- 1

4

4-1 (Discovery of Electron)

Heinrich Geissler

Sir William Crookes

.. 2398 Heinrich Geissler

0.01 % 20 Sir William Crookes (Cathode rays)

Crookes

1

2 3

- 2

Crookes

Sir Joseph John Thomson 4-2 Thomson

Thomson Thomson Thomson

()

BvqF

R v2/R

qvBR

mv

2

BR

v

m

q (4-1)

- 3

A B S

B R v ()

B

Ev

qvBqE

E d

V E

dB

Vv

(4-2)

V d PP

(4-2) (4-1)

=

2 (4-3)

Thomson q/m 1.76 1011 Thomson Thomson Thomson 4-1 (q /m) 8103 m 3102 V 2103 T 6102 m

. . . .

- 4

.

.

.

1.875107 m/ s 1.56251011 C / kg 1,200 V

4-1 Thomson

1.4 10-3 9.13 1.0 322

- 5

Thomson Robert A. Millikan 4-3 Millikan

4-2

Millikan ()

m q

qE

Emg

q

mgqE

mg

E dV

- 6

= ()

(4-4)

v

Millikan 1.6 10-19 2 3 5 Millikan 9.1 10-31

4-2 1.01013 kg 6.1104 N/ C

1.61017 C

- 7

4-2 3 10-6 (vT) 2 1,000 2.0 800 1.29 kg/m3 = 1.810-5 N.s.m- 2

4-4

Thomson

.. 2443 Thomson 10-10

Thomson

11 11 10 10 11

Rutherford Thomson Rutherford (Experimentalist) ( rays) Rutherford (Scattering Experiment)

- 8

4-5 (Rutherfords scattering experiment)

.. 2454 Rutherford ,Hans Geiger Ernest Marden (alpha particle ) 2,000

Thomson Thomson Rutherford

1.

2.

3.

- 9

4. (backward

scattering) (head on collision) 50

Rutherford ( 10 14 )

(classical physics)

= 12

2 =

(+)()

2

=2

2

m r

v = 2

F = ma

2

=

2

2

= = 1

22 =

1

2

2

- 10

r

= (+)()

=

2

: E = EK + EP

= 1

2

2

+ (

2

)

= 1

2

2

(4-5)

E (E 0) (ionization energy)

4-6

(bullet) (target nucleus) r { (impact parameter)}

= = ()( r)

1

22 =

()

2 ()

- 11

= 4 x 107 m/s m = 4u1.661027 kg Q = +2e = +2( 1.66 x 10-19 C ) = +79e = +79( 1.66 x 10-19 C ) K = 9 109 Nm2 / C2 r 7 x 10-15 1015 m

=

1010

1015 = 100,000

r r

:

4-3 2.21018 J

0.5281010 m

- 12

Rutherford

1.

2. 3.

Rutherford

4-7 Bohr

Niels Bohr Rutherford Max Planck Bohr Bohr

- 13

(stationary state) 1

Planck 2

nmvr

2

h n

2

h E = Ei Ef = h Ei > Ef Ei Ef Bohr

Bohr

m r v Fc

r

mvFc

2

Fc

(FE) 2

21

r

qkqFE

e

- 14

mr3

mke2r = (mvr)2

mvr n mke2r = n2 2

2

2

2

nmke

rn

(4-6)

r

keE p

2

r

ke2

2

1

= +

= r

ke2

2

1

2

2

2

nmke

rn

(4-7)

r

mv

r

keFE

2

2

2

22

42 1

2

1

n

emkEn

- 15

n = 1 () n = 1 0.529 (Bohr radius a0) 21.76 10 19 (ground state) () n 2, 3,4. En (exited state)

(electronvolt) eV

1 eV = 1.6 10 19 J

(electronvolt) 1

e 1 W = qV

1 eV = (1.6 10 19 C) (1 V) = 1.6 10 19 J

- 16

Niel Bohr h

ni nf

22

42 1

2

1

n

emkEn

(4-8)

(Rydberg s equation) RH (Rydberg constant) = 1.0974 10 7 m-1

=

22

111

if

Hnn

R

- 17

4-8 (gas discharge tube) (line spectrum) (emission line spectrum)

(absorption line spectrum)

- 18

.. 2428 (J.J.Balmer) 6.56 10 7 , 4.86 10 7 , 4.34 10 7 , 4.10 10 7 (series) (Balmer series) (Rydberg)

22

111

if

Hnn

R

(4-9)

n = 3,4,5 6 n 7 n n = (series limit)

1 3

5

- 19

(Lymann Series)

nf = 1 , ni = 2, 3, 4 1

= [

1

12

1

2]

(Balmer Series)

nf = 2 , ni = 3, 4, 5 . 1

= [

1

22

1

2]

(Paschen Series)

nf = 3 , ni = 4, 5, 6 . 1

= [

1

32

1

2]

(Bracket Series)

nf = 4 , ni = 5, 6, 7 . 1

= [

1

42

1

2]

(Pfund Series)

nf = 5 , ni = 6, 7, 8 . 1

= [

1

52

1

2]

- 20

4-4 n = 3

=

= 13.6

2

1 E3 ---> E2

1 = 3 2

1 = 3 2

=

[1.5(3.4)] 1.6 1019

6.6 1034

1 = 4.6 10

14 2 E3 ---> E1

2 = 3 1

2 = 3 1

=

[1.5(13.6)] 1.6 1019

6.6 1034

2 = 2.9 10

15 3 E2 ---> E1

2 = 2 1

2 = 2 1

=

[3.4(13.6)] 1.6 1019

6.6 1034

2 = 2.5 10

15 3 4.6 1014 , 2.9 1015 2.5 1015 4-3 n = 3

- 21

Bohr

Bohr (shell) (Zeeman effect) (Stark effect)

4-9 1,500 K (continuous spectrum) (black body)

(cavity)

- 22

T

B

B

.. 2443 1. 2. T T4 B = T 4 - (Stefan Boltzmann constant law)

B 1 1 -(Stefan Boltzmann constant)

5.67 10 8 T

3. T

T

1max 3max 10898.2 T - (4-10)

()

(Wiens displacement law) -

max 4,700 6,200 -

- 23

Lord Rayleigh and Sir James Jeans Maxwell (classical physics) (oscillator) 4-10 (Plancks quantum theory of radiation)

.. 2443 Max Planck Planck Planck 2

1. E = nh (4-11) E

h Planck ( Plancks constant) 6.625 10-34 n 1,2 ,3 ......

- 24

2.

Planck

Planck .. 2448 Planck Planck 4-11

(James Franck) (Gustav L. Hertz)

4.9 ( 4.9 ) () 4.9 4.9 4.9 4.9 4.9

- 25

4.9 253.5 4.9 4.9 6.7 10.4

- 26

4-12

(X-rays) .. 2438 (Wilhelm K.Roentgen) 1

2 3 .. 2449 (Charles G. Barkla) .. 2456 (Max von laue) 1.1 10- 11 - 4.8 10- 11

- 27

2

V eV 0.1 100

() (bremsstrahlung radiation or breaking radiation)

min (continuous X-rays)

V eV ()

- 28

V

hmax = eV h

eVc

min

max

=

V (4-12)

h, c e () = 1240

V ; (

1240)

( sJh .1062.6 34 ; smc / 103 8 ; Ce 106.1 19 )

V 12,400 min 1

A min 12,400 (n = 1 K) K L M N L L ( K L) K M N K K , K K (K - series)

- 29

L M , N , O , L (L - series)

(characteristic X-rays) ( X-rays fluorencence)

4-5 1,000

0

mineV

hc

Volt

smJs

1000 106.1

/103 1063.619

834

min

= 12.4 4-13 .. 2455 10 9 - 10 10 (NaCl)

- 30

(Sir William Bragg)

- 31

P Q d P Q (1 2 3) (4-13)

n = 1, 2, 3,.

n = 1 1 n = 2 2 2d sin = n (Bragg s equation)

d

4-6 0.154 34.5 2 = =

2 (34.5)

= (1)(0.154 109)

2 (0.566)

= 0.128 x 10-9 4-13 .. 2430 (Heinrich Hertz) (Threshold frequency)

2d sin = n

- 32

(Photoelectric effect) (Photoelectrons)

A C

C () I1 C A

A A A C A C CA

A C A A (Stopping potentia) (Ek) max A

() = 1

22 = V (4-14)

- 33

Vs I2 Vs () C ()

0 C

1. 2. 1

- 34

.. 2448 (Albert Einstein) (Photon) h h hv (Work function)

(4-15) (Ek) max Wo h f = (Ek) max + Wo (Einsteins photoelectric equation)

h0 = Wo 0 Wo (R.A.Milikan) .. 2457 h maxkS EeV

WheVS

=

(4-16)

h = (Ek) max + Wo

- 35

(slope)

e

h

h

W (eV) 2.5 1.9 4.5 2.2 4.6 2.3 4.5

.. 2464

- 36

4-7 2.3 eV 5,000 oA

W 0hf 0

hc

0 hc

W

h 6.625 10-34 J.s c 3 108 m/s W 2.3 1.6 10-19 J

0 5394.9 oA

4-8 2537 oA 1.9 eV ) ) ) EK hf W

0

hc

W

c 3 108 m/s h 6.625 10-34 J.s 2537 10-10 m W 1.9 1.6 10-19 J EK 4.67 10-19 J

12

2mv EK

2v 2

v 1.02 106 m/s ) 0qV

0V

19

19

4.67 10

1.6 10

Jcoulomb

2.99 volt

- 37

4-4 0.4 eV 4,000

A . . . . . . 3,000

A

4-14 .. 2466 (Arthur Holly Compton) (Scattered x-ray)

a) b)

- 38

2 (Compton effect)

E = mc2 E = h h = mc2

2c

hm

c

hp (4-17)

- 39

()

2 1 0

(1 cos )h

m c . (4-18)

c 0

h

m c

c 0.02426 oA ( 4-18 ) ( 4-18 ) 4-9 1 oA 180o ) ) ) 2 1 (1 cos )c 1 1 oA , c 0.02426 oA , 180o 2 1 0.02426 (1 - 180cos

o ) 2 1.04852 oA

- 40

) 1 2hf hf

hc1 2

1 1

574.38 eV 4-5 0.124

1.0 % 4-15

.. 2467 Louis De Broglie () De Broglie (matter waves) De Broglie (wave mechanics)

E E = h E = pc p c

h = pc

=

(4-19)

(De Broglie wavelengt)

De Broglie 2 De Broglie (Standing wave)

- 41

2 r = n

(4-20)

n 1, 2, 3, r

= mv

h

mv

hnr 2

=

2 = (4-21)

2

4-10 100 eV =

=

= (6.6 1034)(3 108)

100 ( 1.6 1019)

= 12.38 4-16

De Broglie 100 eV 1.2 A

- 42

..2470 (C.Davisson and L.Germer) (G.P.Thompson)

(Electron gun)

V ** G C D

2d sin = n (4-22)

d

- 43

() ()

4-11 1 40

=

= 6.6 1034

(103)(40)

= 1.65 1034

1 4-12 1.67 x 10-27 kg 1,450 m/s d 0.282 nm ) )

) hp

hmv

34

27

6.63 10

1.67 10 1450( )( )

J.skg m/s

0.274 x 10-9 m 0.274 nm

) 2d sin n : n 1

12

sind

1 0.2742 0.282

sin

nm

nm

29.1 o

- 44

4-17

2 x x k k () () x

p = h/ .. 2470 (Werner Heisenberg) (uncertainty

principle)

- 45

h/2

(4-23)

x p

2

px ( (p = 0) (x =) (x =0) (p = ) px px , py , pz x , y z E E = t =

(4-24)

4-13 0.05 kg 300 m/s 0.01% p mv 0.05 kg (300 m/s) 15 kg.m/s

p (0.0001)(15) kg.m/s

1.5 10-3 kg.m/s

- 46

x p

34

3

6.6 10 2

1.5 10

( ) /

( )

J.skg.m/s

7.0 10-32 m 7.0 10-32 m 4-14 9.1 10 31 2 10 6 v 0.2 10 6 ( 10 % ) = = (9.1 x 10-34 kg)(0.2 x 106 m

s)

= 1.82 x 10-28 kg ms

= 2

= 1.05 x 10-34 Js

=

= 1.05 10

34

1.82 x 10-28 kgm

s

= 0.577 x 10-6 m

5.77 x 10-7 m 4-6 1,000 1 10%

- 47

4-18 .. 1925 (Quantum mechanics) (Erwin Schrodinger) (wave packet) (group velocity) 1 x

= = sin2

=

E

=2

2=

2

22=

22

82

2

82

2

2=

- 48

4-19 (Electron microscope) 2 .. 1929 1934 1,200 0.000 05 0.000 25 0.14 3.5 2 60 90

1 2

- 49

3

- 50

1. 2 [ 2.12 ] 2. /

[ 6.6 1015 /, 1/8] 3. 13.6 eV

n = 3 n = 2 [ 658 nm] 4..

[ 912 ] 5. [ 3.248 1015 Hz] 6. (-3.4 eV) (-13.6 eV)

[ 10.2 eV, 1218 UV] 7. 2 [ (2.47, 2.92 1015 Hz] 8.

1 [ 1.63 10-18 J] 9. ) 10-5 m [ 290 K ] ) 1 oA [ 2.90 107 K ] 10. 5727 oC [ 4833.3 oA ] 11. 3840 oA ) [ 3.23 eV ] ) 2000 oA [ 2.97 eV ] 12. 2.3 eV UV 2480 oA [ 9.76 105 m/s]

- 51

13. UV 1.2 10-7 m 10-8 J [ 9.9 1014 Hz ] 14. 4046 oA

1.6 V 5769 oA 0.45 V (h)

) [ 2.28 eV ] ) h/e [ 5.23 10-15 V/s ] 15. 0.620 oA 90o [ 0.644 oA ] 16. 2 104 m/s [ 3.63 10-8 m ] 17. 100 kV [ 42 ] 18. 500 m/s 0.01% [ 2.32 103 m ] 19. 10-8 [ 3.3108 eV ]