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Unformatted text preview: Principal. The potential energy of an electron in a Hydrogen atom in a Coulomb field of the proton is V = − ke 2 r while its kinetic energy is as usual given by K = p 2 2 m It can be shown that for the Hydrogen atom the Kinetic energy K is related to the potential energy by K = − 1 2 V Finally, assume that the typical sizes and momenta are approximately equal to the uncertainty in these, i.e., r Δ x and p Δ p . From these starting points, derive an expression for the size of an atom r in terms of the fundamental constants , m e , k , e , and using the values of the constants show that this gives a sensible size for the atom. Values: k = 1 4 πε = 9 × 10 9 C 2 N − 1 m − 2 = 1.055 × 10 − 34 J s m e = 9.1 × 10 − 31 kg e = 1.6 × 10 − 19 C...
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 Spring '09
 DUDKO
 mechanics, Fundamental physics concepts, Hydrogen atom, Heisenberg Uncertainty Principal, regular phase delays, individual antenna element

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