近代物理

1. 近代物理 量子力學

2. 光是什麼? 是遵從牛頓力學的粒子 還是一種波動現象?

3. 馬克斯威爾(Maxwell)的電磁學理論預言了電磁波的存在,並且以3x108m/s的速度傳遞,從而證實光即為電磁波。馬克斯威爾(Maxwell)的電磁學理論預言了電磁波的存在,並且以3x108m/s的速度傳遞,從而證實光即為電磁波。 然而光電效應的實驗結果顯示,光在與物質交互作用時又表現出粒子的性質,我們稱此現象為光的量子化,此粒子稱為光子。

4. Max Planck • Introduced the concept of “quantum of action” • In 1918 he was awarded the Nobel Prize for the discovery of the quantized nature of energy

5. 光電效應是以光打在金屬表面，將電子自其表面打出而形成電流通路的現象。實驗發現只要光的頻率夠大，即使很弱的光都能打出電子，愛因斯坦解釋，光與電子的作用像是一種粒子間的碰撞，只要粒子的動能夠大就能將電子從束敷狀態打出來，因此光波在這個實驗中是以粒子呈現的，被稱為光子。光電效應是以光打在金屬表面，將電子自其表面打出而形成電流通路的現象。實驗發現只要光的頻率夠大，即使很弱的光都能打出電子，愛因斯坦解釋，光與電子的作用像是一種粒子間的碰撞，只要粒子的動能夠大就能將電子從束敷狀態打出來，因此光波在這個實驗中是以粒子呈現的，被稱為光子。 光子的能量=h f (光的頻率) (普朗克常數)

6. Uniqueness of Atomic Spectra • Other atoms exhibit completely different line spectra • Because no two elements have the same line spectrum, the phenomena represents a practical and sensitive technique for identifying the elements present in unknown samples

7. Emission Spectra Examples

8. Absorption Spectrum, Example • A practical example is the continuous spectrum emitted by the sun • The radiation must pass through the cooler gases of the solar atmosphere and through the Earth’s atmosphere

9. In 1885, Johann Balmer found an empirical equation that correctly predicted the four visible emission lines of hydrogen • Hα is red, λ = 656.3 nm • Hβ is green, λ = 486.1 nm • Hγ is blue, λ = 434.1 nm • Hδ is violet, λ = 410.2 nm • n is an integer, n = 3, 4, 5,…The spectral lines correspond to different values of n. RH is the Rydberg constant, • RH = 1.097 373 2 x 107 m-1 n>>2, l = 4/RH = 3.646 x 10-7 = 364.6 nm

10. Other Hydrogen Series • Other series were also discovered and their wavelengths can be calculated • Lyman series: • Paschen series: • Brackett series:

11. 原子的結構 J.J. Thomson的陰極射線管實驗發現物質的組成單元-原子中存在一種基本粒子,它很輕,帶1.6x10-19庫倫的負電,人們稱之為電子。 拉塞福的散射實驗決定了原子的結構

12. Joseph John Thomson • 1856 – 1940 • Received Nobel Prize in 1906 • Usually considered the discoverer of the electron • Worked with the deflection of cathode rays in an electric field

13. Early Models of the Atom • J. J. Thomson established the charge to mass ratio for electrons • His model of the atom • A volume of positive charge • Electrons embedded throughout the volume

14. Early Models of the Atom, 2 • Rutherford • Planetary model • Based on results of thin foil experiments • Positive charge is concentrated in the center of the atom, called the nucleus • Electrons orbit the nucleus like planets orbit the sun

15. 拉塞福的散射實驗決定了原子的結構。他利用氦離子束(即α- 粒子)撞擊金箔，結果顯示大部分的α- 粒子幾乎不被偏折，而極少數被偏折的卻以180o的角度反彈,這表示原子核的質量與電荷集中在很小的空間中，約為10-13cm範圍內。

16. Rutherford’s Thin Foil Experiment • Experiments done in 1911 • A beam of positively charged alpha particles hit and are scattered from a thin foil target • Large deflections could not be explained by Thomson’s model

17. Difficulties with the Rutherford Model • Atoms emit certain discrete characteristic frequencies of electromagnetic radiation • The Rutherford model is unable to explain this phenomena • Rutherford’s electrons are undergoing a centripetal acceleration • It should radiate electromagnetic waves of the same frequency • The radius should steadily decrease as this radiation is given off • The electron should eventually spiral into the nucleus • It doesn’t

18. Niels Bohr • 1885 – 1962 • An active participant in the early development of quantum mechanics • Headed the Institute for Advanced Studies in Copenhagen • Awarded the 1922 Nobel Prize in physics • For structure of atoms and the radiation emanating from them

20. Bohr Postulates: • Dynamic equilibrium : Coulomb law and Newton’s law • Stability: stationary orbits without radiation problem • Quantization of angular momentum • Emission/absorption of light due to the transition between • different states

21. 如果假設電子與原子核類比於行星繞日的軌道運動，則根據馬克士威爾的電磁輻射理論，加速度運動的電荷將放出電磁波，而失去其運動的能量，最後終將被原子核捕獲。基於此波爾提出他氫原子模型。如果假設電子與原子核類比於行星繞日的軌道運動，則根據馬克士威爾的電磁輻射理論，加速度運動的電荷將放出電磁波，而失去其運動的能量，最後終將被原子核捕獲。基於此波爾提出他氫原子模型。 波爾假設電子繞原子核運動時存在某些穩定的軌道，在這些軌道上運動時，電子不會輻射，因此能量不會損失。這些軌道的大小滿足普朗克量子化的條件；角動量=h/2p的整數倍，h是普朗克常數。當電子在不同軌道之間躍遷時，會發出電磁輻射，因此呈現光譜線。

26. Louis de Broglie • 1892 – 1987 • Originally studied history • Was awarded the Nobel Prize in 1929 for his prediction of the wave nature of electrons

27. 德布洛依 光子的能量=hf 光子的動量=h/l

28. 駐波(standing wave) 共振(resonance)

29. Particle nature of electron Gamma-ray hit the hydrogen atom in the chamber. The electron of H is kicked out and the Gamma ray is converted into a pair of electron (green) and positron(red). The gas in the chamber is in a superheated state, which is unstable to condense into drop.

30. X-ray Electron beam

32. 費因曼(Feynmann)

33. Tunneling • The potential energy has a constant value U in the region of width L and zero in all other regions • This a called a square barrier • U is the called the barrier height

34. 在微觀的原子尺度上，粒子運動的法則不再是牛頓力學，而是廿世紀初發展出來的量子力學。根據量子力學，在微觀的原子尺度上，粒子運動的法則不再是牛頓力學，而是廿世紀初發展出來的量子力學。根據量子力學， (1)粒子運動的能量和軌道都可能是分離的，即量子化。 (2)粒子也可能越過能量障礙，出現在牆的另一邊，此即 量子穿隧效應。

35. More Applications of Tunneling – Scanning Tunneling Microscope • An electrically conducting probe with a very sharp edge is brought near the surface to be studied • The empty space between the tip and the surface represents the “barrier” • The tip and the surface are two walls of the “potential well”

36. Scanning Tunneling Microscope • The STM allows highly detailed images of surfaces with resolutions comparable to the size of a single atom • At right is the surface of graphite “viewed” with the STM

37. 以電子穿隧掃瞄顯微鏡探測砷化鎵的表面結構，藍色代表鎵原子，紅色代表砷原子。以電子穿隧掃瞄顯微鏡探測砷化鎵的表面結構，藍色代表鎵原子，紅色代表砷原子。

39. A metastable state is a state whose lifetime is much longer than the typical 10-8 s • An incident photon can cause the atom to return to the ground state without being absorbed • Therefore, you have two photons with identical energy, the emitted photon and the incident photon • They both are in phase and travel in the same direction

40. Laser light is coherent • The individual rays in a laser beam maintain a fixed phase relationship with each other • There is no destructive interference • Laser light is monochromatic • The light has a very narrow range of wavelengths • Laser light has a small angle of divergence • The beam spreads out very little, even over long distances • The emitted photons must be confined in the system long enough to enable them to stimulate further emission • This is achieved by using reflecting mirrors

41. 雷射工作原理

42. 雷射的應用 • Applications include: • Medical and surgical procedures • Precision surveying and length measurements • Precision cutting of metals and other materials • Telephone communications