Answer
The identity of "Y" is the element: Krypton.
Work Step by Step
$6.02 \times 10^{23}$ atoms = 1 mol of atoms.
If 1 mol of this element has a mass of 83.80 g, then the molar mass for this type of atom is equal to 83.80 g/mol.
Since the atomic weight is numerically equal to the molar mass, this element weighs $83.80$ $u$.
Using a periodic table, we can see that Krypton ("Kr") has exactly this weight.