A lanthanide ion A ⁴⁺ has no electrons in its 4 f subshell. Another lanthanide ion B ²⁺ has an exactly half-filled 4 f subshell. The atomic numbers of the elements A and B are, respectively:

Step-by-step solution

The general electronic configuration of lanthanides involves the Xenon core (atomic number 54 ). For a lanthanide ion, the number of electrons in the 4 f subshell is given by: Number of 4 f electrons = Z - 54 - charge For ion A ⁴⁺ , the 4 f subshell is empty ( 0 electrons): 0 = Z_ A - 54 - 4 Z_ A = 58 For ion B ²⁺ , the 4 f subshell is exactly half-filled ( 7 electrons): 7 = Z_ B - 54 - 2 Z_ B = 63 Thus, the atomic numbers of A and B are 58 and 63 , respectively. Answer: 58 and 63