The order (big o) of the operation that determines if an item is in a list in an unsorted, array-based implementation is O(n), where n is the number of elements in the array. This is because in the worst case scenario, the item being searched for may be at the end of the array, requiring a linear search through all elements of the array. Therefore, the time it takes to determine if an item is in the list increases linearly with the size of the array.