( ).. 36.40 He. 36.41 As Si. a). b) Si. (Si 10,Si 20%.) 36.42? (). n n X. 36.43. a) n b) n c) Z 36.44 (He 1 ),,. 36.5 36.45. n1 n2. n2 n3 ( )?. 36.46 0.50 mw 3.0 mm. a). b) 2.0 m 100. W. 36.47 (Al 2 O 3 ). 3.00 kw 685 nm 10.0 ns. a)? b). 36.48 543 nm, 5.00 mw 633 nm, 4.00 mw.?? 36.49? 36.50 n? 36.51 %?
583? 36.52 n n 2. 36.53 36.2 0.0073c., Z 0.500c? 36.54 n4.? 36.55 105.66 MeV/c 2.? 36.56 n2? 36.57 He.,? 36.58 10.6 m?(.) 36.59 45? 36.60. n3 n2? 36.61 ( ). 36.62 n3 n2. 36.63 n4.?? 36.64 n1 a 0 0.053 nm. a) n6. n1? b) n6 n1()? (, )? c) (a) (He )? 36.65 (1s). (a 0 0.05295 nm)..