E原子的量子理论

1、Chapter 22 The quantum theory of Atoms1 The experimental law of atomic spectrum2 Bohrs model of the Atom 3 To explain Hydrogen Atom by Bohrs Theory 7 The physical significance of the quantum number and their interrelations4 Wave-particle dualism of matter particle5 Uncertainty relation（uncertainty p

2、rinciple）6 The statistical meaning of wave function Schrdinger equation8 One-dimensional potential well 9 LaserChapter 22 Quantum theory of AtomsIn 1897，Thomson confirmed existence of electron with experiment.Then, electron was affirmed to be a part of atom. One of the central task of Physics was to

3、 exploring the mystery interior of atom. 汤姆逊从实验上确认了电子的存在。之后，确认电子是原子的组成粒子。物理学的中心问题之一就是探索原子内部的奥秘In 1911，Rutherford proposed the nuclear model of the atom. 卢瑟福提出有核原子模型In 1913，Geiger and 马斯顿 proved the correctness of Rutherfords model of the atom. 盖革和马斯顿证明了卢瑟福原子模型的正确性In 1913，Bohrs assumption of the mode

4、l of hydrogen atom was put forward. It explained the spectrum of the hydrogen atom. 玻尔发表氢原子结构理论，解释了氢原子光谱。The history of the quantum theorys : In 1924，de Broglie put forward the hypothesis of that microscopic particle has wave-particle duality. 德布罗意提出微观粒子具有波粒二象性的假设。In 1925，Pauli proposed the exclusio

5、n principle. 泡利提出不相容原理In 1925，DavissionGermer experiment proved the wave nature of electron.戴维逊革末实验证实了电子的波动性。In 1925，Heisenberg developed the matrix mechanics. 海森伯创立矩阵力学In 1926，Schrdinger published wavelike equation. It was soon realized that the two streams were simply different mathematical approa

6、ches to the same physical ideas.薛定谔发表波动方程. 很快认识到二者是同一物理思想的不同数学描述.In 1927，Heisenberg published uncertainty principle. 海森伯发表不确定原理1 The experimental law of atomic spectrum 1 The experimental law of hydrogen atomic spectrumIn 1885, Balmer concocted an empirical formula of hydrogenVisible spectrum:wavele

7、ngth:Frequency: Wave number 波数:Invisible spectrum:Ultraviolet spectrumInfrared spectrumRitzs combination principle 里兹合并原理spectral termAlkaline metal:2 The difficulty of the classical theory(1) Rutherford nuclear structure(2) The difficulty of the classical theoryFor an orbiting electron in a hydroge

8、n atom to lose energy as it accelerates, the radius r of the orbit must decrease. an radiating electron will spiral down into the nucleus, thereby destroying the planetary nature of the model.As the electron spirals in, its frequency of rotation will vary continuously, and this implies that the atom

9、 should emit electromagnetic waves with continuously varying frequencies. +Bohrs idea： Bohr assumed that the classical electromagnetic theory did not necessarily apply to atomic phenomena. Could we apply Planck energy quantization and Einstein photon theory to explain the spectrum? Classical theory:

10、 Destroyed the planetary nature of the model.Emitted electromagnetic waves with continuously Experimental fact: Observations show that the hydrogen atom emits energy only at certain fixed discrete frequencies Conclusion:The predictions of continuously varying frequencies from the planetary model do

11、not agree with experimental observations.2 Bohrs model of the atom1 The Bohr Model of the Atom(1) The postulate of Stationary States 定态假设Only certain discrete values of radii are possible, with corresponding energies in those orbits(2) The postulate of quantum transition 量子跃迁假设 An electron could cha

12、nge from one stable orbit of radius rn to another radius rk by acquiring sufficient energy (3) The postulate of angular momentum 角动量假设In any stable orbit the angular momentum must be an integer multiple of Plancks constant Angular momentum:2 The energy level formula 能级公式(1) Orbital radius rn：(2) Ene

13、rgy level formulaThe angular momentum of the orbiting electron:The electrical attraction between the electron and the nucleus is the centripetal force:Orbital radius rnBohr radius r1To express the total energy in terms of the quantum number n Niels Bohr was awarded the Nobel prize in physics in 1922

14、.3 The explanation of hydrogen spectrum by using Bohrs theoryAn electron could change from one stable orbit of radius rn to another of larger radius rk by acquiring sufficient energy If an atom jumps between two stationary states，the frequency emitted (absorbed) radiation is given byIn theory：R=1.09

15、7373107m-1In experiment：R=1.096776107m-1The energy level diagram:Lyman seriesultraviolet rangeBalmer seriesvisible regionPaschen seriesinfrared rangeThe achievement and limitation of Bohrs theory:Achievement: The ultimate test of any theory is whether or not it agrees with experiment. The Borr model

16、 of the atom certainly had striking success in predicting and explaining the physical basis for Rydbergs formula giving the spectral lines of atomic hydrogen. Limitation: Some of the spectral lines were composed of a number of fine lines. Bohrs circular orbits could not account for all these lines.

17、4 Wave-particle dualism of object particle1 de Broglie wave A particle of mass m moving with speed v has a wave structure, 运动着的粒子可以与一列传播着的波相联系着de Broglie referred to the wave as a matter wave or de Broglie wave.The electron could be considered as a matter wave(b) de Broglie equationWave property：，Pa

18、rticle property：E，Pde Broglie equation:(a) de Broglies hypothesis of matter wave 2 Wave-particle dualism of real particle(a) The reason of being long time undetectedThe speed v moved particle (vN2, absorption dominates N1N2 光吸收占优 If N1N2, optical magnifying dominates N1N2 . To achieve optical magnif

19、ying, we must attempt to make N1N2.为实现光放大，就要设法使N1N2 .The conditions of population inversion realized 实现粒子数反转的条件(1) To absorb energy from outside and make atoms being in upper state as many as possible (pumping) 必须从外界吸入能量，使尽量多的粒子处于激发态（泵浦）.(2) Active medium has proper energy structure.激活物质（工作物质）有适当的能级

20、结构。 4 The realization of population inversionHelium-Neon Gas laser粒子数反转的实现-He-Ne激光器 He和Ne以4-10:1混合作为工作物质封入抽空的玻璃管，玻璃管上两端有电极，加高压使气体放电，其电子与 He原子碰撞使其激发到高能态 E2, Ne有一个能级E3与He的E2相近，在E2上的He原子与Ne原子相碰使Ne原子激发到E3.而Ne原子还有一个能级E2，由于就近激发，使Ne原子 E3上原子比 E2上原子多 粒子数反转。5 Cavity 谐 振 腔Totally reflecting mirrorPartially ref

21、lecting mirrorLaser beamIn order to realize light oscillation, besides the amplifying element, it is necessary to have positive feedback system, resonance system, and output system, being similar to the oscillation circuit in electron technology. 象电子技术中的振荡电路，要实现光振荡，除了有放大元件外，还必须有正反馈系统，谐振系统和输出系统。 The

22、active medium which realize population inversion in laser is the amplifying element and the functions of the cavity are positive feedback, resonance and output.在激光器中实现粒子数反转的工作物质就是放大元件，而谐振腔就起着正反馈、谐振和输出作用。 Because of spontaneous emission, the atoms being upper state will transit to lower state emittin

23、g photons.由于自发辐射，处于激发态的原子又回到基态，辐射自发辐射光子。The photons shoot far and near in all directions. The photons departure from the axial transgress the cavity 辐射的光子射向四面八方，偏离轴向的光子逸出腔外。 Only if the photons parallel to the axial direction of cavity can be reflected back and forth in the cavity. It becomes the outside influence factor of the stimulated emission and induces the stimulated emission axial directed.只有平行轴向的光子可在谐振腔内来回反射，成为引起受激辐射的外界因素， 最后产生轴向的受激辐射。 The emitted photon has