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mexam2 - Quantity Coulombs Constant Electron Mass Electron...

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Quantity Symbol Value Coulombs Constant k C = 1 / 4 π o 8 . 98 × 10 9 Nm 2 / C 2 Electron Mass m e 9 . 1 × 10 - 31 kg Electron Charge e - 1 . 6 × 10 - 19 C Electron Volt eV 1 . 6 × 10 - 19 J Permitivity o 8 . 85 × 10 - 12 C 2 Nm 2 Magnetic Permeability μ o 4 π × 10 - 7 N · A 2 Speed of Light c 3 . 0 × 10 8 m / s Planck’s Constant h 6 . 6 × 10 - 34 m 2 kg / s Integrals Value R -∞ du e - αu 2 p π α R -∞ du u 2 e - αu 2 1 2 α p π α R 0 du u n e - αu n ! α n +1 R du sin 2 ( αu ) u 2 - sin(2 αu ) 4 α R du cos 2 ( αu ) u 2 + sin(2 αu ) 4 α R + 1 2 - 1 2 duu 2 sin 2 ( nπu ) - 6+ n 2 π 2 24 n 2 π 2 n = 2 , 4 , 6 , 8 R + 1 2 - 1 2 duu 2 cos 2 ( nπu ) - 6+ n 2 π 2 24 n 2 π 2 n = 1 , 3 , 5 , 7 R (cos( θ )) α sin( θ ) - 1 α +1 (cos( θ )) α +1 R (sin( θ )) α cos( θ ) +1 α +1 (sin( θ )) α +1
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Problem 1. You have an electron which moves around a proton forming hydrogen. 1. (Symbol) Starting from Newton’s law, the coulomb law, and the Bohr quantization condition for the angular momentum, determine the velocity and radius of the n - th orbit 2. (Symbol) Determine the magnitude of the electric field
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