This problem is asking for the last orbital filling in the ground state of radium (7s²), iodine (5p⁵), gold (5d¹⁰ 6s¹) and uranium (5f³ 6d¹ 7s²). In such a way, we need to bear to mind their complete electron configurations, however, that would be long an unnecessary process because we can use the attached file for the identification of the orbitals they are in.
Thus, we can find radium in period 7 group 2A, which means the last orbital in its electron configuration is 7s².
Next, we find iodine in period 5 group 7A, which means the last orbital in its electron configuration is 5p⁵.
Then, we find gold in period 6 group 1B, which means the last orbital in its electron configuration is 5d⁹ and in some cases it has two, 5d¹⁰ and 6s¹.
Finally, we find uranium in period 7 group 3B, which means the last orbital in its electron configuration is 5f³, and in some cases we also include 6d¹ and 7s².
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