ph2a_quiz3

# ph2a_quiz3 - Principal The potential energy of an electron...

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PROBLEM 1 A "phased-array" of radio antennae can be electronically "pointed" by introducing regular phase delays between successive antennae. Assume that the system operates at frequency ν and wavelength λ . The antenna are "line" shaped, much longer than a single wavelength in the dimension out of the plane. (a) [2 pts] Determine the smallest phase delay Δϕ (in radians) that causes the antennae to direct its transmitted beam into the angle θ , in terms of θ , λ , and d. (b) [2 pts] Does the antenna direct radio beams into only one angle? If not, give an expression for the other angles. (c) [1 pt] The wave generator is replaced by a wave received that sums the waves from each individual antenna element. Describe any other changes that would have to be made to use the antenna to receive radiation from angle θ as depicted in the figure.

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PROBLEM 2 [5 points] The size of the Hydrogen atom can be estimated from the Heisenberg Uncertainty
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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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ph2a_quiz3 - Principal The potential energy of an electron...

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