Answer
$XeF_2$
Work Step by Step
Atomic weights (g/mol): $Xe: 131.29,\ F: 18.998$
Molar mass $F_2$: 38.00 g/mol
Mass of Xe: 0.526 g
Mass of the product: 0.678 g
Mass of fluorine $F_2$: 0.678 - 0.526 = 0.152 g
Number of moles:
Xe: $0.526/131.29=3.99\times10^{-3}\ mol$
$F_2$: $0.152/38.00=4.00\times10^{-3}\ mol\ F_2 = 8.0\times10^{-3}\ mol\ F$
Normalizing by the smallest amount of moles:
Xe: 1.0
F: 2.0
Empirical formula of the product: $XeF_2$