Final answer:
Europium has several electron containing orbitals up to 4f, with all but the 4f orbitals fully occupied by paired electrons. It has 6 paired electrons within the 4f subshell, and all seven 4f orbitals are partially filled.
Step-by-step explanation:
To determine how many electron containing orbitals Europium has, we need its electron configuration: [Xe]6s²4f⁷. Orbitals are defined by the principal quantum number (n) and the azimuthal quantum number (l), which indicates the shape (s, p, d, or f). Europium has orbitals from 1s up to 4f represented in its electronic configuration.
Regarding the number of paired electrons in Europium, electrons pair up in all orbitals except the 4f orbitals, which are partially filled. Europium's 4f orbitals have 7 electrons, hence there are 6 paired electrons in the 4f subshell and all other electrons in the inner shells are paired. To find this, we consider the Pauli exclusion principle which states that each orbital can hold 2 electrons with opposite spins.
Europium has partially filled orbitals in its 4f subshell, and since it has 7 electrons in this subshell while a complete f subshell would hold 14 electrons, all the 4f orbitals are partially filled (7 orbitals).