To determine the family/group and electronic configuration of the element with atomic number $Z = 114,$ we need to follow these steps:$\\$1. Identify the position of the element in the periodic table:$\\$• The element with $Z = 114$ is known as Flerovium (Fl).$\\$• It is located in the 7th period of the periodic table.$\\$2. Determine the group/family:$\\$• Flerovium is in Group 14 of the periodic table, which is the Carbon family.$\\$3. Determine the electronic configuration:$\\$• The electronic configuration of an element is determined by filling electrons into the atomic orbitals following the Aufbau principle, Hund's rule, and the Pauli exclusion principle.$\\$• For $Z = 114,$ the electrons fill up to the 7p orbital.$\\$4. Write the electronic configuration:$\\$• The electronic configuration of Flerovium is $[Rn]5f^{14}6d^{10}7s^{2}7p^{2}. \\$5. Match with the given options:$\\$• Option 1: Carbon family, $[Rn]5f^{14}6d^{10}7s^{2}7p^{2} \\$• Option 2: Oxygen family, $[Rn]5f^{14}6d^{10}7s^{2}7p^{4} \\$• Option 3: Nitrogen family, $[Rn]5f^{14}6d^{10}7s^{2}7p^{6} \\$• Option 4: Halogen family, $[Rn]5f^{14}6d^{10}7s^{2}7p^{5} \\$The correct option is Option 1, which corresponds to the Carbon family and the electronic configuration $[Rn]5f^{14}6d^{10}7s^{2}7p^{2}. \\$Therefore, the element $Z = 114$ belongs to the Carbon family with the electronic configuration $[Rn]5f^{14}6d^{10}7s^{2}7p^{2}.$