Explanation:

The group number of an element is determined by the number of valence electrons in the outermost shell of its atom.

- Valence electrons are the electrons in the outermost energy level of an atom that are involved in chemical bonding.
- The electronic configuration given [Xe]4F145S2 belongs to the element Gadolinium (Gd) which has an atomic number of 64.
- To determine the number of valence electrons for Gd, we need to look at the electron configuration of the atom.

The electron configuration of Gd can be written as:

1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 5s2 5p6 4f7 5d1 6s2

- The outermost energy level for Gd is the 6s subshell.
- The electron configuration for the 6s subshell is 6s2.
- Therefore, Gd has 2 valence electrons in its outermost shell.

- The group number of an element is determined by the number of valence electrons in the outermost shell of its atom.
- The elements in the periodic table are arranged in groups based on their valence electrons.
- Since Gd has 2 valence electrons in its outermost shell, it belongs to group 2.

However, it should be noted that for some elements, the group number may not directly correspond to the number of valence electrons in the outermost shell. This is due to the unique electronic configurations of these elements.