To determine the position and configuration of the element with atomic number $Z = 114$:

1. Identify the preceding Noble Gas: Radon ($^{86}\text{Rn}$) is the noble gas ending the 6th period.
2. Fill orbitals for the 7th period: According to the Aufbau principle, electrons fill the $7s$, $5f$, $6d$, and $7p$ orbitals in that order. $Z = 86$ (Rn) Add 2 electrons to $7s$: $86 + 2 = 88$ Add 14 electrons to $5f$: $88 + 14 = 102$ Add 10 electrons to $6d$: $102 + 10 = 112$
3. Determine valence electrons: We have $114 - 112 = 2$ electrons remaining. These go into the $7p$ orbital.

• Configuration: $[\text{Rn}] 5f^{14} 6d^{10} 7s^2 7p^2$.

4. Identify the Family: The general valence shell configuration $ns^2 np^2$ corresponds to Group 14, which is the Carbon family.