The Best Example of Celestial Bronze Working on Immortals i Could Find

He pulled an arrow from his quiver and turned the razor-sharp tip so it glinted in the firelight. “Celestial bronze, Percy. An immortal weapon. What would happen if you shot this at a human?”
“Nothing,” I said. “It would pass right through.”
“That’s right,” he said. “Humans don’t exist on the same level as the immortals. They can’t even be hurt by our weapons. But you, Percy—you are part god, part human. You live in both worlds. You can be harmed by both, and you can affect both. That’s what makes heroes so special. You carry the hopes of humanity into the realm of the eternal. Monsters never die. They are reborn from the chaos and barbarism that is always bubbling underneath civilization, the very stuff that makes Kronos stronger. They must be defeated again and again, kept at bay. Heroes embody that struggle. You fight the battles humanity must win, every generation, in order to stay human. Do you understand?”

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The Sea of Monsters, Chapter 18