Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.
•• Consider an electron in an external magnetic f of 1.0 T, and recall that the energy of an electron in magnetic field is given by Eq. (9.27), as E = ±μBB.(a) Make a plot of the ratio of the probability that the electron’s moment is aligned with the field (the low-energy state) to the probability that it is anti-aligned (the high-energy state) versus the absolute temperature T. (b) What is the ratio at room temperature? (c) How low does the temperature have to be in order for this ratio to be 2?
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