Optical Spectroscopy and Atomic Structure PHYS 0219 Optical Spectroscopy and Atomic Structure 1
Optical Spectroscopy and Atomic Structure This experiment has four parts: 1. Spectroscope Setup - Your lab TA will demonstrate this. 2. The Continuous Spectrum 3. The Mercury (Hg) Spectrum 4. The Hydrogen (H) Spectrum and Atomic Structure An atom consists of electrons orbiting a dense, heavy nucleus made of protons and neutrons. N P P N N N P PHYS 0219 Optical Spectroscopy and Atomic Structure 2
Quantum Mechanics tells us that the angular momentum of an electron in orbit around the nucleus is quantized, which means it can only take on specific values. Therefore the radius of an electron orbit is also quantized. So electrons can only exist in certain orbits (sometimes called shells) around the nucleus. Each orbit has an energy given by the Balmer Formula: E n E n 0, n1, 2,3, 2 For Hydrogen: 0 13.6 ev E ev = electron-volt The energy of an electron in a 1.0 Volt potential. n = 1 n = 2 n = 3 n = 4 PHYS 0219 Optical Spectroscopy and Atomic Structure 3
Bohr pictured the electrons as standing waves on a circular string. n = 2 Node Node Node Antinode Antinode 2 2 n = 6 n = 10 n = 20 PHYS 0219 Optical Spectroscopy and Atomic Structure 4
The Hydrogen atom is actually three dimensional, so the standing wave patterns are more complicated than what Bohr imagined. n 1 0 m 0 Schrödinger Equation: 2 2 2 nlm 1 nlm 1 nlm r sin V 2 2 2 r E 2r r r sin sin m r,, R ry, nlm nl l nlm n nlm Many of the energy levels are degenerate, which means that there may be multiple standing waves shapes that all have the same energy. n 2 0 m 0 n 2 1 m 0 n 2 1 m 1 PHYS 0219 Optical Spectroscopy and Atomic Structure 5
PHYS 0219 Optical Spectroscopy and Atomic Structure 6
n 6 1 m 0 PHYS 0219 Optical Spectroscopy and Atomic Structure 7
Energy n, 0 E n 4, E4 E0 16 n 3, E E 9 3 0 Energy Level Diagram e n 2, E E 4 2 0 E E2 E1 E E E 2 2 2 1 e E 3E 4 0 0 0 Energy Absorbed The electron gains this much energy E E1 E2 E E E 2 2 1 2 E 3E 4 0 0 0 Energy Emitted The electron loses this much energy n 1, E E 1 0 To change orbits, an electron must absorb or emit energy exactly equal to the difference in energy between the two orbits. PHYS 0219 Optical Spectroscopy and Atomic Structure 8
Energy n n 4 n 3 e n 2 An electron will emit a photon (particle of light) if it goes from a higher to lower orbit. g The energy of the photon will be exactly equal to the energy difference of the two orbits. The energy lost by the electron is gained by the photon, so E E E E n 1 g i PHYS 0219 Optical Spectroscopy and Atomic Structure 9 f
The energy of a photon is: h = Plank s constant h 15 4.136 10 ev s E g hc c = speed of light 15 8 hc 4.136 10 ev s 2.9979 10 m s 1240 ev nm From the previous equation: c 8 2.9979 10 m s E E E g i hc E E 1 1 E n n n n f 0 0 2 2 0 2 2 i f f i = wavelength 1 E 0 1 1 hc n n 2 2 f i Rydberg constant: R E0 13.6 ev 1 hc 1240 ev nm 91.18 nm This is the wavelength of an electron going from infinity to the ground state. PHYS 0219 Optical Spectroscopy and Atomic Structure 10
Example: An electron drops from the third energy level to the second energy level. What is the wavelength of the photon emitted? 1 E 0 1 1 hc n n 2 2 f i 1 1 1 1 1 1 1 2 2 91.18 nm 2 3 91.18 nm 4 9 1 3 1.52310 1 The initial orbit is n i = 3 and the final orbit is n f = 2. 5 nm nm 66 3 1.523 10 1 nm The emitted photon will appear red. Visible Light Violet 380 nm Red 750 nm PHYS 0219 Optical Spectroscopy and Atomic Structure 11
1 E 0 1 1 hc n n 2 2 f i We can use this equation to calculate the wavelength of light produced by various combinations of initial and final energy levels. These combinations are broken up into series based on the final energy level. Series Lyman Balmer Paschen Brackett Pfund ni n 1 n 2 f f n 3 f n 4 f n 5 f 2 3 4 5 6 7 8 9 10 122 103 97.3 95.0 93.8 93.1 92.6 92.3 92.1 656 486 434 410 397 389 384 380 1876 1282 1094 1005 955 923 902 4052 2626 2166 1945 1818 1737 7460 4654 3741 3297 3039 Note that only the Balmer series produces lines with visible wavelengths. Violet 380 nm Visible Light Red 750 nm PHYS 0219 Optical Spectroscopy and Atomic Structure 12
1 1 Eg E n n 0 2 2 f i You will plot: E g versus 1 n 2 i E g hc slope E 0 intercept E n E 0 0 2 f 4 PHYS 0219 Optical Spectroscopy and Atomic Structure 13
Diffraction grating maxima from the Physical Optics lab: s ym m y 2 2 m s m sin m 4 3 2 m = 1 m = 1 2 3 4 We can use this equation to determine the wavelength of light based on the measured angle from the center. s = line spacing (distance between lines) m = order of the spectrum s m sin m Second Order m = 2 First Order First Order m = 1 m = 1 Second Order m = 2 PHYS 0219 Optical Spectroscopy and Atomic Structure 14
Emission Lines Wavelengths of light emitted by electrons going from higher to lower orbits. Doublet Lines Second Order First Order First Order Second Order Mercury (Hg) Spectrum Second Order First Order First Order Second Order Hydrogen (H) Spectrum PHYS 0219 Optical Spectroscopy and Atomic Structure 15
Top View Source Collimator Collimator Telescope Graduated circle for measuring angle Prism Table Diffraction Grating The Optical Spectroscope Eyepiece Telescope m s m sin m PHYS 0219 Optical Spectroscopy and Atomic Structure 16
Example: If the diffraction grating has 600 lines per mm, what are the wavelengths of the following measured angles? s 3 1 10 m 1667 10 9 m 1667 nm 600 lines 600 lines mm First order 1 23.2 1 17.0 1 15.1 1667 nm sin 23.2 656 nm 1 1667 nm sin17.0 486 nm 1 1667 nm sin15.1 434 nm 1 Second order 2 52.0 2 35.7 2 31.4 1667 nm sin52.0 656 nm 2 1667 nm sin35.7 486 nm 2 1667 nm sin31.4 434 nm 2 PHYS 0219 Optical Spectroscopy and Atomic Structure 17
Optical Spectroscopy and Atomic Structure 1. Setup the Optical Spectroscope (The TA will demonstrate the procedure). 2. Find the ranges of colors (blue, green and red) in the continuous spectrum. 3. Measure the emission lines of Mercury (Hg) to calibrate the diffraction grating. 4. Measure the emission lines of the Hydrogen (H) spectrum. 5. Plot photon energy versus 1/n 2 i to determine the ground state energy. PHYS 0219 Optical Spectroscopy and Atomic Structure 18