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ps12 - Homework for Physics 316 Modern Physics...

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Homework for Physics 316, Modern Physics I (Hoffstaetter/Drasco/Thibault) Due Date: Monday, 05/02/05 - 9:55 in 132 Rockefeller Hall Exercise 1: The atomic weight of iron is 55.85, and solid iron has a density of 7 . 8 g/cm 3 . When a strong magnetic field is applied to a sample of iron, the magnetization (or magnetic moment density) reaches a maximum value of 1 . 83 J/T/cm 3 . (a) Assuming that the magnetic moments of all the atoms are parallel, find the magnetic moment of an iron atom. (b) If the alignment is not complete, is your answer to (a) an underestimate or an overestimate of the true value. (from [1,10-7]) Exercise 2: Consider a particle moving in a circle with tangential momentum p t and angular momentum L = rp t . Let Δ s be the statistical spread of its position along the circle and φ be the angular position of the particle. (a) Show that the relation Δ s Δ p t ~ / 2 can be rewritten as Δ φ Δ L ~ / 2. (c) In terms of wave mechanics, estimate the range of angular momenta of wave functions that must
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