USAAAO 2026, I кръг — Задача 7

USAAAO 2026 - First Round · 9 февруари 2026 г.

Problem writers

Problem writers: Srihari (Hari) Balaji, Vincent Bian, Ferdinand, Hagan Hensley, Elizabeth Lee, Joe McCarty, Lucas Pinheiro, Feodor Yevtushenko

Условие

Use the following information for Questions 7 and 8. One of Stephen Hawking’s most famous predictions was the existence of Hawking radiation. Specifically, black holes act like thermal blackbodies and thus must emit blackbody radiation. According to Hawking, a black hole radiates a blackbody spectrum with peak wavelength λmax\lambda_{max} proportional to its Schwarzschild radius RsR_s. Treat the surface of the blackbody as being at the black hole’s event horizon.

According to the laws of thermodynamics and blackbody radiation, under this model, how does the power PP radiated by a black hole scale with its mass MM?

(a) P∝M−5P \propto M^{-5}

(b) P∝M−4P \propto M^{-4}

(c) P∝M−3P \propto M^{-3}

(d) P∝M−2P \propto M^{-2}

(e) P∝M−1P \propto M^{-1}

Отговори

Решение

Оригинал в Архива: usaaao_first_exam_2026.pdf · официални решения: usaaao_first_exam_solutions_2026.pdf