Elements with atomic numbers from \(Z\) = \(87\) to \(Z\) = \(114\) are present in the \(7^{ th}\) period of the periodic table. Thus, the element with \(Z\) = \(114\) is present in the \(7 ^{th}\) period of the periodic table.
In the \(7^{ th}\) period, first two elements with \(Z\) = \(87\) and \(Z\)= \(88\) are \(s\)-block elements, the next \(14\) elements excluding \(Z\) = \(89\) i.e., those with \(Z\) = \(90\)- \(103\) are \(f\) - block elements, ten elements with \(Z\) = \(89\) and \(Z\) = \(104 - 112\) are \(d\) - block elements, and the elements with \(Z\) = \(113\) \(- 118\) are \(p\) - block elements.
Therefore, the element with \(Z\) = \(114 \) is the second \(p\) - block element in the \(7^{ th}\) period.
Thus, the element with \(Z\) = \(114\) is present in the \(7 ^{th}\) period and \(14^{ th}\) group of the periodic table.