搜索
ÆQW ._*N 9 | 3A Y Tl19 92‘:f 7dQT 33n $1.1PJD T$ E’M# :O:1.1.1 A 8(RadiationofBlackBody):O7^ Cd nJ KP 3; {; Tii 3fC wnvX }l 9 &%; {3 [ } 3; #0p H 2Eνdνw 9K*℄C+:GK(ν,ν+dν)a3[ ; N[ ; ,DEν3 3Nq$83 3N1.1j3 yq K1896= W.Wien p 3M $ P yS )h A wp3e‘ v Eνdν=C1ν3exp(−C2ν/T)dν.(1)W C1 C2Y n‘ ) eyjr%o0 Wv : )h℄ Wien39Wt ’21911=3jNK ,\~3 w/ Wienv KÆ{.x 1λ∼=1/ν∼=∞)p : ℄ 2y| Y J.W.Rayleigh J.H.JeansA wp3v Eνdν=8πc3kTν2dν∼=Tν2dν.(2)Wv 3&gO/wp Kn5x3ÆTC: ; {Yu{ Pd YE=E0sinn1πxLsinn2πyLsinn3πzL.(3)W ni=0,±1,±2,··· , *n1 7Rh3zvC+YΔk=πL3.(4) T- H9; { +5ω=c|k| , vX:3; {1 ,DYg(ω)dω=Xkδ(ω−c|k|)dω=Sk=ω/cdω∼=ω2dω∼=ν2dν.(5)17rhK5 j3; mW? *n; {3G 1 3Hm; YkT/2 , +20Eνdν∼12kTg(ω)dω∼=kTν2dν.(6)Wd Rayleigh-Jeansv $j83 3N1-1+r%o0 Wv Kν→0 : ey℄ 2O , -ν→∞ Nzh B 1.1.2 ISH.Hertz91888=Pu ; / -({S U 0X&w- &5; ’ b0J.J.Thomson91896=Pu;|% q+ ( 0 yU M 3 ;| X&j=’ Wu 5wp3n9 (1)H9?3X& 3;. !Knk?3 UGν0 -U 3Gνν0 d$ 3YD5K& |&~ 05;|m-P (2)*n ;|3; [:U 3Gν5} (3)-y 3Gνν0 d$ K(V{ A& ; / W dQ2‘:f ;%,/3 1.1.3V^ G\ 3 4 /1885= BalmerPu ℄?|3rD Ny WÆ3 y\r%3p l?eν=1λ=R122−1n2,n=3,4,······(7)W R=109677.581cm−1 YRydberg ) 03 ! rH9P9AX&?|3 NIÆ 1908= W.Ritz 7 8A ?|P 3 Ny3{)eν r% wp3 eνnm=T(n)−T(m).(8)W n mY3 ℄\) q+ }l b Y (?| N| W}39 M*F N3zHYD5/ew k? 21.1.4V^ B L1895= R¨ontgenPu X y 9/g BequerrelPu 4 3ElU 1898= e ZPu W Puw/ ?|| fi 3 *℄ 9+i5‘I3Sx yr%z v! ?|7lr%U ’a;3β | M?|7 j 3 6(?| O 3’a;3 | ’℄;3 |x 39 1904= ThomsonPA wp31 ℄; mFW}K?|j ?|3bb&CY10−8cm M;|NKPj 3l5 !3A W1 Y“Lh-f1 ” ,K1911= RutherfordWh 2α | )?| 203)h PuW1 dQT ~ 03&MD} u , 8A ?|j3℄; W/jKn 3d;j(10−12cm) J ?|i 3q W /jKWd; ?| M;|NWoz?| v ,Rutherford3?|1 0 V &3 8 rh‘:; ;|K?| S ;2H J&|G[ ; { ,M~ ; , Wo?| H3;| k&“0”?| jh W ?| d“o~” ,u U3‘ w/ ?| a?3 w TlW’J9 $1.2Planck-Einstein -^1 | \Q38~ 3Planck91900=% 3 Y =Wienv : ~ 03 C[ ;NW}eya3 x 891900=10E19uPw3F_Sjq wp3 v Eνdν=C1ν3exp(C2ν/T)−1dν.(9)5g3 Wv : ℄ 2. Y $ T Wv Planckt(0 v (9)r%mf Eνdν=kC2νexp(kC2ν/kT)−1C1kC2ν2dν.(10)3W kYBoltzmann ) +W-$‘o0 ,|ν2dν ℄p9vX:; {G 1 3:,DÆ)g(ω)dω3 , ,|Eν≡kC2νexp(kC2ν/kT)−1(11)/eT GYν3G ; {1 3Hm; T- +r%J f Eν=kC2νexp(kC2ν/kT)−1=ddβln(1−exp(−βkC2ν)).(12)W β=1/kT J9:+%‘3K5 v E=−ddβlnZ=−ddβlnX{ǫ}exp(−βǫ)=P{ǫ}ǫe−βǫP{ǫ}e−βǫ(13)zpO +r%o0 K C[ bBj +5lnZ=−ln1−e−βkC2ν=ln11−e−βkC2ν.(14), GYν3u{1 3EWÆ)YZ(ν)=11−e−βkC2ν=1+e−βkC2ν+e−2βkC2ν+e−3βkC2ν+···=∞Xn=0e−nβkC2ν.(15)J v :EWÆ)3?*Z=P{ǫ}e−βǫzpO +20 W1 /ei5wp 3WÆ; ǫ0=0,ǫ1=kC2ν,ǫ2=2kC2ν,ǫ3=3kC2ν,···(16)3 Planck2 S$ z kC2=h NvX:nGYν3v 3; {1 3; WÆ3y\ *℄ǫν=hν(17)43\)k Wt Pw91900=12E4u 2+YE%k36 Planckv r%mm Eνdν=8πhν3c31exp(hν/kT)−1dν.(18)Wv Kν→∞ P!YWienv M-ν→0 +75Eνdν∼=8πhν3c311+hνkT−1dν=8πhν3c3kThνdν=8πν2c3(kT)dν.(19) 7Rayleigh-Jeansv x KWv y|f Planck ) , 9 n‘:f 3S ^ Planck3 r%T C[ 3 ey ,- y\-RK)f :3t( rt(0; {; | r;m2 T‘:f 703P9 83 Einstein 8K1905=2W T ; /3 yY M’2jNK r Einstein-y |(quanta)3g 1sYGYν3; {[ 3 ~Kn | 3 M* |i5 3; Eν=hν=h2π2πν≡¯hω.(20)7rho*zH$ ; {3 ; & }m|p|=Ec.(21)3 20 |3 Y|p|=hνc=hλ=h2π2πλ=¯h|k|.(22), 5p=¯hk 2 |3g +dr%W T ; / - |U 0X&w- n |3; r%mn;|i - 3G y& 1 |3; y& ;|dr%s^X&3Q uA M X&j=’ ’ w- P;3p l?12mv2=hν−A.(23)5Wd,/ Y (-νν0=A/h ;|dQ X&j’ ,M|&P ; / |3g0Planck-Einstein3}m K1923=3Compton} j20 bP3^ {n_}‘ pNq$$10f11 3:v $1.3Bohr -^1N.Bohr91911=9E_. GZ& KThomson /3Cavendish ELH _℄9Manchester3Rutherford /3 t MRutherfordq83 B4 w T ?|3a? Y1912=4E W Bohr[KManchesterH /nE ,83m |Q r03H/? d KW O Bohr3 $r%&g 7wp (1)?|;yM\d;ya?7!K9:WÆ3; H/3m x:j W : Y?: , Cm; 3r fu f i P ; { Ar K n?:a%GV3T \ (2)K n?:aGV ?|i (P 3; {G X3 P3p q hν1,2=E1−E2.(24)W E1 E2 z/3?:3; $k, Bohr $ 3 5 F ?|i5; | 3?: O ?|K n?:a3GV&/gG3Planck-EinsteinFFl?3; {3P (i lM [[rhW F #|;J?|3WÆ;2k?p Y Bohr7-y 7^H/? 8sY -3n?:3 |)nV & Wn:7H/3f /eP℄‘:f q 3) uKm+%{p Bohr w W PO/℄?|3;23 r +‘1 ;|Ky# V(r)=−e2r=−κr(25)j3(d:(E0)YnR 1 PÆoY2a 3?IT +r6%O E=−κ2a,T2=4π2ma3κ.(26)( v 3{nO/rD#8 Nr“ ”$8/S133 3 B14) W nv ha +20T2=4π2mκ−κ2E3=4π2mκκ38|E|3=π2mκ22|E|3.(27), ;|o?| v3GYν=1T=1πκs2m|E|3/2=1πκs2m(−E)3/2.(28)39+?℄?|j;|3x: WÆ3 zr%2n\)n;%ve Yex:3 |) , 7r%m ν(n)=1T(n)=1πκs2m|E(n)|3/2.(29)W \)n=n0,n0+1,n0+2,······m Yq |) Bohr3H/? -n→∞ H/x:3 Yr%3‘:f .’ p- + ; E(n)H9n3 }m Bohr? *n |:3; r% E(n)=hν(n)f(n).(30)W ν(n)YH/9E(n)3;|‘: 1G Mf(n)NYnd j3Æ) -n→∞ +rhBohr38OF 20hνn,(n−1)=E(n)−E(n−1)∼=E′(n)Δn=E′(n).(31)W E′(n)Y; Æ)3/) +uK 549 Y B!54 +r 54Æ)f(n)3/)f′(n)=df(n)dn=ddnE(n)hν(n)#=E′(n)hν(n)+E(n)hddn1ν(n)!7=E′(n)hν(n)−E(n)hν2(n)dν(n)dE(n)dE(n)dn=E′(n)hν(n)1−E(n)dlnν(n)dE(n)#.(32)3 +T2E′(n)=hν(n)f′(n)1−E(n)dlnν(n)dE(n)#−1.(33) T- rhH/? +O); {3[ Gνn,n−1K |)n & P℄9;2;|[ 3‘:G 1;|o?| H3 1Gν(n) , +5hν(n)∼=hνn,n−1∼=E′(n)=hν(n)f′(n)1−E(n)dlnν(n)dE(n)#−1.(34) T s hhν(n) y 2(28) +20f′(n)=1−E(n)dlnν(n)dE(n)=1−32=−12.(35), -nO& +5f(n)=−12n+D,(36)W DY ) Bohr WS - |)nO Æ 1+5E(n)=hν(n)f(n)=hν(n)−12n+D.(37)Jw# ν(n)=1πκs2m|E(n)|3/2(38)(y 5E(n)=−|E(n)|=hν(n)f(n)=hπκs