(b) The extrema of ψ2(r) for 0 < r< ∞may be found by squaring the given function, differentiating with respect to r, and setting the result equal to zero: −−−=−1322406()/raaeπwhich has roots at r= 2aand r= 4a. We can verify directly from the plot above that r= 4ais indeed a local maximum of 2002.rAs discussed in part (a), the other root (r= 2a) is a local minimum. (c) Using Eq. 39-43 and Eq. 39-41, the radial probability is Prrrrarae20022002232482./==−FHGIKJ−π(d) Let x = r/a. Then 22/224322003000012(2)(44 )881[4! 4(3!) 4(2!)] 18xxrrPr dredrxx e dxxxx e dxaa∞∞∞∞−−−⎛⎞=−=−+⎜⎟⎝⎠=−+=∫∫∫∫where we have used the integral formula 0∞−z=xe dx nnx!. 54. (a) The plot shown below for |200(r)|2is to be compared with the dot plot of Fig. 39-22. We note that the horizontal axis of our graph is labeled “
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