The coordination number of the lanthanide ion in the complex [Eu H2O 8]3+ is 8. This is because there are 8 water molecules H2O surrounding and bonded to the europium Eu ion in the complex.The electronic configuration of the neutral europium Eu atom is [Xe] 4f7 6s2, where [Xe] represents the electron configuration of the noble gas xenon. When the Eu atom loses 3 electrons to form the Eu3+ ion, it loses both 6s electrons and one 4f electron. Therefore, the electronic configuration of the Eu3+ ion is [Xe] 4f6.The coordination number of 8 in the [Eu H2O 8]3+ complex can be explained by the size and electronic configuration of the Eu3+ ion. Lanthanide ions have a high charge density due to their small size and high charge, which leads to strong electrostatic interactions with ligands. In this case, the ligands are water molecules. The 4f orbitals in the Eu3+ ion are compact and do not extend far from the nucleus, so they do not contribute significantly to the bonding with the ligands. The 8 water molecules can effectively surround and bond to the Eu3+ ion, resulting in an octahedral coordination geometry. This coordination number is common for lanthanide ions, as it allows for effective bonding and stabilization of the complex.