Lanthanoid contraction is caused due to:

The imperfect shielding of outer electrons by 4f-electrons from the nuclear charge

The correct answer is option 4. The imperfect shielding of outer electrons by 4f-electrons from the nuclear charge.

Lanthanoid contraction refers to the gradual decrease in the atomic and ionic sizes of the lanthanide elements as you move from Lanthanum \((La)\) to Lutetium \((Lu)\) across the series. This contraction occurs despite the fact that additional electrons are being added to the 4f-orbitals. Here's a detailed explanation of why this happens:

Key Points:

1. Addition of Electrons to 4f Orbitals:

As you move across the lanthanide series from \(La\) to \(Lu\), electrons are added to the 4f orbitals. These orbitals are located in the inner part of the atom and are not very effective at shielding the nuclear charge from the outer electrons.

2. Increasing Nuclear Charge:

The number of protons in the nucleus increases from \(La\) to \(Lu\). This means that the nuclear charge increases as you move across the series. Specifically, the number of protons goes from 57 in Lanthanum to 71 in Lutetium.

3. Imperfect Shielding by 4f Electrons:

The \(4f\) electrons are poor at shielding the nucleus because they are located relatively close to the nucleus and have a complex shape. As a result, they do not shield the outer electrons (which are in higher energy levels) very effectively from the increased nuclear charge. This imperfect shielding means that the effective nuclear charge experienced by the outer electrons increases as you go from \(La\) to \(Lu\).

4. Effect on Atomic and Ionic Radii:

As the effective nuclear charge increases, the attraction between the nucleus and the outer electrons becomes stronger. This increased attraction pulls the outer electrons closer to the nucleus, leading to a decrease in both atomic and ionic radii.

Summary:

Lanthanoid Contraction: It is caused by the increased nuclear charge that is not fully shielded by the additional 4f electrons. This results in a stronger effective nuclear charge felt by the outer electrons, leading to a decrease in the size of the atoms and ions across the lanthanide series.

Incorrect Options:

Appreciable Shielding by 4f Electrons: If the shielding were appreciable, the lanthanides would not contract as much.

Shielding by 5d Electrons: The 5d orbitals are not directly involved in this contraction.

Same Effective Nuclear Charge: The effective nuclear charge actually increases across the series, leading to the contraction.

Thus, the lanthanoid contraction is due to the imperfect shielding of outer electrons by the 4f-electrons from the increasing nuclear charge