How the effective nuclear charge (Zeff) experienced by a valence electron in tin (Sn) compare to the Zeff experienced by a valence electron in tellurium (Te)? Why is this true?
Relative Zeff Explanation of Difference
A) Tin has larger Zeff
Tin is farther to the left on the periodic table, which is the physical reason that it has a larger Zeff.
B) Tin has larger Zeff
Tin has the same number of core electrons as polonium but fewer valence electrons, so there is less repulsion in the valence shell.
C) Tin has smaller Zeff
Tin is farther to the left on the periodic table, which is the physical reason that it has a smaller Zeff.
D) Tin has smaller Zeff
Tin has the same number of core electrons as polonium but fewer protons, so the “net� positive charge attracting valence electrons is smaller.
E) Zeff(Sn) = Zeff(Te)
Tin and tellurium are in the same row of the periodic table, so they have the same effective nuclear charge.ÂÂ
The Correct Answer and Explanation is :
The correct answer is C) Tin has smaller Zeff.
Explanation:
Effective nuclear charge ((Z_\text{eff})) refers to the net positive charge experienced by an electron in an atom. It is calculated as (Z_\text{eff} = Z – S), where (Z) is the atomic number (number of protons) and (S) is the shielding or screening constant due to inner electrons.
Tin (Sn) and tellurium (Te) are in the same period (row) of the periodic table, which means their valence electrons occupy the same principal energy level ((n=5)). However, tellurium is to the right of tin, meaning it has more protons in its nucleus ((Z_\text{Te} = 52) vs. (Z_\text{Sn} = 50)).
- Trend Across a Period: As you move from left to right across a period, (Z_\text{eff}) increases. This is because:
- The number of protons increases, enhancing the nucleus’s positive charge.
- The shielding effect by core electrons remains roughly constant, as the electrons being added are in the same principal energy level and do not contribute significantly to shielding each other.
- Comparison Between Sn and Te:
- Tin has fewer protons than tellurium, so its nucleus exerts a weaker attractive force on its valence electrons. This results in a smaller (Z_\text{eff}).
- Tellurium’s greater nuclear charge more effectively pulls on the valence electrons, overcoming the shielding effect.
- Why Tin Has a Smaller (Z_\text{eff}): Tin’s position farther to the left on the periodic table means it has fewer protons, leading to a smaller net attractive force experienced by its valence electrons compared to tellurium. Therefore, its effective nuclear charge is smaller.
In conclusion, tin has a smaller (Z_\text{eff}) than tellurium because it has fewer protons while having similar shielding effects, resulting in a weaker net pull on its valence electrons.