Electron Shielding and Effective Nuclear Charge

If an electron is far from the nucleus (i.e., if the distance r between the nucleus and the electron is large), then at any given moment, many of the other electrons will be between that electron and the nucleus (Figure 1.1). Hence the electrons will cancel a portion of the positive charge of the nucleus and thereby decrease the attractive interaction between it and the electron farther away. As a result, the electron farther away experiences an effective nuclear charge (Zeff) that is less than the actual nuclear charge Z

. This effect is called electron shielding.

Figure 1.1

: This image shows how inner electrons can shield outer electrons from the nuclear charge.

As the distance between an electron and the nucleus approaches infinity, Zeff approaches a value of 1 because all the other (Z−1) electrons in the neutral atom are, on the average, between it and the nucleus. If, on the other hand, an electron is very close to the nucleus, then at any given moment most of the other electrons are farther from the nucleus and do not shield the nuclear charge. At r≈0, the positive charge experienced by an electron is approximately the full nuclear charge, or Zeff≈Z. At intermediate values of r, the effective nuclear charge is somewhere between 1 and Z:

1≤Zeff≤Z.