Hand radical on the left - the side-form of 手. Marks 拍 as a hand-action verb: clapping, slapping, patting, taking a photo (拍照, originally 'striking the shutter'). Same radical in 打, 拿, 推, 拉 - almost every manual-action character.
Right side 白 carries the sound: bái → pāi with regular b-/p- alternation. The same phonetic appears in 怕 (pà), 拍 (pāi), 帕 (pà), 迫 (pò) - a tidy b-/p- cluster. Sound only here; no semantic contribution from 'white.'
