Chemistry: Principles and Practice
Chemistry: Principles and Practice
3rd Edition
ISBN: 9780534420123
Author: Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Publisher: Cengage Learning
bartleby

Videos

Question
Book Icon
Chapter 7, Problem 7.67QE
Interpretation Introduction

Interpretation:

The wavelength (nm) of the line in spectrum of Li2+ ion that results from transition of an electron from Bohr orbit with n equals to 3 to n equals to 1 has to be determined. Also, the spectrum region of electromagnetic radiation has to be identified.

Concept Introduction:

The wave nature of any light can be described by its frequency, wavelength, and amplitude. The wavelength (λ, lambda) of the light is defined as the distance between two successive peaks. Its SI unit is meter. The frequency (v) is defined as the number of waves that can pass through the one point in 1 second. Its SI unit is s1. The amplitude (A) of the light wave is maximum height of a wave.

The relation between frequency (v) and wavelength (λ) of the light is as follows:

  v=cλ        (1)

Here, c is the speed of light and its value is 3.00×108 m/s.

The relation between the energy (E) of a photon and frequency (v) is as follows:

  E=hv        (2)

Here, h is known as Plank’s constant and its value is 6.626×1034 Js.

The expression to calculate the energy of each wave function for any atomic species with one electron is as follows:

  En=2.18×1018Z2 Jn2        (3)

Here,

Z is the nuclear charge or number of protons in nucleus of atomic species.

n is the principal quantum number for Bohr orbit.

Expert Solution & Answer
Check Mark

Answer to Problem 7.67QE

The wavelength of the line of hydrogen spectrum for a given transition is 11.4 nm and spectrum region is far ultraviolet.

Explanation of Solution

Substitute 3 for n and 3 for Z in equation (3).

  E3=2.18×1018(3)2 J(3)2=2.18×1018 J

Substitute 1 for n and 3 for Z in equation (3).

  E1=2.18×1018(3)2 J(1)2=1.96×1017 J

The expression to calculate the energy released in the transition from n equals to 3 to 1 is as follows:

  ΔE(31)=E1E3        (4)

Substitute 1.96×1017 J for E1 and 2.18×1018 J for E3 in equation (4).

  ΔE(31)=1.96×1017 J(2.18×1018 J)=1.74×1017 J

Therefore, the energy released in the given transition is 1.74×1017 J.

Substitute cλ for v in equation (2).

  E=h(cλ)        (5)

Rearrange equation (5) to calculate the value of λ as follows:

  λ=hcE        (6)

Substitute 1.74×1017 J for E, 6.626×1034 Js for h, and 3.00×108 m/s for c in equation (6).

  λ=(6.626×1034 Js)(3.00×108 m/s)1.74×1017 J=(1.14×108 m)(1 nm109 m)=11.4 nm

Since the wavelength of transition is 11.4 nm, therefore, the spectrum region of this electromagnetic radiation is far ultraviolet.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 7 Solutions

Chemistry: Principles and Practice

Ch. 7 - Prob. 7.11QECh. 7 - Prob. 7.12QECh. 7 - Why is the Heisenberg uncertainty principle an...Ch. 7 - Prob. 7.14QECh. 7 - Prob. 7.15QECh. 7 - Prob. 7.16QECh. 7 - Prob. 7.17QECh. 7 - Prob. 7.18QECh. 7 - Prob. 7.19QECh. 7 - Prob. 7.20QECh. 7 - Prob. 7.21QECh. 7 - Prob. 7.22QECh. 7 - An AM radio station broadcasts at a frequency of...Ch. 7 - An FM radio station broadcasts at a frequency of...Ch. 7 - Prob. 7.25QECh. 7 - Prob. 7.26QECh. 7 - Prob. 7.27QECh. 7 - Prob. 7.28QECh. 7 - This laser emits green light with a wavelength of...Ch. 7 - Prob. 7.30QECh. 7 - What is the energy (in kJ) of 1 mol of photons...Ch. 7 - Prob. 7.32QECh. 7 - Prob. 7.33QECh. 7 - Prob. 7.34QECh. 7 - Prob. 7.35QECh. 7 - Prob. 7.36QECh. 7 - Prob. 7.37QECh. 7 - Prob. 7.38QECh. 7 - Prob. 7.39QECh. 7 - Prob. 7.40QECh. 7 - Prob. 7.41QECh. 7 - Prob. 7.42QECh. 7 - Prob. 7.43QECh. 7 - Prob. 7.44QECh. 7 - Prob. 7.45QECh. 7 - Prob. 7.46QECh. 7 - Prob. 7.47QECh. 7 - Prob. 7.48QECh. 7 - Prob. 7.49QECh. 7 - Prob. 7.50QECh. 7 - Prob. 7.51QECh. 7 - Prob. 7.52QECh. 7 - Prob. 7.53QECh. 7 - Prob. 7.54QECh. 7 - (a) How many subshells are present in the n = 4...Ch. 7 - Prob. 7.56QECh. 7 - Prob. 7.57QECh. 7 - Prob. 7.58QECh. 7 - In what region of space is the probability of...Ch. 7 - Prob. 7.60QECh. 7 - Prob. 7.61QECh. 7 - Prob. 7.62QECh. 7 - Sketch an orbital contour that is expected for an...Ch. 7 - Prob. 7.64QECh. 7 - Prob. 7.65QECh. 7 - Prob. 7.66QECh. 7 - Prob. 7.67QECh. 7 - Prob. 7.68QECh. 7 - Prob. 7.69QECh. 7 - Prob. 7.70QECh. 7 - Prob. 7.71QECh. 7 - Prob. 7.72QECh. 7 - Prob. 7.73QECh. 7 - Prob. 7.74QECh. 7 - Prob. 7.75QECh. 7 - Prob. 7.76QECh. 7 - Prob. 7.77QECh. 7 - Prob. 7.78QECh. 7 - Prob. 7.79QECh. 7 - What are the four quantum numbers of the highest...Ch. 7 - Prob. 7.81QECh. 7 - Prob. 7.82QECh. 7 - Prob. 7.83QECh. 7 - Prob. 7.84QECh. 7 - Prob. 7.85QECh. 7 - Prob. 7.86QECh. 7 - Prob. 7.87QECh. 7 - Prob. 7.88QECh. 7 - Prob. 7.89QECh. 7 - Prob. 7.90QECh. 7 - Prob. 7.91QECh. 7 - Prob. 7.92QECh. 7 - Prob. 7.93QECh. 7 - Prob. 7.94QECh. 7 - Prob. 7.95QECh. 7 - Prob. 7.96QECh. 7 - Prob. 7.97QECh. 7 - Use the aufbau procedure to obtain the electron...Ch. 7 - Prob. 7.99QECh. 7 - Prob. 7.100QECh. 7 - Prob. 7.101QECh. 7 - Prob. 7.102QECh. 7 - Prob. 7.103QECh. 7 - A baseball weighs 142 g. A professional pitcher...
Knowledge Booster
Background pattern image
Chemistry
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Text book image
General Chemistry - Standalone book (MindTap Cour...
Chemistry
ISBN:9781305580343
Author:Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; Darrell
Publisher:Cengage Learning
Text book image
Chemistry & Chemical Reactivity
Chemistry
ISBN:9781133949640
Author:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher:Cengage Learning
Text book image
Chemistry & Chemical Reactivity
Chemistry
ISBN:9781337399074
Author:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher:Cengage Learning
Text book image
Chemistry for Engineering Students
Chemistry
ISBN:9781337398909
Author:Lawrence S. Brown, Tom Holme
Publisher:Cengage Learning
Text book image
Chemistry: The Molecular Science
Chemistry
ISBN:9781285199047
Author:John W. Moore, Conrad L. Stanitski
Publisher:Cengage Learning
Text book image
Chemistry: Principles and Practice
Chemistry
ISBN:9780534420123
Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Publisher:Cengage Learning
Quantum Numbers, Atomic Orbitals, and Electron Configurations; Author: Professor Dave Explains;https://www.youtube.com/watch?v=Aoi4j8es4gQ;License: Standard YouTube License, CC-BY
QUANTUM MECHANICAL MODEL/Atomic Structure-21E; Author: H to O Chemistry;https://www.youtube.com/watch?v=mYHNUy5hPQE;License: Standard YouTube License, CC-BY