USAAAO 2022, II кръг — Задача 1

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

The energies of an electron in a hydrogen atom are given by

En=−13.606 eVn2E_n = -\frac{13.606\ \mathrm{eV}}{n^2}

where n=1,2,3,…n = 1, 2, 3, \ldots represents the principal quantum number of the shell in which the electron is located.

The Ly-α\alpha spectral line is produced when an electron transitions from the n=2n = 2 to the n=1n = 1 energy level. Astronomers observe that the wavelength of the Ly-α\alpha line in a distant receding galaxy’s emission spectrum is Δλ=7.13 nm\Delta\lambda = 7.13\ \mathrm{nm} greater than the value measured in a lab.

Calculate the object’s approximate distance from us in Mpc (assuming Hubble’s constant H0=70 km/s/MpcH_0 = 70\ \mathrm{km/s/Mpc}).

Отговори

Решение

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