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Unformatted text preview: 1 Constants to remember 1. Electron and proton mass m e c 2 = 0 . 511MeV m p c 2 = 938 . MeV 2. Speed of sound ( ∼ typical molecular velocity) and light sound ∼ 300m / s c = 3 × 10 8 m / s 3. Typical wavelength of visible light. λ red ∼ 600nm λ blue ∼ 400nm 4. Typical wavelength of X-rays. Energy ∼ 50kilo- Volts 5. 2 π is annoying, often use ~ = h 2 π ~ c = 197eV nm = 1970eV ˚ A (1) 6. The fine structure constant is a pure number and is is the only dimensionless quantity that can be made out ~ ,c and e α EM = e 2 4 π o ~ c ’ 1 137 (2) The coulomb potential between to objects with Z 1 e charge and Z 2 e charge is U = 1 4 π o Z 1 eZ 2 e r (3) = α EM Z 1 Z 2 ~ c r (4) 7. A typical atomic size is 1 a o = ~ m e cα = ~ 2 m e 2 4 π o ∼ . 5 ˚ A 1 ˚ A = 0 . 1nm 8. The picture of the atom is the following (the circle is the electron and the dot is the nucleus) m-15 10 × = 5 A R c e = h/m λ = 0.5 A a Solid Angles 1. For a patch on the sphere of area A , the solid angle is defined as Ω ≡ A r 2 (5) in analogy to θ = s/r . Like radians, the units of solid angle are dimensionless. However, we some- times use the unit ster-radians to denote that a given dimensionless numbers corresponds to a def- inite solid angle. 10/ Google Image Result for http://hyperphysics.phy-astr.gsu.edu/hbase/math/immath/sphel.gif http://images.google.com/imgres?imgurl=http://hyperphysics.phy-ast…ysics%26um%3D1%26hl%3Den%26client%3Dsafari%26rls%3Den-us%26sa%3DG Spherical Polar Coordinates Applications LaPlacian Gradient Divergence Curl Index HyperPhysics **** HyperMath ***** Geometry Go Back Cylindrical Polar Coordinates With the axis of the circular cylinder taken as the z-axis, the perpendicular distance from the cylinder axis is designated by r and the azimuthal angle taken to be f . Applications LaPlacian Gradient Divergence Curl Index FIG. 1: Figure illustrating spherical coordinates and the concept of solid angle. You should be able to show d Ω = sin(Θ) d Θ dφ 2. For a small area dA you should be able to show from the picture below that d Ω = dA r 2 = sin(Θ) d Θ dφ (6) The area of a little patch of area dA on the sphere is dA = r 2 d Ω = r 2 sin(Θ) d Θ dφ (7) The volume of the patch is dV = r 2 d Θ dφdr 3. The integral of some quantity over the sphere is Z sphere d Ω ... = Z π d ΘsinΘ Z 2 π dφ... (8) 4. For a small cylindrical stip as shown below you should be able to show that d Ω = 2 π sin(Θ) d Θ (9) Rutherford Experiments The Rutherford experiments shot α particles ( 4 2 He) onto gold nuclei 197 79 Au. A schematic of the appartus is shown in Fig. 3 1. When alpha ( z α = +2) particles impinge on a nu- cleus of charge + Ze the distance of closest approach D is found by equating the initial kinetic energy with the final potential energy K = 1 2 m α v 2 α = 1 4 π o ( Ze )( z α e ) D (10) 1 2 m α v 2 α = α EM Zz α ~ c D (11) i.e....
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This note was uploaded on 01/25/2012 for the course PHYSICS 251 taught by Professor Staff during the Fall '11 term at SUNY Stony Brook.
- Fall '11