100 19 20

1896 Becquerel 1879 Crookes

1898 Marie Curie 1897 Thomson

1904 Thomson 1900 Planck

1909 Millikan 1905 Einstein

1911 Rutherford

1913 Bohr

5. 1 5. 1. 1 1924 de Broglie

E = mc2 E = h

mc2 = h

p p = mc

p

p

1927

5. 1. 2 F = m a a t

p = m t = 0 + at

1927 Heisenberg

x p x p h

m x m h

h h = 6.626 1034 Js

5. 1 m = 9.11 1031 kg x = 1012 m

7.27 10 8 ms1

1010 x = 1012 m

x

5. 1

m = 9.111031 kg h = 6.626 1034 Js

m = 10 g

x

5. 1. 3

5. 2

1926 Schdinger

5. 2. 1

E V m h

x + 3 = 5 x = 2

fx= x2 + C C f x= 2 x f x= x2

Fxyz

m V E

xyz xyz

r xyz

x y

xyz r

P r OP 0 ~

OP z 0 ~

OP x 0 ~ 2OP OP xOy

r x = r sin cos

y = r sin sin

z = r cos

x = r sin cos y = r sin sin z = r cos r2 = x2 + y2 + z2

r

r

r

r Rr r = Rr

R r r

Y = r = Rr Y Y

m m

l l

R r n n R r

E n eV

R Y

100 200 210

5. 2. 2 100 200 210 nlm

1. n 1234 n n KLMN

n = 1 K n

n

E Z eV 1 eV = 1.602 1019 J

n

H n = 1 E = 13.6 eV n = 2 E = 3.40 eV

n E = 0 0

n 1234 n

n n

2. l n l

n n l 01234 n 1 spdf g

n = 3 l 012 spd

l n = 4 l 4 4

l = 1 p 4p l = 0 s 4s

l = 2 d 4d l = 3 f 4f

4 4 n

M

M |M| l

p p = m kgms1 ms1 m kg M M = J s1 J

M M = J J M p p = m m p

J m

r

J kgm2 M kgm2s1 M = J s1

p p = m kgms1 ms1 m kg M M = J s1 J kgm2 kgm2s1

E n l n l

n l l E

E l n

3. m m l m

l m 0 1 2 3 l 2 l + 1 l = 2 m = 0 1 2 5

m l p l = 1m 0+ 11 3 p 3

pz m = 0 2pz 210

px py m = + 1 m = 1 px py

m l = 1m 3 3 p

m 3 2p 3 2p 3

3d 5 3d 5

m z Mz

m 0 1 2 3 l Mz z

l = 1

z Mz

z O

m = 1 z Mz OAO

zO

zOA m = 1A = 45

m = 1 OB z 135

m = 0 OC z 90

m z Mz Mz z

nlm 3 nlm 2 3 1

3 5. 2 n = 3 3 nlm

n = 3 l 012 l = 0 m 1 0 l = 1 m 3 01+ 1 l = 2 m 5 01+ 12+ 2

nlm 1 + 3 + 5 9

3 3 3 3 3 3 3 3 30 1 1 12 2 2 2 20 0 +1 10 +1 1 +2 2

n l m 3 0 03 1 0 3 1 1 3 1 + 132 0 3 2 1 3 2 + 1 3 2 2 3 2 + 2

4. ms

Ms

ms

Ms

3 nlm 4 n l m ms

4 n l m ms

5. 3 4 n = 4l = 3 l = 3 m = 0 1 2 3 7 7

nlmms 2 7 = 14

0 1 1 2 2 3 3 n l m ms 4 3 4 3 4 3 4 3 4 3 4 3 4 3

0 1 1 2 2 3 3 n l m ms 4 3 4 3 4 3 4 3 4 3 4 3 4 3

5. 2. 3 1.

W= V

| |2 W = | |2 V

| |2 r

2.

2s

2p

| |2 r

| |2

5. 2. 4 | |2 s p

| |2

y = kx + b 1 1 2

z = ax + by + c 2 1 3

r xyz 3 1 4

1. r= RrY r Rr r

Y r | |2 r | R |2 r

| R |2 r

s r 0 | R |2

2s 1s 3s

p r 0 | R |2

2p 1 3p 2

d r 0 | R |2 3d

2. r

1s r

r

r r

| R |2 r W = | R |2 V

r 4r2 V = 4r2 r

r W = | R |2 4r2 r W= V

Dr= 4 r2 | R |2Dr

Dr r r Dr= 4r2 | R |2

Dr r 1s Dr= 4r2 | R |2

Dr = 4r2 | R |2

Dr = 4r2 | R |2

Dr r Dr = 4r2 | R |2

1s Dr= 4r2 | R |2

1s r = ao

ao = 53 pm ao

2s3s

2s 1s 3s 2s

2s3s

Drr O

1s2s3s2p3p3d

ns n np n 1 nd n 2

n l

n l 1

1s

2s2p 1s

3s3p3d 2s2p

3.

a0

RY

Y ( ) | Y ( ) | 2 2pz | Y ( ) | 2 = cos2

2pz 2pz

5. 3

n

n E4s = E4p = E4d = E4f = n E1s < E2s < E3s < E4s <

n

5. 3. 1 1.

2

+ 3 2

Z * = Z Z Z *

l 4s4p4d4f

n l

2. l l

n l 3s

3s 3p 3d

l

n l n n E4s < E3d

4s 3d E4s < E3d

E5s < E4d

3. Pauling

1s 3s3p 2s2p 5s4d5p 4s3d4p 7s5f6d7p 6s4f5d6p

1s nsn2fn1dnp

p d f

5. 3. 2 1.

Pauli

Hunt

df p

2.

* * 6 C carbon 1s2 2s22p2

7 N nitrogen 1s2 2s22p3

11 Na sodium 1s2 2s22p63s1 12 Mg magnesium 1s2 2s22p63s2

* 19 K potassium [Ar] 4s1 ** 21 Sc scandium [Ar] 3d14s2 ** 4s 3d 3d 4s 22 Ti titanium [Ar] 3d24s2 23 V vanadium [Ar] 3d34s2 20 Ca calcium [Ar] 4s2 18 Ar argon 1s2 2s22p63s23p6

24 Cr chromium [Ar] 3d54s1 25 Mn manganese [Ar] 3d54s2 26 Fe iron [Ar] 3d64s2 27 Co cobalt [Ar] 3d74s2 28 Ni nickel [Ar] 3d84s2 29 Cu copper [Ar] 3d104s1 30 Zn zinc [Ar] 3d104s2 22 Ti titanium [Ar] 3d24s2 23 V vanadium [Ar] 3d34s2

31 Ga gallium [Ar] 3d104s24p1 32 Ge germanium [Ar] 3d104s24p2 33 As arsenic [Ar] 3d104s24p3 34 Se selenium [Ar] 3d104s24p4 35 Br bromine [Ar] 3d104s24p5 36 Kr krypton [Ar] 3d104s24p6 29 Cu copper [Ar] 3d104s1 30 Zn zinc [Ar] 3d104s2

37Rbrubidium [Kr] 5s1 38Srstrontium [Kr] 5s2 39Yyttrium [Kr] 4d15s2 40Zrzirconium [Kr] 4d25s2 41Nbniobium [Kr] 4d45s1 42Momolybdenum [Kr] 4d55s1 43Tctechnetium [Kr] 4d55s2 44Ruruthenium [Kr] 4d75s1 45 Rhrhodium [Kr] 4d85s1

46 Pdpalladium [Kr] 4d105s0 47 Agsilver [Kr] 4d105s1

Ce 1s22s22p63s23p63d104s24p64d104f15s25p65d16s2 Xe 1s22s22p63s23p63d104s24p64d105s25p6

57 La lanthanum [Xe] 4f05d16s2 58 Ce cerium [Xe] 4f15d16s2 59 Pr praseodymium [Xe] 4f35d06s2 60 Nd neodymium [Xe] 4f45d06s2 61 Pm promethium [Xe] 4f55d06s2 62 Sm samarium [Xe] 4f65d06s2 63 Eu europium [Xe] 4f75d06s2 64 Gd gadolinium [Xe] 4f75d16s2

65 Tb terbium [Xe] 4f95d06s2 66 Dy dysprosium [Xe] 4f105d06s2 67 Ho holmium [Xe] 4f115d06s2 68 Er erbium [Xe] 4f125d06s2 69 Tm thulium [Xe] 4f135d06s2 70 Yb ytterbium [Xe] 4f145d06s2 71 Lu lutetium [Xe] 4f145d16s2

74 W tungsten [Xe] 4f145d46s2 75 Re rhenium [Xe] 4f145d56s2 76 Os osmium [Xe] 4f145d66s2 77 Ir iridium [Xe] 4f145d76s2 78 Pt platinum [Xe] 4f145d96s1 79 Au gold [Xe] 4f145d106s1 80 Hg mercury [Xe] 4f145d106s2 72 Hf hafnium [Xe] 4f145d26s2 73 Ta tantalum [Xe] 4f145d36s2

13 2429 414244454647 575864 7879

5. 3. 3 Werner

1.

2 1 1s 1 2

8 2 1 2s 2p 8 4 3

2 1 3s 3p 8 4 3 8

3 1 4s 4p 18 9 3 18 3d 5

3 1 5s 5p 18 9 3 18 4d 5

4 32 16 32

4 32 16 32

Cr [ Ar ] 3d5 4s1 3d5 4s1 Cr

2.

f

s IA IIA

12 ns1 ~ 2

p IIIA IVA VA VIA VIIA 0 VIIIA

13 18 6 ns2 np1 ~ 6

p

s p s p

8 0 VIII A

d III B IV B V B VI B VII B VIII

3 10 8 n1d1~ 10 ns0 ~ 2

d n1d

456

La

d n1d ns

8 VIII

ds I B II B

1112 n1d10 ns1~ 2

ds ns

ds d

f f n2f 0 ~ 14 n1 d0 ~ 2 ns2

f n2f f III B

K E4s < E3d 4s E4s < E 3d 5. 3. 4

Cu Cu+ 4s E4s > E3d

1 Z = 1

Ens = Enp = End = Enf

2 Z > 1 Z

3 n l

l Ens < Enp < End < Enf

4

1 ~ 14 E4s > E3d

15 ~ 20 E4s < E3d

21 E4s > E3d

Cu E4s > E3d K E4s < E3d

5. 3. 5 Slater

E

1

2s 2p3s 3p = 0

2 = 0.35 1s = 0.30

3ns np n1 = 0.85 n2 = 1.00

4ndnf = 1.00

5. 4 K 19 3d 4s

3d 4s

4s 4s =+ 1.00 10= 16.8 0.85 8

4s = 16.8 = 4.11 eV

3d 3d =1.00 18 = 18

= 1.51 eV 3d = 1.00 18 = 18

E4s < E3d K 4s E4s = 4.11 eV E3d = 1.51 eV K 1s2 2s2 2p6 3s2 3p6 4s1

Fe 1s2 2s2 2p6 3s2 3p6 3d6 4s2 5. 5 Fe 26 3d 4s

4s =+ 1.00 10+ 0.85 140.35 1= 22.25

= 11. 95 eV 4s = 22.25

3d == 19.75 + 1.00 180.35 5

= 59.03 eV 3d = 19.75

Fe E4s > E3d 4s E4s = 11.95 eV E3d = 59.03 eV

ns np

5. 4

5. 4. 1 1 1.

2 r

r > r

3

2. 1

Z r r

d5d10f7f14 Z

d5d10f7f14 r

3 Na S6 r 80 pm 16 pm

4 Sc Ni8 r 38 pm 5.4 pm

CuZn d10 r

16 pm 5.4 pm

Z* r

Z* r

Yb 4f14 6s2f r/pm 183 182 182 181 183 180 208 180 r/pm 177 176 176 176 176 194 174 Eu 4f7 6s2f

r/pm 183 182 182 181 183 180 208 180 r/pm 177 176 176 176 176 194 174 Eu Yb r

15 r 9 pm

n2f Z* r

r/pm 183 182 182 181 183 180 208 180 r/pm 177 176 176 176 176 194 174 15 9 pm

15

Zr Nb Mo Tc Rur/pm 160 146 139 136 134 Hf Ta W Re Osr/pm 159 146 139 137 135

2 Z r r

Z r r

IA Li 152 pm Na 186 pm K 232 pm Rb 248 pm Cs 265 pm

r /pm Ti 147 V 134 Cr 128 Mn 127 Fe 126 Zr 160 Nb 146 Mo 139 Tc 136 Ru 134 Hf 159 Ta 146 W 139 Re 137 Os 135 r 10 pm

r r /pm Ti 147 V 134 Cr 128 Mn 127 Fe 126 Zr 160 Nb 146 Mo 139 Tc 136 Ru 134 Hf 159 Ta 146 W 139 Re 137 Os 135

5. 4. 2 1.

E1s = 13.6 eV = 0 eV

E = 0 eV 13.6 eV E1s = 13.6 eV = 13.6 eV E = 0 eV

eV 1 eV W = 1.602 1019 C 1 V = 1.602 1019 J 1 1.602 1019 C 1V

E = 1.602 1019 J 13.6 6.02 1023mol1 = 1312 kJmol1

1 mol 1 mol 1 mol M+ I1

1 mol M+ 1 mol 1 mol M2+ I2 I3I4 In

1 mol H 1312 kJmol1 kJmol1

1s

2. Z r 1 I1

I1 /kJmol1 Li Be B C N O F Ne 520 900 801 1086 1402 1314 1681 2081

I1 / kJmol1 Li Be B C N O F Ne 520 900 801 1086 1402 1314 1681 2081 I1Be> I1B I1N > I1O

B [ He ] 2s2 2p1 2p Be 2s2 I1 Be I1Be> I1B

N [ He ] 2s2 2p3 2p3 I1 O I1N > I1O

O [ He ] 2s2 2p4 2p4 2p3 I1 N

Ne [ He ] 2s2 2p6 I1 /kJmol1 Li Be B C N O F Ne 520 900 801 1086 1402 1314 1681 2081

I1 /kJmol1 Sc Ti V Cr Mn Fe Co Ni Cu Zn 633 659 651 653 717 762 760 737 746 906 Z

Zn [ Ar ] 3d10 4s2 Zn I1 I1 /kJmol1 Sc Ti V Cr Mn Fe Co Ni Cu Zn 633 659 651 653 717 762 760 737 746 906

2

Z I1 r I1

I1 /kJmol1 Be 900 Mg 738 Ca 590 Sr 550 Ba 503

Ti V Cr Mn Fe Co Ni Cu Zn 659 651 653 717 762 760 737 746 906 I1 /kJmol1 Zr Nb Mo Tc Ru Rh Pd Ag Cd 640 652 684 702 710 720 804 731 868

I1 /kJmol1 Zr Nb Mo Tc Ru Rh Pd Ag Cd 640 652 684 702 710 720 804 731 868 Hf Ta W Re Os Ir Pt Au Hg 659 728 759 756 814 865 864 890 1007

3. Z* r

I1 < I2 < I3 < I4 <

In /kJmol1

I1 I2 I3 I4 I5 I6 Li 520 7298 11815 Be 900 1757 14849 21007 B 801 2427 3660 25026 32827 C 1086 2353 4620 6223 37830 47277 N 1402 2856 4578 7475 9445 53267

B I1I2 I3 B I1 I2 I3 I4 I5 B 801 2427 3660 25026 32827

B 1s2 2s2 2p1 3 I1 I2 I3 I4 I5 B 801 2427 3660 25026 32827

I4 I1 I2 I3 I4 I5 B 801 2427 3660 25026 32827

I1 I2 I3 I4 I5 B 801 2427 3660 25026 32827 I2 I1 = 1626 kJmol1 I3 I2 = 1233 kJmol1 I4 I3 = 21366 kJmol1

I1 I2 I3 I4 I5 B 801 2427 3660 25026 32827

BIV BIII LiIBeIICIV NV

1. 5. 4. 3 1 mol 1mol M E1 E2E3E4

Fg+ e = Fg H = 328 kJmol1 E1 = H = 328 kJmol1

E H

2. Z r E

B C N O FE /kJmol1 27 122 141 328 E

E B C N O FE /kJmol1 27 122 141 328

N [ He ] 2s2 2p3 2p B C N O FE /kJmol1 27 122 141 328

N B C N O FE /kJmol1 27 122 141 328

F

F E

O S Se

F Cl F2 Cl2 ?

F2 Cl2

F2 Cl2

|H5| > | H6 | F2 Cl2

5. 4. 4 I E

1932

4

Li Be B C N O F 0.98 1.57 2.04 2.55 3.04 3.44 3.98

F 3.98 Cl 3.16 Br 2.96 I 2.66 Li 0.98 Na 0.93 K 0.82 Rb 0.82 Cs 0.79

F Cs

< 2.0 > 2.0

1934 Mulliken

1957 Allred Rochow