Which statement is not correct?

La is actually an element of transition series

The correct answer is option 3. La is actually an element of transition series. 

Let us break down why each statement is correct or incorrect.

1. \(La(OH)_3\) is less basic than \(Lu(OH)_3\):

In the lanthanide series, basicity of the hydroxides generally increases with increasing atomic number. This increase in basicity is due to the decrease in ionic radius as you move from \(La\) to \(Lu\). As the ionic radius decreases, the charge density of the ion increases, leading to stronger attraction of hydroxide ions (OH⁻) and thus more basic behavior.

Therefore, \(La(OH)_3\) (lanthanum hydroxide) is more basic than \(Lu(OH)_3\) (lutetium hydroxide). The statement that \(La(OH)_3\) is less basic than \(Lu(OH)_3\) is not correct.

2. In lanthanide series, ionic radius of \(Ln^{3+}\) ions decreases:

This statement is correct. As you move from Lanthanum \((La)\) to Lutetium \((Lu)\) in the lanthanide series, the ionic radius of the Ln³⁺ ions decreases. This phenomenon is known as lanthanide contraction. The decrease in radius is due to the poor shielding effect of the \(4f\) electrons as the number of protons in the nucleus increases, resulting in a greater effective nuclear charge that pulls the electrons closer.

3. \(La\) is actually an element of transition series:

This statement is incorrect. Lanthanum \((La)\) is not part of the transition series (\(d\)-block elements). Instead, Lanthanum is part of the lanthanide series (\(f\)-block elements), which consists of elements filling the 4f orbitals. The transition series refers to elements in the d-block of the periodic table, such as iron, copper, and zinc.

4. Atomic radius of Zn and Hf are same because of lanthanide contraction:

This statement is approximately correct. Lanthanide contraction refers to the gradual decrease in size of the \(f\)-block elements and their subsequent elements in the periodic table. Due to this contraction, elements such as Zinc \((Zn)\) and Hafnium \((Hf)\) have similar atomic radii despite being in different groups. This similarity in size arises because of the increased nuclear charge and the decrease in the size of the f-block elements, which affects the size of elements that follow them.

Summary:

\(La(OH)_3\) being less basic than \(Lu(OH)_3\) is incorrect because \(La(OH)_3\) is actually more basic. Lanthanide contraction leads to a decrease in the ionic radius of \(Ln^{3+}\) ions as you move from \(La\) to \(Lu\). Lanthanum \((La)\) is part of the lanthanide series, not the transition series. The atomic radius of \(Zn\) and \(Hf\) being similar is a consequence of lanthanide contraction.

The incorrect statement is: "La is actually an element of transition series."