Determine the molecular structure and hybridization of the central atom \(\mathrm{X}\) in the polyatomic ion \(\mathrm{XY}_{3}+\) given the following information: A neutral atom of \(\mathrm{X}\) contains 36 electrons, and the element \(Y\) makes an anion with a \(1-\) charge, which has the electron configuration \(1 s^{2} 2 s^{2} 2 p^{6}\).

From the given information, a neutral atom of X contains 36 electrons. To determine its electron configuration, we'll use the periodic table to find out which element it is. The atomic number of X (number of protons) is equal to the number of electrons. Since there are 36 electrons, X is element 36, or Krypton (Kr). The electron configuration of Kr is [Ar]\(4s^{2} 3d^{10} 4p^{6}\). Now, let's find out which element Y is. We know that Y makes an anion with a \(1-\) charge that has an electron configuration \(1s^{2} 2s^{2} 2p^{6}\). This is the electron configuration of a complete second shell, with 10 electrons. Therefore, Y must be a period 2 element with 9 electrons (since the anion has one extra electron), which is Fluorine (F). The electron configuration of F- would be that of the neutral Neon atom: \(1s^{2} 2s^{2} 2p^{6}\).

Now, let's draw the Lewis structure for the ion XY3+. Since X is the central atom, we'll place it in the center and surround it with three Y atoms. Keep in mind that X has lost one electron to make a \(1+\) charge, so its electron configuration is now [Ar]\(4s^2 3d^{10} 4p^5\). Each F- has one lone pair and one single bond with X. Therefore, the Lewis structure of XY3+ will have X in the center, bonded to three Y atoms, each with three lone pairs.

To determine the hybridization of the central atom X, we will count the number of electron domains (bonding and non-bonding electron pairs) around X. In XY3+, X is bonded to three Y atoms, so there are three bonding electron pairs. Since X has one unpaired electron left in its outer shell after forming the three bonds, it has only one non-bonding electron pair. This means X has a total of four electron domains (three bonding pairs and one non-bonding pair). Based on the number of electron domains, we can determine the hybridization of the central atom. In this case, X (Kr+) has four electron domains, which corresponds to sp3 hybridization. So, the molecular structure of XY3+ is trigonal pyramidal, with the central atom X (Kr+) having sp3 hybridization.