/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 62 Assume that a hydrogen atom's el... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 62

Assume that a hydrogen atom's electron has been excited to the \(n=5\) level. How many different wavelengths of light can be emitted as this excited atom loses energy?

Short Answer

Expert verified
The hydrogen atom's electron is excited to the \(n=5\) level and can undergo a series of possible transitions as it loses energy and falls to lower energy levels. By identifying all possible transitions (5 鈫� 4, 5 鈫� 3, 5 鈫� 2, 5 鈫� 1, 4 鈫� 3, 4 鈫� 2, 4 鈫� 1, 3 鈫� 2, 3 鈫� 1, 2 鈫� 1), we find that the excited atom can emit a total of 10 unique wavelengths of light as it loses energy.

Step by step solution

01

Identifying the energy levels in a hydrogen atom

In a hydrogen atom, the energy levels are quantized and are given by the principal quantum number n. The electron in a hydrogen atom can only exist in specific energy levels (n = 1, 2, 3, and so on). In this exercise, the electron is excited to the n=5 level. We will now identify the possible transitions as the electron loses energy and falls to lower energy levels.
02

Identifying the possible transitions

When the electron moves to a lower energy level, it gives off energy in the form of light. The wavelengths of light emitted during these transitions can be found using the formula for the energy difference between two energy levels in a hydrogen atom. The possible transitions for an electron in the n = 5 level are: 1. 5 鈫� 4 2. 5 鈫� 3 3. 5 鈫� 2 4. 5 鈫� 1 However, we should also consider the subsequent transitions when the electron is at the other energy levels: 5. 4 鈫� 3 6. 4 鈫� 2 7. 4 鈫� 1 8. 3 鈫� 2 9. 3 鈫� 1 10. 2 鈫� 1
03

Counting the unique wavelengths

Now that we have identified all possible transitions for the electron, we can count up the unique wavelengths emitted during these transitions: 1. 5 鈫� 4 2. 5 鈫� 3 3. 5 鈫� 2 4. 5 鈫� 1 5. 4 鈫� 3 6. 4 鈫� 2 7. 4 鈫� 1 8. 3 鈫� 2 9. 3 鈫� 1 10. 2 鈫� 1 There are a total of 10 unique wavelengths of light that can be emitted as the excited hydrogen atom loses energy.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The first ionization energies of As and Se are 0.947 and \(0.941 \mathrm{MJ} / \mathrm{mol},\) respectively. Rationalize these values in terms of electron configurations.

Given the valence electron orbital level diagram and the description, identify the element or ion. a. A ground state atom b. An atom in an excited state (assume two electrons occupy the \(1 s\) orbital) c. A ground state ion with a charge of -1

A particle has a velocity that is \(90 . \%\) of the speed of light. If the wavelength of the particle is \(1.5 \times 10^{-15} \mathrm{m},\) what is the mass of the particle?

Which of the following sets of quantum numbers are not allowed? For each incorrect set, state why it is incorrect. a. \(n=3, \ell=3, m_{\ell}=0, m_{s}=-\frac{1}{2}\) b. \(n=4, \ell=3, m_{\ell}=2, m_{s}=-\frac{1}{2}\) c. \(n=4, \ell=1, m_{\ell}=1, m_{s}=+\frac{1}{2}\) d. \(n=2, \ell=1, m_{\ell}=-1, m_{s}=-1\) e. \(n=5, \ell=-4, m_{\ell}=2, m_{s}=+\frac{1}{2}\) f. \(n=3, \ell=1, m_{\ell}=2, m_{s}=-\frac{1}{2}\)

How many valence electrons do each of the following elements have, and what are the specific valence electrons for each element? a. Ca b. O c. element 117 d. In e. Ar f. Bi
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Analysis

Read Explanation

Chemistry Branches

Read Explanation

Nuclear Chemistry

Read Explanation

Physical Chemistry

Read Explanation

The Earths Atmosphere

Read Explanation

Ionic and Molecular Compounds

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.