原子模型 Atomic Model 有了正確的原子模型, 才會發明了雷射

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1 原子模型 Atomic Model 有了正確的原子模型, 才會發明了雷射

2 原子結構中的電子是如何被發現的? ( ) 可以參考美國物理學會 ( American Institute of Physics ) 網站 For in-depth information, check out the American Institute of Physics' History Center exhibit on the discovery of the electron at

3 西瓜模型 ( Plum Pudding Model ) by J. J. Thompson 西瓜模型 : 帶負電的西瓜子 ( 電子 ) 帶正電的西瓜肉 atomic size ~ Å Plum Pudding model negatively charged plum ( electron ) positively charged pudding

4 Rutherford 模型 ( Rutherford Model ) scattering of α particles ( experiment by Rutherford ) : ( ) Thomson and Rutherford in 1930s most particles scattered at very small angles about 1 in 8000 particles scattered at angles > 90 o

5 原子核 ( nuclei ) m α 7000 m e electrons negligible m Au,positive part 50 m α, but if the mass was spread uniformly over the whole atom ( r m, Å ) Au positive part could not cause large deflection ( 大散射角度的機會 1 / ) The positive part of the atom has to be concentrated in an extremely small volume ( r m )

6 原子半徑中絕大部分 的空間是空無一物的! 原子半徑 ~ m 原子核半徑 ~ m α 粒子撞到原子核的機會 ~ / /10 4 Robert P. Crease, a member of the philosophy department at the State University of New York at Stony Brook and the historian at Brookhaven National Laboratory, asked physicists to nominate the most beautiful experiment of all time. The New York Times listed the 10 winners of this polling and Rutherford s experiment is one on them.

7 Planetary Model ( 行星模型 ) 行星模型的問題 ( 從古典物理的觀點來看 ) : if e - moves in circle at constant frequency equivalent to 2 mutually perpendicular SHM of charge charge undergoing SHM would radiate EM wave EM wave carries away energy e - loses energy and spirals into the nucleus ( within 10-8 s ) ( 1 ) atom would be unstable ( 2 ) radiate EM wave of continuous frequency ( because e - circulating frequency as radius )

8 氫原子光譜 ( Spectrum of Hydrogen Atom ) Low pressure H gas each element has a characteristic set of lines visible spectrum of H consists of 4 lines : nm, nm, nm, nm ( Balmer series ) an empirical relation : 1/λ = R ( 1/n 2 k 1/n 2 j ) Rydberg-Ritz formula R = x 10 7 m -1, n k, n j : integers, n j = n k +1, n K +2,..

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10 例 : for 氫原子 n k =2, n j = 3, 4, 5 n k = 1, n j = 2, 3, 4 n k = 3, n j = 4, 5, 6 frequency lines in the visible range Balmer series frequency lines in the UV range Lyman series frequency lines in the infrared Paschen series 為什麼原子會發射不連續的光譜線? 為什麼每一種元素的原子的發射譜線都不一樣? 古典物理 ( 如簡單的原子行星模型 ) 無法解釋!

11 波耳原子模型 ( The Bohr Atom ) 波耳假設 ( Bohr s Postulates ) (1) 假設 1 : electron can take only certain orbits with angular momentum L = mvr = nh, n = 1, 2, 3,.. h = h / 2π (2) 假設 2 : electron in the allowed orbits does not radiate EM radiation (3) 假設 3 : radiation occurs only when e - goes from one allowed orbit of energy E i to another lower energy E f. The radiated frequency is υ = ( E i E f )/h

12 波耳氫原子模型的光譜線 h L = mvr = nh v = n mr F radial = ma radial ( 等速率圓周運動 ) e 2 = mv 2 / r 4πε o r 2 e 2 m = n 2 h 2 4πε o r 2 r m 2 r 2 r n = n 2 4π h 2 ε r o, r o = o e 2 m only radius r o, 4r o, 9r o.. are allowed 例 : 電子環繞原子的最小半徑 r o = 0.53 Å 4π ε o h 2 e 2 m

13 轉動角動量的量子化 ( quantization of angular momentum L ) 同時意味了 電子軌道半徑的量子化 ( quantization of radius r ) 能量的量子化 ( quantization of energy ) ( 或 不連續性的變化 ) E total = K.E. + P.E. e 2 = ½ mv 2 ( 氫原子只有一個電子及一個質子 ) 4π ε o r e 2 since = mv 2 / r ( F radial = m a radial ) 4π ε o r 2 ½mv 2 e = ½ 2 e E total = - ½ 2 4π ε o r 4π ε o r e 2 E = ( r = n 2 r o ) 8π ε o n 2 r o e E n = 4 m 1 = E o / n 2 e, E o = 4 m, n = 1, 2, 3, 8 ε 2 o h 2 n 2 8 ε 2 o h 2

14 例 : 氫原子中電子的能階 E n=1 = = ev ground state ( 基態 ) E n>1 : excited state ( 激發態 ) ev ev ev ev 所有的物理系統都趨向於最低的能量狀態 ( All physical systems tend to seek the lowest energy state available to them. )

15 Excited State Ground State

16 原子光譜線 ( Spectral Lines ) E n = E o / n 2 If electron jump from E i E f and emits a photon υ = ( E i E f ) / h ( - E = o /n 2 i ) ( - E o /n 2 f ) h E = o 1 1 ( - ) h n 2 f n 2 i E o 1/λ = ( 1/n 2 f 1/n 2 i ) hc = R Bohr ( 1/n 2 f 1/n 2 i ) R Bohr = E o / hc x 10 7 m -1 與 Rydberg-Ritz formula 的結果大致相同

17 X-ray, V ( 幾千伏特 ) Typical x-ray Spectrum I υ max

18 原子的發射光譜 原子的吸收光譜

19 The Franck-Hertz 實驗 ( Franck-Hertz Experiment ) Hg vapor Grid Plate i V o V r (~1V) e - reaching G E k = ev o In vacuum V r > V o e - turned back V r < V o e - reaches P i

20 with vapor of element Hg vapor Grid Plate e - lose K.E. through collisions with atoms i ( energy absorbed by the vapor ) V o V r (~1V) For the case of Hg vapor : 4.9 ev 6.7 ev e - e - 0 ev ev ev ev

21 雷射 ( Laser ) ( Light Amplification by Stimulated Emission or Radiation ) 波耳原子模型 原子中的電子能階 氫原子

22 e - absorb energy ( through photon or e - collision ) excited state decay to lower energy state through spontaneous emission stimulated emission spontaneous emission : in all directions an incoming photon of the correct energy ( E i E f ) cause resonance and induce e - drop from E i to E f stimulated emission

23 3 features of stimulated emission : (1) 1 photon in, 2 photons out light amplification (2) emitted photon in the same direction as the incoming photon (3) emitted photon in step ( in phase 同相, coherent ) with the incoming photon

24 除了 stimulated emission 外, 要產生雷射還有兩個重要的條件 : (1) population inversion (2) metastable state a higher energy state in which e - can stay for a much longer time than in an ordinary excited state ( 10-3 sec vs sec for example ) more time to enhance population inversion stimulated emission occur before spontaneous emission

25 雷射的操作與特性 ( Operation and Characteristics of a Laser ) Characteristics of a laser : (1) unidirectional (2) high intensity 例 : He-Ne laser : ~ 100 W/m 2 ( ~ 4000 times of sunlight ) (3) nearly monochromatic ( 單一頻率 ) (4) coherent

26 T.H. Maiman holding the first laser ( 1960 )

27 紅寶石雷射 ( Ruby Laser ) 一種固態雷射 E 3, E 4 : short-lived excited state ( ~ 10-8 sec ) E 2 : long-lived ( ~ 3x10-3 sec ) metastable state E 1 : ground state e - decay readily from E 3, E 4 E 2, but not from E 2 E 1 (1) optical pumping : E 1 E 3, E 4 (2) E 3, E 4 decays to E 2 readily (3) a spontaneously emitted photon ( E 2 E 1 ) triggers series of stimulated emission laser at nm (4) pulse laser ( several pulses per flash ) E4 E3 E2 E1

28 氦氖雷射 ( He-Ne Laser ) 一種氣體雷射 1st continuous-wave laser ( 1960 ) ( 15% He, 85% Ne ) 100 % reflective ~ 1 % transparent (1) collision between e - and He ions ( E 1,He E 2,He ) (2) collision between He and Ne ( E 2,He E 3,Ne ) collision between e - and Ne ( E 1,Ne E 3,Ne ) (3) ( E 3,Ne E 2,Ne ) red laser ( nm wavelength ) E 2,Ne decays quickly to E 1,Ne

29 Reading a compact disc