Understanding the Problem

We are given that an element has its outermost shell (n) with 2 electrons and the penultimate shell (n-1) with 8 electrons. We need to find the effective nuclear charge (Z_eff) for a valence electron using Slater's Rules.

Step 1: Recall Slater's Rules

Slater's Rules provide a method to calculate the shielding constant (S), which represents how much the inner electrons shield the valence electron from the full nuclear charge (Z). The effective nuclear charge is then given by:

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

where Z is the atomic number and S is the shielding constant.

Step 2: Determine the Atomic Number (Z)

The electronic configuration described is: (n-1)s² (n-1)p⁶ n s². This is the configuration of a Group 2 element (e.g., Magnesium, Z=12).

For Magnesium (Z=12):

• Penultimate shell (n=2) has 8 electrons (2s²2p⁶).
• Outermost shell (n=3) has 2 electrons (3s²).

Thus, Z = 12.

Step 3: Apply Slater's Rules for Shielding Constant (S)

We are calculating S for one valence electron in the ns orbital.

According to Slater's Rules:

1. Electrons in groups higher than the electron in question contribute 0 to S.
2. Electrons in the same group (ns np) contribute 0.35 each (but 0.30 for 1s).
3. Electrons in the (n-1) shell contribute 0.85 each.
4. Electrons in the (n-2) or lower shells contribute 1.00 each.

For our valence electron (3s):

• The other electron in the same 3s orbital (same group) contributes: 1 electron × 0.35 = 0.35
• Electrons in the penultimate shell (n-1 = 2): 8 electrons × 0.85 = 6.80
• Electrons in lower shells (n-2 = 1): 2 electrons × 1.00 = 2.00

Total shielding constant S = 0.35 + 6.80 + 2.00 = 9.15

Step 4: Calculate Effective Nuclear Charge (Z_eff)

Z_eff = Z - S = 12 - 9.15 = 2.85

Final Answer

The effective nuclear charge is $2.85$ unit.

Therefore, the correct option is: 2.85 unit

Related Topics

• Periodic Trends: Effective nuclear charge explains trends like atomic size, ionization energy, and electronegativity across the periodic table.
• Slater's Rules: An empirical set of rules to estimate the shielding of electrons and calculate Z_eff.
• Electronic Configuration: The arrangement of electrons in shells and subshells around the nucleus.

Key Formulae and Theory

Slater's Formula for Z_eff:

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

Shielding Constant (S) Rules Summary:

• Same group (ns, np): 0.35 per electron (except 0.30 for 1s).
• (n-1) shell: 0.85 per electron.
• (n-2) or lower shell: 1.00 per electron.
• Groups higher than n: 0.00 per electron.

Theory: The effective nuclear charge is the net positive charge experienced by an electron in a multi-electron atom. It is less than the actual nuclear charge due to shielding by other electrons. This concept is fundamental to understanding chemical bonding and periodic properties.