USAAAO 2022, I кръг — Задача 15

USAAAO 2022 - First Round · 5 февруари 2022 г.

Условие

A star with mass $M$ goes through an energy generating nuclear reaction $4\ {}^1H \rightarrow\ {}^4He + Energy$. Here, the burning efficiency of the p-p(proton-proton) chain is 0.007, meaning that each mass $m$ yields $0.007mc^2$ of energy. Assuming that the has a total available hydrogen mass for nuclear reaction amounts to half of its original mass, and the luminosity($L$) stays constant throughout the burning phase, get an expression of the hydrogen burning lifetime of the star.

(a) $1.625 \times 10^{18}s(\frac{M}{M_{\odot}})^{-2}$

(b) $3.15 \times 10^{14}s(\frac{M}{M_{\odot}})^{-2}$

(c) $1.625 \times 10^{18}s(\frac{M}{M_{\odot}})^{2}$

(d) $3.15 \times 10^{14}s(\frac{M}{M_{\odot}})^{2}$

(e) None of the above

Отговори

Решение

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Оригинал в Архива: usaaao_first_exam_2022_problems.pdf · официални решения: usaaao_first_exam_2022_solutions-1.pdf