Dear student,

For a many electron atom EPE = -<Ze2/r >
Here the brackets represent an average -- we must take an average because the electron does not remain at one fixed value of r .
Earlier, we noted that Eorb = -Ze2/2 <1/r> These averages are dominated by contributions at SMALL r. When r is SMALL,
(1/r) is LARGE; thus, the larger the fraction of its time an electron spends at SMALL r, the MORE NEGATIVE -Ze2/2 <1/r> will be,and the ELECTRON will be "BOUND" MORE TIGHTLY to the nucleus (i.e Eorb will be more NEGATIVE).

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