How can I quantitative define barium in barium peroxide?

Answer 1

Wet chemistry: dissolve a known quantity, precipitate the Barium as sulphate, and weigh the precipitate.

Instrumental chemistry:
Atomic absorption or emission spetrometry from a solution with known mass of BaO2 (and impurities)
Directly by X-ray resonance spectrometry (e.g. with hand-held instruments).