Final answer:
Effective nuclear charge (Zeff) is the net positive charge experienced by an electron, calculated as Z - S, where Z is the atomic number and S is the shielding constant. Zeff increases across a period, causing a decrease in the atomic radius despite an increase in the number of electrons.
Step-by-step explanation:
Understanding Effective Nuclear Charge (Zeff)
The concept of effective nuclear charge often symbolized as Zeff, is crucial for explaining various properties of atoms in computational studies. Zeff represents the net positive charge experienced by an electron in a multi-electron atom. The concept becomes important when we want to understand why, despite an increase in the number of electrons across a period, the atomic radius tends to decrease. This is due to the increase in Zeff, which tightly holds the outer electrons closer to the nucleus.
The formula to calculate Zeff is:
Zeff = Z - S
where Z is the atomic number, representing the number of protons in the nucleus, and S is the shielding constant. The shielding constant is essentially an approximation for the effect of electron-electron repulsions that reduce the full nuclear charge experienced by an outer electron. This accounts for the shielding or screen effect by the nonvalence (inner) electrons.
As illustrated in graphs correlating Zeff and atomic number, there is a clear trend across periods in the periodic table. As we move from left to right across a period, Zeff increases due to the addition of protons in the nucleus and the increase in shielding is less significant than the addition of nuclear charge, thus resulting in a smaller covalent radius for elements with more protons.