Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 28

When an electron falls from \(\mathrm{n}=3\) to \(\mathrm{n}=2\) in a hydrogen atom, what is the value of the energy released, given that \(A\) is the energy needed to remove an electron from the ground state of a hydrogen atom to an infinite distance from the atom? 1\. \(0.14 \mathrm{~A}\) 2\. \(0.17 \mathrm{~A}\) 3\. \(1.00 \mathrm{~A}\) 4\. \(5.00 \mathrm{~A}\)

Short Answer

Expert verified
The energy released is \(0.14 \mathrm{~A}\).

Step by step solution

01

Finding The Energy Difference Formula

The energy difference between two energy levels, n1 and n2, in a hydrogen atom can be found using the Rydberg formula: \[ E = -A \left(\frac{1}{n1^2} - \frac{1}{n2^2} \right) \] In our case, n1 = 2 and n2 = 3, and A is the energy needed to remove an electron from the ground state to an infinite distance from the atom.
02

Substituting The Values

Now, we substitute the values of n1 and n2 into the equation: \[ E = -A \left(\frac{1}{(2)^2} - \frac{1}{(3)^2} \right) \]
03

Simplifying The Equation

Simplify the equation to obtain the energy difference: \[ E = A \left( \frac{1}{4} - \frac{1}{9} \right) \]
04

Finding The Common Denominator

Find a common denominator to further simplify the equation: \[ E = A \left( \frac{9 - 4}{(4)(9)} \right) \]
05

Simplifying The Fractions

Simplify the fractions: \[ E = A \left(\frac{5}{36}\right) \] Now, express the energy released as a fraction of A: \[ \frac{E}{A} = \frac{5}{36} \]
06

Converting To Decimal and Choose the Correct Option

Convert the fraction to a decimal: \[ \frac{5}{36} \approx 0.14 \] Therefore, the energy released is 0.14A. The correct answer is option 1. \(0.14 \mathrm{~A}\).

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Two converging lenses are in contact. If the focal lengths are each \(5 \mathrm{~cm}\), what is the equivalent focal length of the combination? 1\. \(0.1 \mathrm{~cm}\) 2\. \(2.5 \mathrm{~cm}\) 3\. \(5.0 \mathrm{~cm}\) 4\. \(10.0 \mathrm{~cm}\)

The example given in \(\underline{\text { Table } 1}\) of a system exhibiting dipole-dipole interactions shows the molecule \(\mathrm{SO}_2\). What is the shape of this molecule? 1\. Linear 2\. Bent 3\. T-shaped 4\. Trigonal planar

A myopic person's eye has a relaxed focal length of \(1.9 \mathrm{~cm}\). What is the maximum distance from the eye at which she can see an object clearly, and what is the magnification of the lens for an object at this point? A. \(0=1 \mathrm{~cm}, m=-\frac{1}{2}\) B. \(0=38 \mathrm{~cm}, m=-\frac{1}{38}\) C. \(0=38 \mathrm{~cm}, n=-\frac{1}{19}\) D. \(0=50 \mathrm{~cm}, \mathrm{mt}=-\frac{1}{50}\)

The author's statement that selective incapacitation may "end up permitting harmful people from the middle class to evade a sanction that less privileged offenders cannot" (lines 32-34) assumes that: 1\. there are more offenders in the lower class than in the middle class. 2\. the dangerous repeat offenders are lower class and not middle class. 3\. harmful middle class people can use their money to avoid prison. 4\. lower class offenders do not deserve to suffer incarceration.

Opponents of Darwin's theory regarding coral reef transformation would disagree with which of the following statements? 1\. Coral reef's change from fringing reef's to barrier reef's, and then into free-floating atolls. 2\. Atolls are farther from land masses than are barrier reef's. 3\. Fringing reef's inevitably developed into barrier reef's because volcanic islands gradually sank into the ocean. 4\. As a result of the end of the Ice Age, increased expanses of water aided in the transformation of fringing reef's into barrier reef's.
See all solutions

Recommended explanations on English Textbooks

Semiotics

Read Explanation

English Language Study

Read Explanation

Multiple Choice Questions

Read Explanation

Cues and Conventions

Read Explanation

Key Concepts in Language and Linguistics

Read Explanation

Summary Text

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.

Sign-up for free