Chemistry Practice Problems Effective Nuclear Charge Practice Problems Solution: Figure shows the radial probability distribution f...

Solution: Figure shows the radial probability distribution functions for the 2s orbitals and 2p orbitals.How would you modify Slater’s rules to adjust for the difference in electronic penetration of the nucleus for the 2s and 2p orbitals?

Problem

Figure shows the radial probability distribution functions for the 2s orbitals and 2p orbitals.

A line graph has distance from the nucleus in angstroms on the X-axis, ranging from 0 to 10 with intervals of 1, and probability on the Y-axis (unscaled, increasing).  Curves are shown for 1s, 2s, and 2p orbitals. The 1s electrons have a sharp, high peak of probability at around 0.5 angstroms then return to near-0 probability by 2.5 angstroms from the nucleus.  1s electrons are much closer to the nucleus — they screen the valence electrons. The 2s electrons have a very small peak at 0.5 angstroms, returning to 0 probability by 1 angstrom; 2s electrons experience greater nuclear attraction than the 2p electrons.  The curve then reaches a broad, medium-height probability at around 2.5 angstroms, before gradually decreasing to near-0 by 7 angstroms. The 2p electrons have a broad, medium-height probability roughly approximating the second portion of the 2s curve, except they peak at around 2 angstroms before gradually decreasing to near-0, again by 7 angstroms.


How would you modify Slater’s rules to adjust for the difference in electronic penetration of the nucleus for the 2s and 2p orbitals?

Solution

We have to explain how we can modify Slater’s rules to adjust for the difference in electronic penetration of the nucleus for the 2s and 2p orbitals.


Slater’s rules allow us to calculate the effective nuclear charge (Zeff) experienced by an electron.

Outer electrons experience less nuclear charge than the inner electrons because inner electrons screen (shield) the outer electrons from the nucleus.

The orbitals that belong to the same energy level (n) are called a groupFor example, 3s, 3p and 3d all belong the the n=3 energy level therefore, they belong within the same group.


Slater’s rules for electrons in s and p orbitals are:

  • Electrons in the same group shield 0.35, except 1s orbital which shields 0.30.
  • Electrons in the n-1 group shield 0.85.
  • Electrons in the n-2 or lower groups shield 1.00.
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