Съдържание

USAAAO 2022, II кръг — Задача 5

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Всички материали от USAAAO 2022

2022 National Astronomy Competition · 10 т.

Instructions (Please Read Carefully)

The top 5 eligible scorers on the NAC will be invited to represent USA at the next IOAA. In order to qualify for the national team, you must be a high school student with US citizenship or permanent residency.

This exam consists of 3 parts: Short Questions, Medium Questions and Long Questions.

The maximum number of points is 200.

The test must be completed within 2.5 hours (150 minutes).

Please solve each problem on a blank piece of paper and mark the number of the problem at the top of the page. The contestant’s full name in capital letters should appear at the top of each solution page. If the contestant uses scratch papers, those should be labeled with the contestant’s name as well and marked as “scratch paper” at the top of the page. Scratch paper will not be graded. Partial credit will be available given that correct and legible work was displayed in the solution.

This is a written exam. Contestants can only use a scientific or graphing calculator for this exam. A table of physical constants will be provided. Discussing the problems with other people is strictly prohibited in any way until the end of the examination period on March 26th. Receiving any external help during the exam is strictly prohibited. This means that the only allowed items are: a calculator, the provided table of constants, a pencil (or pen), an eraser, blank sheets of papers, and the exam. No books or notes are allowed during the exam. Exam is proctored and recorded. You are expected to have your video on at all times.

Условие

There is an electron with its mass $m_e$ that orbits a proton with mass $m_p$ at a radius $r$ . If we only assume the Coloumbic attraction,

(a) Write an expression of the total energy and the orbital momentum of the electron.

(b) Rewrite the expression of the total energy $E$ in terms of the orbital momentum $L$ , both from the part(a).

Use $e$ for the electric charge quantity and assume that $m_p$ is incomparably greater than $m_e$ ( $m_p \gg m_e$ ).

Отговори

Решение

Оригинал в Архива: usaaao_second_exam_2022_problems.pdf · официални решения: usaaao_second_exam_2022_solutions.pdf