Physics 214: Common Formulae and Constants in Physics, Study notes of Quantum Physics

Download Physics 214: Common Formulae and Constants in Physics and more Study notes Quantum Physics in PDF only on Docsity! Physics 214 Common Formulae: will be provided on exams 1 1/11/2007 SI Prefixes Power Prefix Symbol 109 Giga G 106 Mega M 103 Kilo k 100 10-3 Milli m 10-6 Micro µ 10-9 Nano n 10-12 Pico p Conversion Constants and Physical Data speed of light c = 2.998 × 108 m / s Planck constant h = 6.626 × 10-34 J·s = 4.135 × 10-15 eV·s Planck constant / 2π =ℏ 1.054 × 10-34 J·s = 0.658 × 10-15 eV·s electron charge e = 1.602 × 10-19 C energy conversion 1 eV = 1.602 × 10-19 J conversion constant h c = 1240 eV·nm= 1.986× 10-25 J-m useful combination h2/2me = 1.505 eV nm 2 Bohr radius 2 2(4 ) / o o e a m eℏπε= = 0.05292 nm Rydberg energy 4 2 2/ 2(4 ) e o hcR m e ℏπε∞ = = 13.606 eV Coulomb constant 1/ (4 ) o κ πε= = 8.99 × 109 N·m2 / C2 Avagadro constant NA = 6.022 × 1023 / mole electron mass me = 9.109 × 10 –31 kg = 0.511 MeV/c2 proton mass mp = 1.673 × 10 –27 kg = 938.3 MeV/c2 neutron mass mn = 1.675 × 10 –27 kg = 939.6 MeV/c2 hydrogen atom mass mH = 1.674 × 10–27 kg Electron magnetic moment µε = 9.2848 × 10-24 J/T = 5.795 × 10-5 eV/T Proton magnetic moment µ p = 1.4106 × 10-26 J/T = 8.804 × 10-8 eV/T Trigonometric identities cos cos 2cos cos 2 2 θ φ θ φθ φ + −   + =         sin sin 2sin cos 2 2 θ φ θ φθ φ + −   + =         cos( ) cos cos sin sinθ φ θ φ θ φ+ = − sin( ) sin cos cos sinθ φ θ φ θ φ+ = + 1 1 2 2 3 3sin( ) sin( ) sin( )A t A t A tω φ ω φ ω φ+ + + = + 2 2 22 cosA B AB Cφ+ + = (φ here is the external angle) Interference: Slits, Holes, etc Far-field pathlength difference: 1 2 sinr r dδ θ≡ − ≈ Phase difference: sin 2 d d d y L φ δ θ θ π λ λ λ λ ≡ = ≈ ≈ i if θ small Principal maxima: max 0,1, 2, ...d sin m mθ λ= ± = Two sources, same I1: 2 14 cos ( / 2)I I φ= where 2 /φ πδ λ= Single slit: sina aδ θ= sin 2 a a a a y L δβ θ θ π λ λ λ λ ≡ = ≈ ≈ minsin with 1, 2, 3...a m mθ λ= ± = Single slit: 2 1 0 sin( / 2) / 2 I I β β   =     where 2 sin /aβ π θ λ= N slit 2 1 sin( / 2) where 2 sin / sin( / 2)N N I I d φ φ π θ λ φ   = =    0 0slit: / hole: 1.22 / ca or Dθ λ θ λ α≈ ≈ ≈ Approx. grating resolution: min 1 Nm λ λ ∆ =