Effective Nuclear Charge (Zeff)

Effective Nuclear Charge (Zeff)

To understand effective nuclear charge (Zeff), let's consider a concert:

Photo by The Come Up Show / CC BY

• People closer to the stage at a concert are going to be more into it. The music is louder and they really get a close connection with the artist. People in the highest rows in the stadium get less of that connection with the artist performing.
• This helps to explains the concept of nuclear shielding. Inner electrons (or people sitting in the front rows in our example) shield the outer electrons (or people sitting in the highest rows) from the attractive force of the nucleus (or artist in our example)

Effective Nuclear Charge

This is the nuclear charge that is "felt" by a valence electron.

Core Electrons Vs Valence Electrons

Label the core and valence electrons in the diagram below:

• Valence electrons are attracted to the positively charged nucleus BUT valence electrons are repelled by the core electrons
• Note that electrons in the same shell "feel" the same attraction to the nucleus (since they are they same distance from the nucleus, just like how the people in the same row would feel the same connection to the artist)

$\boxed{Z_{eff}=Z-S}$

Zeff is the effective nuclear charge

Z is the atomic number (# of protons)

S is the # of shielding electrons

Are the shielding electrons core electrons or valence electrons? ________

What would be the effective nuclear charge for Lithium?

Photo by Greg Robson / CC BY

The Periodic Trend

• As we move to the right across the periodic table, the # of core electrons stays the same but the # of protons increases. Therefore, Zeff increases.
• With 🡹 protons, can pull the electrons in closer → 🡹 Zeff
• Effects of shielding are less with more protons

• As we move down a group of the periodic table, the # of core shells increases and the valence electrons get further from the nucleus. This increased distance from the nucleus leads to a smaller Zeff.
• 🡻 a group → 🡹 shells
• 🡹 shells → 🡹 shielding
• 🡹 shielding →🡻 Zeff