Q.The bromine atom possesses 35 electrons. It contains 6 electrons in 2p orbital, 6 electrons in 3p orbital and 5 electrons in 4p orbital. Which of these electrons experiences the lowest effective nuclear charge?

The key idea is that effective nuclear charge ($Z_{\text{eff}}$) decreases as the principal quantum number $n$ increases, because outer electrons are more shielded from the nucleus by inner electrons.

Reasoning:

1. All three orbitals are p-orbitals (same subshell type), so shielding per electron is similar — the main difference is the shell number $n$.
2. $Z_{\text{eff}}$ felt by an electron is roughly $Z - S$, where $S$ (shielding constant) increases with the number of inner electrons. Electrons in higher $n$ are farther out and shielded by more core electrons. …

The question is about effective nuclear charge — the net positive charge felt by an electron after accounting for the shielding (or screening) by other electrons. The bromine atom has 35 electrons arranged in shells: 1s, 2s, 2p, 3s, 3p, 4s, 3d, and 4p. You are specifically asked to compare the 2p, 3p, and 4p electrons.

The intuition is simple: electrons in higher principal energy levels (larger $n$) are, on average, farther from the nucleus. They are shielded from the full nuclear charge by the inner electrons. So, the 4p electrons (with $n=4$) should feel a weaker pull from the nucleus than the 3p ($n=3$) or 2p ($n=2$) electrons. Let's confirm this with reasoning.

1. What is effective nuclear charge? The actual nuclear charge is $Z = 35$ for bromine. But each electron does not feel all 35 protons because inner electrons repel it and "block" some of the nuclear attraction. The effective nuclear charge is given by:

where $S$ is the shielding constant (the number of protons screened by other electrons). A larger $S$ means a smaller $Z_{\text{eff}}$.

2. How does shielding vary with $n$?

   Electrons in the same shell (same $n$) shield each other partially, but electrons in inner shells (smaller $n$) are much better at shielding outer electrons. For a given orbital type (p orbital here), as $n$ increases, the electron is farther out and is shielded by all the electrons in lower shells. So $S$ is larger for higher $n$, making $Z_{\text{eff}}$ smaller.

3. Compare the three sets of p electrons:

   • 2p electrons ($n=2$): They are shielded by the 1s electrons (2 electrons) and partially by each other. Their $Z_{\text{eff}}$ is relatively high because they are close to the nucleus.
   • 3p electrons ($n=3$): They are shielded by the 1s, 2s, and 2p electrons (total 10 electrons) plus some from 3s and 3d. Their $Z_{\text{eff}}$ is lower than that of 2p.
   • 4p electrons ($n=4$): They are shielded by all electrons in $n=1,2,3$ shells (28 electrons) plus the 4s electrons. This gives the largest $S$, hence the smallest $Z_{\text{eff}}$.

4. A quantitative check (using Slater's rules):

   Slater's rules provide approximate shielding constants. Bromine's electron configuration is $1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^5$. Slater's grouping treats $(ns,np)$ as one group and $nd$ as a separate group; the rules for an electron in an $ns$/$np$ orbital are:

   • Other electrons in the same $(ns,np)$ group contribute 0.35 each.
   • Electrons with principal quantum number $n-1$ contribute 0.85 each.
   • Electrons with principal quantum number $n-2$ or lower contribute 1.00 each.
   • Electrons further out (higher $n$, or in a higher subshell of the same shell such as $nd$) contribute 0.

   For a 4p electron:

   • Same group (4s and other 4p): 2 (4s) + 4 (other 4p) = 6 electrons. Contribution: $6 \times 0.35 = 2.10$.
   • $n-1$ (all of shell $n=3$: 3s, 3p, and 3d, since all have principal quantum number 3): 2 + 6 + 10 = 18 electrons. Contribution: $18 \times 0.85 = 15.30$.
   • $n-2$ and lower (shells 1 and 2): 2 (1s) + 2 (2s) + 6 (2p) = 10 electrons. Contribution: $10 \times 1.00 = 10.00$. Total $S = 2.10 + 15.30 + 10.00 = 27.40$. So $Z_{\text{eff}} = 35 - 27.40 = 7.60$.

   For a 3p electron:

   • Same group (3s and other 3p only — the 3d electrons are a separate group and, being further out than $(3s,3p)$, contribute 0): 2 (3s) + 5 (other 3p) = 7 electrons. Contribution: $7 \times 0.35 = 2.45$.
   • $n-1$ (shell $n=2$): 2 (2s) + 6 (2p) = 8 electrons. Contribution: $8 \times 0.85 = 6.80$. …