Final answer:
Raphael was hired by Pope Julius II to paint the walls of his private library in the Vatican Palace, while Michelangelo painted the Sistine Chapel's ceiling during the same period.
Step-by-step explanation:
Pope Julius II hired Raffaello Sanzio da Urbino, commonly known as Raphael, to paint his private rooms in the Vatican Palace, including the room used as a library. At the same time, in a different part of the Vatican, the legendary Michelangelo was commissioned to paint the ceiling of the Sistine Chapel. Raphael's work in the library included different allegorical frescoes on each wall representing the four branches of human knowledge: philosophy, theology, poetry, and justice. On the other hand, Michelangelo's frescoes on the Sistine Chapel's ceiling depict religious scenes and have also been celebrated for their vibrant colors and masterful use of chiaroscuro.