Among the following pairs of orbitals which orbital will experience the larger effective nuclear charge? (i) 2s and 3s, (ii) 4d and 4f, (iii) 3d and 3p.

To determine which orbital experiences a larger effective nuclear charge (Z_eff), we need to consider the concept of shielding and penetration. The effective nuclear charge is the net positive charge experienced by an electron in an atom, accounting for the repulsion from other electrons. Generally, electrons in orbitals that are closer to the nucleus experience a higher Z_eff due to less shielding from other electrons. Let’s analyze each pair of orbitals you've mentioned.

Understanding Effective Nuclear Charge

The effective nuclear charge can be calculated using the formula:

Z_eff = Z - S

Where:

• Z is the actual nuclear charge (the number of protons in the nucleus).
• S is the shielding constant, which represents the extent to which other electrons shield the nuclear charge.

Comparing the Orbital Pairs

1. 2s and 3s

The 2s orbital is closer to the nucleus than the 3s orbital. Electrons in the 2s orbital experience less shielding from other electrons compared to those in the 3s orbital. Therefore, the 2s orbital will experience a larger effective nuclear charge than the 3s orbital.

2. 4d and 4f

In this case, both orbitals are in the same principal energy level (n=4), but the 4d orbital is lower in energy and closer to the nucleus than the 4f orbital. The 4f electrons experience more shielding from the inner electrons (especially the 4d electrons), resulting in a lower effective nuclear charge for the 4f orbital. Thus, the 4d orbital experiences a larger effective nuclear charge than the 4f orbital.

3d and 3p

Here, the 3d orbital is more shielded by the 3s and 3p electrons than the 3p orbital is shielded by the 3s electrons. The 3p electrons are closer to the nucleus and experience less shielding from other electrons. Consequently, the 3p orbital will experience a larger effective nuclear charge compared to the 3d orbital.

Summary of Findings

To summarize the comparisons:

• Between 2s and 3s, the 2s experiences a larger Z_eff.
• Between 4d and 4f, the 4d experiences a larger Z_eff.
• Between 3d and 3p, the 3p experiences a larger Z_eff.

In essence, the closer an orbital is to the nucleus, the greater the effective nuclear charge it experiences due to reduced shielding from other electrons. This principle is fundamental in understanding electron behavior and chemical bonding in atoms.