Concept:
The f-block elements consist of two series, the lanthanoids (\(4f\)) and actinoids (\(5f\)), defined by the progressive filling of inner f-subshells.
Their physical and chemical properties exhibit systematic trends across each series governed by shielding effects, metallic bonding, and valence electron availability.
Step 1: Evaluation of Total f-Block Elements:
The lanthanoid series consists of 14 elements (from cerium, \(Z = 58\), to lutetium, \(Z = 71\)) characterized by the progressive filling of the \(4f\) orbitals.
The actinoid series consists of 14 elements (from thorium, \(Z = 90\), to lawrencium, \(Z = 103\)) characterized by the progressive filling of the \(5f\) orbitals.
Together, these two series comprise \(14 + 14 = 28\) elements.
Hence, statement (A) is correct.
Step 2: Physical Hardness of Lanthanoids:
According to NCERT: "The lanthanoids are silvery white soft metals and tarnish rapidly in air. Their hardness increases with increasing atomic number, samarium being steel hard."
The earlier lanthanoids (such as lanthanum, cerium, and praseodymium) are soft and can be cut with a knife.
Therefore, the statement that all the lanthanoids are hard metals is incorrect.
Hence, statement (B) is false.
Step 3: Comparing Actinoid and Lanthanoid Contractions:
The \(5f\) orbitals are more diffuse and extend further in space than \(4f\) orbitals, providing poorer shielding against nuclear charge.
Consequently, the effective nuclear charge increases more rapidly across the actinoid series, leading to an actinoid contraction that is greater from element to element than the lanthanoid contraction.
Hence, statement (C) is correct.
Step 4: Oxidation State Ranges:
In actinoids, the \(5f\), \(6d\), and \(7s\) energy levels are close in energy, allowing valence electrons from all three subshells to participate in bonding and yielding oxidation states up to \(+7\).
In contrast, lanthanoids predominantly show the \(+3\) oxidation state, with only a few showing \(+2\) and \(+4\).
Hence, statement (D) is correct.
Final Answer:
The incorrect statement is (B).