Chemistry & Chemical Reactivity
Chemistry & Chemical Reactivity
10th Edition
ISBN: 9781337399074
Author: John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher: Cengage Learning
bartleby

Videos

Textbook Question
Book Icon
Chapter 6, Problem 54GQ

Excited H atoms have many emission lines. One series of lines, called the Pfund series, occurs in the infrared region. It results when an electron changes from higher energy levels to a level with n = 5. Calculate the wavelength and frequency of the lowest energy line of this series.

Expert Solution & Answer
Check Mark
Interpretation Introduction

Interpretation: The wavelength and frequency of the least energetic in Pfund series of the excited H atom is to be calculated.

Concept introduction:

  • Electronic transitions that take place in excited H atom is,
    1. 1. Lyman series: electronic transitions take place to the n=1 level and it is in ultraviolet region.
  1. 2. Balmer series: electronic transitions take place from n>2 to the n=2 level and it is in visible region.
  2. 3. Ritz-Paschen series: electronic transitions take place from n>3 to the n=3 level and it is in infrared region.
  3. 4. Brackett series: electronic transitions take place from n>4 to the n=4 level.
  4. 5. Pfund series: electronic transitions take place from n>5 to the n=5 level

EnergybetweenthestatesΔE=EfinalEinitial=Rhc(1nfinal21ninitial2)where,R=Rydbergconstanth=Planck'sconstantc=speedoflightn=Principalquantumnumber

As the energy gap between two transition states increases the wavelength of the radiation emitted decreases

  • Planck’s equation,

    E==hcλwhere, E=energyh=Planck'sconstantν=frequency

The energy increases as the wavelength of the light decrease. Also the energy increases as the frequency of the light increases.

  • The frequency of the light is inversely proportional to its wavelength.

  ν=cλwhere, c=speedoflightν=frequencyλ=wavelength

Answer to Problem 54GQ

The wavelength of the least energetic in Pfund series of the excited H atom is 7471.6nm.

The frequency of the least energetic in Pfund series of the excited H atom is 4.012×1013s1.

Explanation of Solution

As the energy gap between two transition states decreases the wavelength of the radiation emitted increases

Hence the line with highest wavelength is produced in Pfund series of H atom when the electronic transitions that take place from the n=6 to the n=5.

Since E=hcλ ,the energy decreases as the wavelength of the light increases. The electronic transitions that taking place from the n=6 to the n=5 has the least energy

The lowest energy line in Pfund series of the excited H atom forms if the transition of electron is from n=6 to the n=5

  R=1.097×107m1h=6.626×10-34J.sc=2.998×108m/sninitial=6nfinal=5

Energy is determined,

EnergybetweenthestatesΔE=EfinalEinitial=Rhc(1nfinal21ninitial2)=1.097×107m1×6.626×1034J.s×2.998×108m/s(152162)=2.6634×1020J/photon

The energy emitted by the photon does not have any sign and absolute value is taken. Hence, the value of energy is 2.6634×1020J/photon

  • The frequency of lowest energy line in Pfund series of the excited H atom is calculated,

According to Planck’s equation,

  E=

Therefore,

  ν=Eh=2.6634×1020J/photon6.626×1034J.s/photon=4.0196×1013s1

The frequency of lowest energy line in Pfund series of the excited H atom is 4.0196×1013s-1

  • The wavelength of lowest energy line in Pfund series of the excited H atom is calculated,

  λ=cν

Substituting the values,

  λ=2.998×108m/s4.0196×1013s1=7.4584×106m=(7.4584×106m)×(1×109nm/m)=7458.4nm

The wavelength of lowest energy line in Pfund series of the excited H atom is 7458.4nm

Conclusion

The wavelength and frequency of the least energetic in Pfund series of the excited H atom is 7471.6nm and 4.012×1013s1 respectively.

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 6 Solutions

Chemistry & Chemical Reactivity

Ch. 6.7 - Helium absorbs light at 587.6 nm. What is the...Ch. 6.7 - Prob. 3.2ACPCh. 6.7 - Prob. 3.3ACPCh. 6.7 - Prob. 3.4ACPCh. 6.7 - Prob. 3.5ACPCh. 6 - Answer the following questions based on Figure...Ch. 6 - Consider the colors of the visible spectrum. (a)...Ch. 6 - Traffic signals are often now made of LEDs...Ch. 6 - Suppose you are standing 225 m from a radio...Ch. 6 - Green light has a wavelength of 5.0 102 nm. What...Ch. 6 - Violet light has wavelength of about 410 nm. What...Ch. 6 - The most prominent line in the emission spectrum...Ch. 6 - The most prominent line in the emission spectrum...Ch. 6 - Place the following types of radiation in order of...Ch. 6 - Place the following types of radiation in order of...Ch. 6 - An energy of 3.3 1019 J/atom is required to cause...Ch. 6 - You are an engineer designing a switch that works...Ch. 6 - The most prominent line in the spectrum of mercury...Ch. 6 - The most prominent line in the spectrum of neon is...Ch. 6 - A line in the Balmer series of emission lines of...Ch. 6 - What are the wavelength and frequency of the...Ch. 6 - Consider only transitions involving the n = 1...Ch. 6 - Consider only transitions involving the n = 1...Ch. 6 - The energy emitted when an electron moves from a...Ch. 6 - If energy is absorbed by a hydrogen atom in its...Ch. 6 - Calculate the wavelength and frequency of light...Ch. 6 - Calculate the wavelength and frequency of light...Ch. 6 - An electron moves with a velocity of 2.5 X 108...Ch. 6 - A beam of electrons (m = 9.11 X 1031 kg/electron)...Ch. 6 - Calculate the wavelength, in nanometers,...Ch. 6 - A rifle bullet (mass = 1.50 g) has a velocity of...Ch. 6 - (a) When n = 4, what are the possible values of ?...Ch. 6 - (a) When n = 4, = 2, and m = 1, to what orbital...Ch. 6 - A possible excited state of the H atom has the...Ch. 6 - A possible excited state for the H atom has an...Ch. 6 - How many subshells occur in the electron shell...Ch. 6 - Prob. 32PSCh. 6 - Explain briefly why each of the following is not a...Ch. 6 - Which of the following represent valid sets of...Ch. 6 - What is the maximum number of orbitals that can be...Ch. 6 - What is the maximum number of orbitals that can be...Ch. 6 - Explain briefly why each of the following is not a...Ch. 6 - Explain briefly why each of the following is not a...Ch. 6 - State which of the following orbitals cannot exist...Ch. 6 - State which of the following orbitals cannot exist...Ch. 6 - Write a complete set of quantum numbers (n, , m)...Ch. 6 - Write a complete set of quantum numbers (n, , and...Ch. 6 - A particular orbital has n = 4 and = 2. What must...Ch. 6 - A given orbital has a magnetic quantum number of m...Ch. 6 - Prob. 45PSCh. 6 - Prob. 46PSCh. 6 - Which of the following are applicable when...Ch. 6 - Prob. 48GQCh. 6 - Give the number of nodal surfaces through the...Ch. 6 - What is the maximum number of s orbitals found in...Ch. 6 - Match the values of l shown in the table with...Ch. 6 - Sketch a picture of the 90% boundary surface of an...Ch. 6 - Complete the following table.Ch. 6 - Excited H atoms have many emission lines. One...Ch. 6 - An advertising sign gives off red light and green...Ch. 6 - Radiation in the ultraviolet region of the...Ch. 6 - A cell phone sends signals at about 850 MHz (where...Ch. 6 - Assume your eyes receive a signal consisting of...Ch. 6 - If sufficient energy is absorbed by an atom, an...Ch. 6 - Suppose hydrogen atoms absorb energy so that...Ch. 6 - Rank the following orbitals in the H atom in order...Ch. 6 - How many orbitals correspond to each of the...Ch. 6 - Cobalt-60 is a radioactive isotope used in...Ch. 6 - Exposure to high doses of microwaves can cause...Ch. 6 - When the Sojourner spacecraft landed on Mars in...Ch. 6 - The most prominent line in the emission spectrum...Ch. 6 - Answer the following questions as a summary quiz...Ch. 6 - Answer the following questions as a summary quiz...Ch. 6 - For an electron in a hydrogen atom, calculate the...Ch. 6 - A solution of KMnO4 absorbs light at 540 nm (page...Ch. 6 - Prob. 71ILCh. 6 - The spectrum shown here is for aspirin. The...Ch. 6 - The infrared spectrum for methanol. CH3OH, is...Ch. 6 - Bohr pictured the electrons of the atom as being...Ch. 6 - Light is given off by a sodium- or...Ch. 6 - Prob. 76SCQCh. 6 - What does wave-particle duality mean? What are its...Ch. 6 - Prob. 79SCQCh. 6 - Suppose you live in a different universe where a...Ch. 6 - A photon with a wavelength of 93.8 nm strikes a...Ch. 6 - Explain why you could or could not measure the...Ch. 6 - Prob. 83SCQ
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
SEE MORE QUESTIONS
Recommended textbooks for you
  • 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 by OpenStax (2015-05-04)
    Chemistry
    ISBN:9781938168390
    Author:Klaus Theopold, Richard H Langley, Paul Flowers, William R. Robinson, Mark Blaser
    Publisher:OpenStax
    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
  • 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
    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
    Chemistry
    ISBN:9781305957404
    Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
    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 by OpenStax (2015-05-04)
Chemistry
ISBN:9781938168390
Author:Klaus Theopold, Richard H Langley, Paul Flowers, William R. Robinson, Mark Blaser
Publisher:OpenStax
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
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
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
Chemistry
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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