氫原子光譜之分析 氫原子的 Bohr 理論模型 利用分光儀分析光譜

Importance of the Hydrogen Atom A structural model can also be used to describe a very small-scale system, the atom ( 利用結構模型描述原子系統 ) The hydrogen atom is the only atomic system that can be solved exactly ( 氫原子為原子系統中唯一有正確解的原子 ) Much of what was learned about the hydrogen atom, with its single electron, can be extended to such single-electron ions as He + and Li 2+ ( 氫原子模型的理論計算可推廣至擁有單一電子的 離子 )

Light From an Atom The electromagnetic waves emitted from the atom can be used to investigate its structure and properties –Our eyes are sensitive to visible light –We can use the simplification model of a wave to describe these emissions

物質 ( 原子 ) 的電子能階 激發態不穩定

Emission Spectra Examples

The Bohr Theory of Hydrogen In 1913 Bohr provided an explanation of atomic spectra that includes some features of the currently accepted theory His model includes both classical and non- classical ideas He applied Planck’s ideas of quantized energy levels to orbiting electrons

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

Bohr’s Assumptions for Hydrogen The electron moves in circular orbits around the proton under the electric force of attraction. ( 電子對原子核做圓周運動 ) Only certain electron orbits are stable and these are the only orbits in which the electron is found. ( 電子在特定的軌道才能穩定的運動 ) Radiation is emitted by the atom when the electron makes a transition from a more energetic initial state to a lower-energy orbit. ( 電子在特定軌道之間躍遷時，吸收或發出 光子 ) The size of the allowed electron orbits is determined by a condition imposed on the electron’s orbital angular momentum. 特定的軌道大小由電子的角動量決定

Bohr’s Assumptions for Hydrogen ( 電子對原子核做圓周運動 ) ( 電子在特定的軌道才能穩定的運動 ) ( 電子在特定軌道之間躍遷時，吸收或發出 光子 ) 特定的軌道大小由電子的角動量決定

Wave Properties of Particles

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

Wave Properties of Particles Louis de Broglie postulated that because photons have both wave and particle characteristics, perhaps all forms of matter have both properties The de Broglie wavelength of a particle is

de Broglie wavelength of a particle (1)Baseball m=1kg ; v=10 m/s (2)Electron

wave nature of electrons L L = 3λ

Mathematics of Bohr’s Assumptions and Results Electron’s orbital angular momentum where n = 1, 2, 3,… (2) The total energy of the atom is The centripetal force The total energy

Bohr Radius n The radii of the Bohr orbits are quantized When n = 1, the orbit has the smallest radius, called the Bohr radius, n is called a quantum number

Radii and Energy of Orbits n=1 n=2 n=3

Wavelength of Emitted Photons The wavelengths are found by R H = Rydberg constant R H = x 10 7 m -1 nini nfnf

Energy Level Diagram

Balmer Series –H  is red, = nm –H  is green, = nm –H  is blue, = nm –H  is violet, = nm

計算 R H 與 h 利用 ，先算 R H 。 再利用 計算 h

Extension to Other Atoms Bohr extended his model for hydrogen to other elements in which all but one electron (He + and Li 2+) had been removed

分光儀

光柵分光儀 Diffraction Grating Spectrometer 瞄準器 望遠鏡 透鏡 物鏡 目鏡

Emission Spectra Examples

End of LectureEnd of Lecture

雙狹縫干涉

Young’s Double Slit Experiment, Schematic Thomas Young first demonstrated interference in light waves from two sources in 1801 The narrow slits, S 1 and S 2 act as sources of waves The waves emerging from the slits originate from the same wave front and therefore are always in phase

雙狹縫干涉 建設性干涉 破壞性干涉 d d

建設性干涉

破壞性干涉

雙狹縫干涉 建設性干涉 破壞性干涉 d d

Diffraction Grating The condition for maxima is The integer n is the order number of the diffraction pattern If the incident radiation contains several wavelengths, each wavelength deviates through a specific angle

講義結束

分光儀

Diffraction Grating Spectrometer The collimated beam is incident on the grating The diffracted light leaves the gratings and the telescope is used to view the image The wavelength can be determined by measuring the precise angles at which the images of the slit appear for the various orders

Emission Spectra Examples

雙狹縫干涉

Young’s Double Slit Experiment, Schematic Thomas Young first demonstrated interference in light waves from two sources in 1801 The narrow slits, S 1 and S 2 act as sources of waves The waves emerging from the slits originate from the same wave front and therefore are always in phase

建設性干涉

破壞性干涉

雙狹縫干涉 建設性干涉 破壞性干涉 d d

Diffraction Grating The condition for maxima is The integer n is the order number of the diffraction pattern If the incident radiation contains several wavelengths, each wavelength deviates through a specific angle

Diffraction Grating Spectrometer The collimated beam is incident on the grating The diffracted light leaves the gratings and the telescope is used to view the image The wavelength can be determined by measuring the precise angles at which the images of the slit appear for the various orders

Emission Spectra Examples

講義結束