Effective nuclear charge and shielding Knowledge-Based Study

Study notes

1. In an atom, the positively charged protons in the nucleus exert an electrostatic attraction on negatively charged electrons. The total positive charge in the nucleus is called the actual nuclear charge, denoted by the atomic number Z.

   However, in multielectron atoms, electrons do not experience this full nuclear charge equally:

   • Core (inner-shell) electrons lie between the nucleus and the outermost electrons.
   • Valence (outer-shell) electrons are repelled by these core electrons.

   This repulsion by inner electrons partially cancels or blocks the attractive pull of the nucleus on the outer electrons. This phenomenon is known as the shielding effect (or screening effect).

   The net positive charge experienced by an electron in a multielectron atom is defined as the effective nuclear charge (Zeff).

   A simplified mathematical model represents this relationship as:

   Zeff = Z − S

   Where:

   • Z is the total atomic number (number of protons in the nucleus).
   • S is the shielding constant, which represents the average number of core electrons between the nucleus and the valence electron.

   For example, a sodium atom (Na, Z = 11) has an electron configuration of 1s2 2s2 2p6 3s1. The 10 core electrons shield the single 3s valence electron. Approximating S ≈ 10, the valence electron experiences an effective nuclear charge of approximately 11 − 10 = +1.

   Understanding how Zeff behaves across the periodic table is fundamental to explaining periodic properties:

   Across a Period (Left to Right)

   Moving from left to right across a period:

   • Each successive element adds one proton to the nucleus (Z increases by 1).
   • Each added electron enters the same principal energy level.
   • Electrons in the same principal energy level provide very poor shielding for each other, meaning the shielding constant (S) increases only slightly.
   • Because Z increases much faster than S, the effective nuclear charge (Zeff) increases significantly across a period.

   Down a Group (Top to Bottom)

   Moving down a column:

   • Both the number of protons and the number of core electron shells increase.
   • The additional inner shells increase the shielding constant (S) at a rate that roughly balances the increase in nuclear charge (Z).
   • Consequently, Zeff felt by the outermost valence electrons remains relatively constant or increases only marginally.

   The magnitude of Zeff strongly dictates other key periodic properties:

   • Atomic Radius: Across a period, as Zeff increases, the valence electrons are pulled more tightly toward the nucleus. This results in a continuous decrease in atomic radius from left to right.
   • First Ionization Energy: A higher Zeff binds valence electrons more strongly. Therefore, removing a valence electron requires progressively more energy, causing first ionization energy to generally increase across a period.

   By contrasting the strong increase of Zeff across a period with the addition of whole energy levels down a group, chemists can predict and explain periodic reactivity and bonding behavior.