Consider the photographic representations of two Hydrogen-atom wave functions be

Question

Consider the photographic representations of two Hydrogen-atom wave functions below, which represent a cross section of |u_nlm|^2 in a plane passing through the origin. The two states have the same values of 1 and m, the brighter the region, the higher the probability density. Give careful physical arguments that allow you to determine (just from these figures) which (A or B) has the higher energy and why. (N.B. it will get you zero credit to get only the right answer. All credit will be given for your explanation of how you got the answer).

Explanation / Answer

Figures tell us that in case B the electron is spending more time in a distance from the nucleus which is greater than that of case A. So case B corresponds to higher n, and so energy (incresing function of n) is higher in case B.

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