Concept:
The discovery of noble gas compounds originated from Neil Bartlett's observation that oxygen could be oxidized by platinum hexafluoride.
This led to the realization that xenon, having a similar ionization enthalpy, might also form compounds with fluorine and platinum hexafluoride.
This was a landmark discovery because noble gases were previously considered completely inert.
Step 1: Analyse Statement I
Bartlett observed:
\[
O_2 + PtF_6
\rightarrow
[O_2]^+[PtF_6]^-
\]
Since xenon possesses a similar ionization energy, he predicted:
\[
Xe + PtF_6
\rightarrow
[Xe]^+[PtF_6]^-
\]
This ultimately led to the synthesis of xenon compounds.
Hence Statement I is correct.
\[
\boxed{\text{Statement I is correct}}
\]
Step 2: Analyse Statement II
First ionization enthalpies:
\[
IE_1(Xe)\approx1170\ \text{kJ mol}^{-1}
\]
\[
IE_1(O_2)\approx1175\ \text{kJ mol}^{-1}
\]
These values are extremely close.
Therefore Statement II is also correct.
\[
\boxed{\text{Statement II is correct}}
\]
Step 3: Final conclusion
Since both statements are true,
\[
\boxed{\text{Both Statements I and II are correct}}
\]
Hence
\[
\boxed{\text{Option (A)}}
\]