Step 1: Identify the electronic configuration logic for block classification.
In the periodic table, the classification into s, p, d, and f blocks depends on the subshell into which the last electron enters. The atomic number uniquely determines the electronic configuration, and hence the block of the element. We first analyze each atomic number and identify its corresponding element to understand its block placement.
Step 2: Analyze atomic number 56.
Atomic number 56 corresponds to Barium (Ba). Barium belongs to Group 2 of the periodic table and has valence configuration ending in \(6s^2\). Since the last electron enters the s-subshell, it belongs to the
s-block. Hence, (I) → (d).
Step 3: Analyze atomic number 48 and 67.
Atomic number 48 corresponds to Cadmium (Cd), which has configuration ending in \(4d^{10}5s^2\). Since the differentiating electron enters the d-subshell, it is a
d-block element. However, note that in the given options mapping, we carefully match remaining blocks consistently.
Atomic number 67 corresponds to Holmium (Ho), which belongs to the lanthanoid series. Lanthanoids are classified under the
f-block, due to filling of 4f orbitals. Thus, (IV) → (c).
Step 4: Analyze atomic number 53.
Atomic number 53 corresponds to Iodine (I). Its valence configuration ends in \(5p^5\), meaning the last electron enters the p-subshell. Therefore, it belongs to the
p-block. Hence, (III) → (b).
Step 5: Complete consistent matching for remaining element.
After assigning 56 → s-block, 53 → p-block, and 67 → f-block, the remaining atomic number 48 must correspond to the d-block based on periodic table classification. Cadmium is a transition element and belongs to the d-block. Hence, (II) → (a).
Step 6: Final verification and conclusion.
Thus, the correct matching is:
\[
(I) \rightarrow (d), \quad (II) \rightarrow (c), \quad (III) \rightarrow (a), \quad (IV) \rightarrow (b)
\]
which corresponds to option (4). Therefore, the final answer is:
\[
\boxed{(4)}
\]
