Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 8: Problem 34

What electron transition in a hydrogen atom, ending in the orbit \(n=3,\) will produce light of wavelength \(1090 \mathrm{nm} ?\)

Short Answer

Expert verified
The electron transition which will produce light of 1090 nm when ending in orbit n=3, begins in orbit \(n=2\).

Step by step solution

01

Convert the Wavelength

Firstly, convert the given wavelength into meters because the Rydberg constant has units of \(m^{-1}\). The wavelength, \(λ\), is given as 1090 nm, which is equal to \(1.090 \times 10^{-6} m\) since 1 nm equals \(1 \times 10^{-9} m\).
02

Substitute in the Rydberg Formula

Next, substitute the converted wavelength and given values into the Rydberg formula. For hydrogen, \(R_H = 1.097 \times 10^7 m^{-1}\) and \(n_2=3\). So, \(1/(1.090 \times 10^{-6} m) = 1.097 \times 10^7 [(1/n_1^2) - (1/3^2)]\).
03

Solve the Equation

Rearrange the equation to solve for \(n_1\), square root the result to find \(n_1\). After calculation, you will find \(n_1=2\).

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

Show that the probability of finding a \(3 d_{x z}\) electron in the \(x y\) plane is zero.

Write an acceptable value for each of the missing quantum numbers. (a) \(n=3, \ell=?, m_{\ell}=2, m_{s}=+\frac{1}{2}\) (b) \(n=?, \ell=2, m_{\ell}=1, m_{s}=-\frac{1}{2}\) (c) \(n=4, \ell=2, m_{\ell}=0, m_{s}=?\) (d) \(n=?, \ell=0, m_{\ell}=?, m_{s}=?\)

On the basis of the periodic table and rules for electron configurations, indicate the number of (a) \(2 p\) electrons in \(\mathrm{N} ;\) (b) \(4 \mathrm{s}\) electrons in \(\mathrm{Rb} ;\) (c) \(4 \mathrm{d}\) electrons in As; (d) \(4 f\) electrons in \(\mathrm{Au} ;\) (e) unpaired electrons in \(\mathrm{Pb} ;\) (f) elements in group 14 of the periodic table; (g) elements in the sixth period of the periodic table.

What is the length of a string that has a standing wave with four nodes (including those at the ends) and \(\lambda=17 \mathrm{cm} ?\)

Without doing detailed calculations, arrange the following electromagnetic radiation sources in order of increasing frequency: (a) a red traffic light, (b) a \(91.9 \mathrm{MHz}\) radio transmitter, (c) light with a frequency of \(3.0 \times 10^{14} \mathrm{s}^{-1}\) (d) light with a wavelength of \(49 \mathrm{nm}\).
See all solutions

Recommended explanations on Chemistry Textbooks

Chemistry Branches

Read Explanation

Inorganic Chemistry

Read Explanation

Chemical Analysis

Read Explanation

Kinetics

Read Explanation

Nuclear Chemistry

Read Explanation

Organic Chemistry

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