USAAAO — 2026 First Round
Questions 7–8
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 proportional to its Schwarzschild radius Rs. 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 P radiated by a black hole scale with its mass M?
Next, interpret the radiated power P from the previous problem as a gradual loss of the black hole’s intrinsic mass-energy E = Mc². Consider the graph of the black hole’s mass versus time. Which of the following best describes the shape of the resulting graph?
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Answer both parts to check. Both must be correct to count as correct.
Source
USAAAO 2026 First Round, Question 7. Question text, choices, and answer were transcribed from the official USAAAO exam and solutions PDFs.