2.28 Explain the concept of effective nuclear charge and how it affects atomic radii and ionization energies.

What is effective nuclear charge (Z*)?

• Effective nuclear charge (Z*) is the net positive charge experienced by an electron in an atom.

• It is calculated as:

  Z* = Z - S

  where Z is the number of protons (nuclear charge) and S is the shielding effect from inner (core) electrons.

How does Z* affect atomic radius?

• As Z* increases, the nucleus pulls electrons closer, decreasing atomic radius.

• Across a Period (→): Z* increases, atomic radius decreases.

• Down a Group (↓): Z* increases slightly, but added electron shells cause atomic radius to increase.

How does Z* affect ionization energy?

• A higher Z* means electrons are held more tightly, making them harder to remove → higher ionization energy.

• Across a Period (→): Z* increases, ionization energy increases.

• Down a Group (↓): Z* increases slightly, but increased shielding makes it easier to remove electrons → ionization energy decreases.

How does Z* compare in Sodium (Na) vs. Fluorine (F)?

• Sodium (Na, Z = 11):

  • Low Z* (strong shielding).

  • Large atomic radius (electrons held loosely).

  • Low ionization energy (easy to remove an electron).

• Fluorine (F, Z = 9):

  • High Z* (weak shielding).

  • Small atomic radius (electrons held tightly).

  • High ionization energy (hard to remove an electron).