Arthur Beiser Concepts of Modern Physics, 6.

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1 2.., Arthur Beiser Concepts of Modern Physics, 6.

2 :, :,, (, ) 69

3 ,, 2.1 ( c = 1 ) m/s ɛ0 µ 0

4 2.2

5 כ 2.3(a) 2.3(b) Young כ 2.4

6 :. ( ). ( ) : ( ) * 2.5

7 2.6

8 ( ) ν ν + dν (3 ) 2.7 G(ν)dν = 8πν2 c 3 dν ε = kt ( ) Rayleigh-Jeans : u RJ (ν)dν = εg(ν)dν = 8πkT c 3 ν 2 dν

9 u RJ (ν) = 8πkT c 3 ν 2 = lim ν u RJ(ν) 2.8

10 Planck Planck : u P (ν) = 8πh c 3 ν 3 e hν/kt 1 (h = J s Planck ) hν kt e hν/kt 1 + hν kt = u P (ν) 8πkT c 3 ν 2 dν = u RJ (ν) (Rayleigh-Jeans!)

11 Planck * : Planck ε n = nhν. / ν, hν ( ) / Planck,!

12 Planck 2.1 ν 1 = 660 Hz E 1 = 0.04 J (a)? hν 1 = ( J s)(660 s 1 ) = J = hν 1 = ( J) = E 1 (0.04 J) ν 2 = Hz (b)? hν 2 = ( J s)( s 1 ) = J = 2.08 ev

38 10 31 J) = 1.10 10 29 E 1 (0.04 J) ν 2 = 5.

13 : ( ) 2.9 (K ev )

14 1 t 10 9 s ( t 1 ) V > V 0 ( ) = כ ev 0 = K max 2.10 V 0

15 ( ) K max ν * ν 0 (ν 0 )

16 Einstein כ ( ) ε = hν ν

17 (ν 0 ) : hν 0 * = (φ = hν 0 ) 2.13 hν = φ + K max = K max = hν φ = h(ν ν 0 ) * K K max.

18 : ( )

19 2.2 λ = 350 nm I = 1.00 W/m 2 ( ) φ = 2.2 ev (a)? hν = hc λ = ( J s)( m/s) ( m) = J = 3.5 ev K = hν φ = ev = 1.3 ev

20 2.2 ( ) (b) 0.50% 1.00 cm 2? n p = E hν t = IA t hν t = IA hν = (1.00 W/m2 )( m 2 ) ( J) = s 1 n e = Pn p = ( s 1 ) = s 1

00 W/m2 )(1.00 10 4 m 2 ) (5.68 10 19 J) = 1.

21 - :,,, :,, Compton,,,.? Bohr (complementary principle).

22 - Young 2.4 : * כ ( ) כ

23 - * [Charles Addams, The New Yorker Magazine, 1940.]

24 X X : 0.01 nm λ 10 nm (0.1 kev hν 100 kev) (Bremsstrahlung, braking radiation) X 2.15 ( ) * hν φ

25 X X λ min (λ min V ) K = ev = hν max = hc λ min 2 ( )

26 X 2.3 V = V? hν max = ev = λ min = c ν max = hc ev = m

27 X X 2.18 * : (polarize) *

28 X Bragg : 2.19(a) 2.19(b)

29 X Bragg : 2.19(a) = ( ) 2 2d sin θ = nλ ( n = 1, 2, 3, )

30 Compton Compton : 2.22 * 100 kev p = E c = hν c

31 Compton Compton : hν = hν + K 2 x : hν c = hν c 3 y : 0 = hν c cos φ + p cos θ sin φ p sin θ 4 - : E = m 2 c 4 + p 2 c 2 = K + mc 2

32 Compton Compton ( ) p K, θ mc 2 ( hν hν ) = (hν)(hν ) (1 cos φ) λ λ = λ C (1 cos φ) (Compton : λ C hmc = pm )

33 Compton Compton λ λ = λ C (1 cos φ)

34 Compton 2.4 X λ = 10.0 pm (a) 45 X? λ = λ + λ C (1 cos φ) = (10.0 pm) + (2.426 pm)(1 cos 45 ) = 10.7 pm (b) X כ? (כ ) φ = 180 = 1 cos φ = 2 = λ = (10.0 pm) + (2.426 pm) 2 = 14.9 pm (c) (recoil)? ( : φ = 180 ) ( c K max = h(ν ν ) = h λ c ) λ = J = 40.8 kev

35 ,, γ γ : λ 10 pm (hν 100 kev) γ e + e * : +e כ, m e c 2 = 0.51 MeV hν > 2m e c 2 = 1.02 MeV, λ < 1.2 pm

36 ,, γ e + e + γ + γ ( )

37 ,, γ 2.6 +x, v = 0.500c (a) x +x? :, :.! (b)? : p 1 p 2 = 2γmv : p 1 c + p 2 c = 2γmc 2 = E 1 = p 1 c = MeV, E 2 = p 2 c = MeV

38 X, γ (a) 2.28(b)

39 di = µidx (µ :, SI m 1 ) I = I 0 e µx * µ,, 2.29

40 MeV µ = 4.9 m 1 (a) 10 cm? I I 0 = e µx = exp[ (4.9 m 1 )(0.10 m)] = 0.61 (b) 1%? x = ln(i /I 0) µ = ln(0.01) (4.9 m 1 ) = 0.94 m

41 (U mgh, U Ec 2 gh ) 2.30 hν = hν ( 1 + gh ) c 2

42 2.31 : ε = hν, U = G M(ε/c2 ) R : ε = hν, U = 0 ε + U = ε + U = hν = hν = GMhν c 2 R ( 1 GM ) c 2 R ν ν = ν ν ν = GM c 2 R

43 ε = hν ( 1 GM ) c 2 R GM c 2 R 1?? = ε = hν 0!! * GM c 2 R 1 2 Schwarzschild : M GM c 2 = 1 R S 2 = R S = 2GM c 2 * : R S 3 km ( R sun = m)

44 (event horizon) :. : : ( ) ( ), X X

( ) = ( ) = {,,, } β ( ), < 1 ( ) + ( ) = ( ) + ( )

( ) = ( ) = {,,, } β ( ), < 1 ( ) + ( ) = ( ) + ( ) { } ( ) = ( ) = {,,, } ( ) β ( ), < 1 ( ) + ( ) = ( ) + ( ) max, ( ) [ ( )] + ( ) [ ( )], [ ( )] [ ( )] = =, ( ) = ( ) = 0 ( ) = ( ) ( ) ( ) =, ( ), ( ) =, ( ), ( ). ln ( ) = ln ( ). + 1 ( ) = ( ) Ω[ (