Ch25 Modern Optics and Matter Waves 講者： 許永昌 老師

Contents Spectroscopy (of atoms) X-ray Diffraction (of crystals) Balmer series for the hydrogen atom Diffraction grating X-ray Diffraction (of crystals) Photons Matter waves The interference and diffraction of matter Energy is Quantized

Spectroscopy (請預讀P763~P766) A spectroscopy is one kind of application of diffraction grating. If you look at the 1st order of diffraction, you will find that the light has the dispersion. If the light source is gas discharge tube, you will get the discrete spectrum instead of continuous spectrum. We can determine its frequencies from its spectral lines. Lens + grating

Exercise If you send a laser beam onto a diffraction grating(d=2mm )+ converging lens (f = 3 cm), you get the distance between two bright fringes is 1cm on the screen located at the focal point of this converging lens. What is the wavelength of this laser beam?

Balmer and the hydrogen atom Hydrogen is the simplest atom. In 1885, J. Balmer found by trial and error that for visible light. Later, other people found that for other lines in the hydrogen spectrum. Challenge: n and m must be integer. Newtonian mechanics does not deal in such “discrete” quantities. However, Standing waves exist for only certain frequencies that are described by an integer called the mode number.

X-ray Diffraction (請預讀P766~P769) This part can be explained by the wave model of light. This part is used to compare with the results of electrons, neutrons, etc. X-ray Diffraction: Configuration: Source: X-ray gotten from cathode rays tube. Target: A single crystal as a diffraction grating. Diffraction Spectrum & Diffraction Pattern (每個q都將晶體轉一轉，看收到的平均強度)

X-ray Diffraction (continue) Reason: You will get the detail information from Solid State Physics. The concept is simple once you understand how to use to represent a wave and a periodic distribution. When it will exhibit a bright spot. You will find that its result confirms the Bragg condition: Dr=2dcosqm=ml, mN, l: (known) the wavelength of light. qm: (known) gotten from the experiment. d: (unknown) the shortest spacing between atom planes.

Photons (請預讀P769~P771) Phenomena: Young’s double slit experiment Classical Particle Classical Wave Short time record i.e. t0 Photon Long time record i.e. t>>0

Photon (continue) Photon model: Massless v=3108 m/s. The energy for one photon ephoton=hf=ħw. The momentum for one photon Planck’s constant: h=6.63 10-34 Js. The superposition of a sufficiently large number of photons has the characteristics of a classical light wave. Q: If only one photon at a time is passing through the experiment, what is it interfering with? Suggestion: The photon is somehow interfering with itself ? ! .

Homework Student Workbook 25.2 25.3

Matter Waves(請預讀P772~P775) Louis de Broglie hypothesis: wave-particle duality Because photons have both wave and particle characteristics, perhaps all forms of matter have both properties. E=hf=ħw.

Exercise If the speed of electron is 4.35106 m/s and its mass is 9.11 10-31 kg, what is the value of its wavelength?

Energy is quantized (請預讀P776~P778) Reason: Standing waves  Confinement. A simple case: A particle confined in a 1D box of length L. l=2L/n, nN. (discrete) p=h/l=hn/(2L). We say that energy is quantized. n is called quantum number. Each value of n characterizes one energy level of the particle in the box.

Homework Student Workbook Student Textbook Terms and Notation 25.6 25.9 Student Textbook 25.38 25.40 Terms and Notation 請自行製造卡片。