51. effective nuclear charge is the net positive charge experienced by an electron in a multi - electron…

Answer:

Effective nuclear charge ($Z_{eff}$) is related to electron - shielding and first ionization energy in the following ways:

Electron - shielding occurs when inner - shell electrons shield outer - shell electrons from the full positive charge of the nucleus. The effective nuclear charge experienced by a valence electron is given by the formula $Z_{eff}=Z - S$, where $Z$ is the atomic number (total number of protons in the nucleus) and $S$ is the shielding constant. As the shielding effect increases, $Z_{eff}$ decreases.

First ionization energy ($IE_1$) is the energy required to remove the outermost (valence) electron from a neutral atom in the gaseous state. A higher $Z_{eff}$ means that the valence electron is more strongly attracted to the nucleus, and thus, a higher $IE_1$ is required to remove it.

Trend from left - to - right across a period: As we move from left to right across a period in the periodic table, the atomic number $Z$ increases while the number of inner - shell electrons (which contribute to shielding) remains the same. The increase in $Z$ leads to an increase in the effective nuclear charge experienced by the valence electrons. Since the shielding effect remains relatively constant, the valence electrons are more strongly attracted to the nucleus. This results in an increase in the first ionization energy across a period.

Trend from top - to - bottom down a group: As we move from top to bottom down a group in the periodic table, the number of electron shells increases. The addition of new electron shells leads to an increase in the shielding effect because there are more inner - shell electrons. Although the atomic number $Z$ also increases, the increase in shielding is more significant. As a result, the effective nuclear charge experienced by the valence electrons decreases. This leads to a decrease in the first ionization energy down a group.

Brief Explanations:

Effective nuclear charge is affected by electron - shielding. Higher $Z_{eff}$ means higher first ionization energy. Across a period, $Z_{eff}$ increases due to increasing $Z$ and constant shielding. Down a group, $Z_{eff}$ decreases due to increased shielding outweighing increased $Z$.