USAAAO 2024, I кръг — Задача 27
USAAAO 2024 - First Round · 10 февруари 2024 г.
Problem writers
Wesley Andrade, Abhay Bestrapalli, Austin Chen, Justin Chen, Ved Gund, Hagan Hensley, Sandesh Kalantre, Evan Kim, David Lee, Joe McCarty, Arjun Patel, Sahil Pontula, Tara Rezaei, Raul Teixeira, Leo Yao, David Zhang
Условие
The Cosmic Microwave Background is made of light that was replied when the Universe first became transparent. It is a blackbody spectrum with temperature equal to the current temperature of the Universe. We observe the peak wavelength of the CMB to be at 1.063 millimeters. When the CMB was released, we can theoretically predict the temperature of the universe to be 3000 Kelvins. How much larger was the density of matter when the CMB was released than now? Select the closest answer.
(a)
(b)
(c)
(d)
(e)
Отговори
- C
Решение
Solution:
We use Wien’s law to find that the temperature of the CMB is 2.726 Kelvin. Then note where a is the scale factor. We find . Now density of matter changes as . Thus the answer is which is closest to
Answer: C
Оригинал в Архива: usaaao_first_exam_2024-3.pdf · официални решения: usaaao_first_exam_2024_solutions-1.pdf