One facet of the central field approximation for many-electronatoms is that inner-shell electrons screen the nuclear charge. Tounderstand how this works quantitatively, first note that theprobability distributions for electrons in different shellsgenerally do not overlap much. For instance, the electrons in the Mshell (n=3) are almost always farther from the nucleus than theelectrons of the K (n=1) and L (n=2) shells. Thus, it is a goodapproximation to assume that the inner shells completely screen thenucleus from the outer shells. For example, if there are tenelectrons altogether in the K and L shells of an atom, then theelectrons in the M shell experience force from a charge of roughlyZ−10, where Z is the charge on the nucleus as an integer multipleof e, the magnitude of the charge on an electron. This is calledthe effective nuclear charge Zeff. Part A In a beryllium atom(Z=4), how many electrons are in the K shell? Part B In xenon(Z=54), what is the effective charge Zeff experienced by anelectron in the M (n=3) shell? Part C How many electrons are therealtogether in the K, L, and M shells of xenon? Recall that for n=3,the orbital quantum number l must be zero, one, or two and that mlcan take any value between postive and negative l. Part D Theenergy for the 5p valence electron in indium (Z=49) is −5.79electron volts. What is the effective nuclear charge Zeffexperienced by this electron?
