To ascertain the veracity of statements concerning elements A', B', C', and D', we consult periodic trends:
- Elements A' and B' are situated in the same period (row). Atomic radius typically diminishes from left to right across a period due to an escalating nuclear charge that draws electrons nearer to the nucleus.
- Elements A', C', and D' reside in the same group (column). Atomic radius generally augments down a group as electron shells are added.
Let us evaluate each option:
- Option A: Atomic Radii Order: \(B' < A' < D' < C'\)
- This is accurate. As A' is positioned to the left of B' within the same period, it follows that \(B' < A'\). Furthermore, with D' and C' located below A', the relationship \(A' < D' < C'\) holds true.
- Option B: Metallic Character Order: \(B' < A' < D' < C'\)
- This is accurate. Metallic character decreases across a period and increases down a group. Consequently, we observe \(B' < A'\) and \(A' < D' < C'\).
- Option C: Element Size: \(D' < C' < B' < A'\)
- This is inaccurate. As previously stated, atomic size increases down a group and decreases across a period.
- Option D: Ionic Radii Order: \(B^{+} < A^{+} < D^{+} < C^{+}\)
- This is accurate, aligning with the general trends of atomic radii and accounting for the influence of ionic charge.
Therefore, the correct selections are: A, B, and D exclusively.