Polarization Diffraction Hydrogen Atom Spectrum

1. PolarizationDiffractionHydrogen Atom Spectrum a Polarized Beam Brewster’s law Diffraction Pattern, Single Slit, double slit Diffraction Grating Circular Apertures Balmer Series and Planck’s Constant

2. Intensity of a Polarized Beam • The intensity of the polarized beam transmitted through the second polarizing sheet (the analyzer) varies as • I = Imax cos2θ • Io is the intensity of the polarized wave incident on the analyzer • This is known as Malus’s law and applies to any two polarizing materials whose transmission axes are at an angle of θ to each other

3. Polarization by Reflection • The angle of incidence for which the reflected beam is completely polarized is called the polarizing angle, θp • Brewster’s law relates the polarizing angle to the index of refraction for the material • θp may also be called Brewster’s angle

4. Diffraction Pattern, Single Slit • The diffraction pattern consists of the central maximum and a series of secondary maxima and minima • The pattern is similar to an interference pattern

5. Two-Slit Diffraction Patterns • The conditions for the first diffraction minimum • a sin θ = λ

6. Diffraction Grating • The condition for maxima is • d sin θbright = mλ • m = 0, ±1, ±2, … • The integer m is the order number of the diffraction pattern • If the incident radiation contains several wavelengths, each wavelength deviates through a specific angle

7. Circular Apertures • The diffraction pattern of a circular aperture consists of a central bright disk surrounded by progressively fainter bright and dark rings • The limiting angle of resolution of the circular aperture is • D is the diameter of the aperture

8. Absorption Spectroscopy • An absorption spectrum is obtained by passing white light from a continuous source through a gas or a dilute solution of the element being analyzed • The absorption spectrum consists of a series of dark lines superimposed on the continuous spectrum of the light source

9. Balmer Series • 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

10. Emission Spectrum of Hydrogen • The wavelengths of hydrogen’s spectral lines can be found from • RH is the Rydberg constant • RH = 1.097 373 2 x 107 m-1 • n is an integer, n = 3, 4, 5,… • The spectral lines correspond to different values of n h=6.6361×10-34 J-sec Planck’s Constant

11. n= … n=6 n=5 n=4 布拉克系列 (Brackett Series) n=3 帕申系列(Paschen Series) 3889 Å 3970 Å 4103 Å 4340 Å 4861 Å 6563 Å n=2 巴爾麥系列 (Balmer Series) (可見光區、近紫外光區) n=1 萊曼系列 (Lyman Series) (紫外光區) Energy-level Diagram for the H atom Lyman series: Paschen series: Brackett series: