Chemistry: Atoms First
Chemistry: Atoms First
3rd Edition
ISBN: 9781259638138
Author: Julia Burdge, Jason Overby Professor
Publisher: McGraw-Hill Education
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Chapter 3, Problem 3.133QP

When one of helium’s electrons is removed, the resulting species is the helium ion. He+. The He+ ion contains only one electron and is therefore a “hydrogen-like ion.” Calculate the wavelengths, in increasing order, of the first four transitions in the Balmer series of the He+ ion. Compare these wavelengths with the same transitions in an H atom. Comment on the differences. (The Rydberg constant for He is 4.39 × 107 m−1.)

Expert Solution & Answer
Check Mark
Interpretation Introduction

Interpretation:

The wavelengths in the increasing order of the first four transitions in the Balmer series of the He+ ion, comparing these wavelengths with the same transitions in an H atom and the comment on the differences between these wavelengths of He+ ion and H atom which occur in the electromagnetic radiation should be described by applying the Rydberg equation in them.

Concept Introduction:

Absorption refers to how much light can be taken in by the material being measured.

When electromagnetic radiation interacts with matter, atoms and molecules may absorb energy and reach to a higher energy state.  With higher energy, these are in an unstable state.  For returning to their normal (more stable, lower energy) energy state, the atoms and molecules emit radiations in various regions of the electromagnetic spectrum.  The spectrum of radiation emitted by a substance that has absorbed energy is called an emission spectrum.

In 1885, Johann Balmer developed a simple equation which could be used to calculate the wavelengths of the four visible lines in the emission spectrum of hydrogen.  Johannes Rydberg developed Balmer’s equation further, giving an equation which could calculate the visible wavelengths and also those of all hydrogen’s spectral lines.

1λ = R(1n121n22)

This equation is known as the Rydberg equation.  Here, λ is the wavelength of a line in the spectrum; R is the Rydberg constant (1.09737316 × 107 m1 for H atom); and n1 and n2 are positive integers, where n2 > n1.

To find: Calculate the wavelengths in the increasing order of the first four transitions in the Balmer series of the He+ ion, comparing these wavelengths with the same transitions in an H atom and the comment on the differences between these wavelengths of He+ ion and H atom which occur in the electromagnetic radiation

Answer to Problem 3.133QP

The wavelengths of the first four transitions in the Balmer series of the He+ ion are 164 nm, 121 nm, 108 nm and 103 nm whereas for H atom, they are 656 nm, 486 nm, 434 nm and 410 nm.  All the Balmer transitions for He+ are in the ultraviolet region whereas the transitions for H atom are all in the visible region.

Explanation of Solution

When one of helium’s electrons is removed, the resulting species is the helium ion, He+.  The He+ ion contains only one electron and is therefore a “hydrogen-like ion”.  Balmer series corresponds to transitions to = 2 level.  The first four transitions in the Balmer series mean the transitions from = 3, 4, 5 and 6 energy levels to the transition = 2 energy level.  The formula to calculate the wavelength from Rydberg equation is

λ = 1R¥(1n12-1n22)

Here, the Rydberg constant for He is 4.39 × 107 m1.

For the transition = 3  n = 2, the wavelength of the He+ ion is calculated as follows:

λ = 1R¥(1n12-1n22)λ = 14.39 × 107m-1 (132-122)λ = -1.64 × 10-7 m

The negative sign indicates that the emission of light occurs.  Wavelengths are always positive signs.  Here, 1 nm = 109 m

λ = 1.64 × 10-7 mλ = 1.64 × 10-7 m × 10nm1 mλ = 164 nm

For the transition = 3  n = 2, the wavelength of the He+ ion is 164 nm.  Simiarly, for the transition = 4  n = 2, the wavelength of the He+ ion is

λ = 14.39 × 107 m-1(142-122)λ = 121 nm

For the transition = 5  n = 2, the wavelength of the He+ ion is

λ = 14.39 × 107 m-1(152-122)λ = 108 nm

For the transition = 6  n = 2, the wavelength of the He+ ion is

λ = 14.39 × 107 m-1(162-122)λ = 103 nm

The Rydberg constant for H atom is 1.097 × 107 m1.  For the transition = 3  n = 2, the wavelength of the H atom is calculated as follows:

λ = 1R¥(1n12-1n22)λ = 11.097 × 107 m-1(132-122)λ = -6.56 × 10-7 m

The negative sign indicates that the emission of light occurs.  Wavelengths are always positive signs.  Here, 1 nm = 109 m

λ = 6.56 × 10-7 mλ = 6.56 × 10-7m × 109 nm1 mλ = 656 nm

For the transition = 3  n = 2, the wavelength of the H atom is 656 nm.  Simiarly, for the transition = 4  n = 2, the wavelength of the H atom is

λ = 11.097 × 107 m-1(142-122)λ = 486 nm

For the transition = 5  n = 2, the wavelength of the H atom is

λ = 11.097 × 107 m-1 (152-122)λ = 434 nm

For the transition = 6  n = 2, the wavelength of the H atom is

λ = 11.097 × 107 m-1 (162-122)λ = 434 nm

All the Balmer transitions for He+ are in the ultraviolet region whereas the transitions for H atom are all in the visible region.

Conclusion

The wavelengths in the increasing order of the first four transitions in the Balmer series of the He+ ion, comparing these wavelengths with the same transitions in an H atom and the comment on the differences between these wavelengths of He+ ion and H atom which occur in the electromagnetic radiation are described by applying the Rydberg equation in them.

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 3 Solutions

Chemistry: Atoms First

Ch. 3.1 - Arrange the following pairs of charged particles...Ch. 3.2 - One type of laser used in the treatment of...Ch. 3.2 - What is the wavelength (in meters) of an...Ch. 3.2 - What is the frequency (in reciprocal seconds) of...Ch. 3.2 - Which of the following sets of waves best...Ch. 3.2 - Calculate the wavelength (in nanometers) of light...Ch. 3.2 - Prob. 3.2.2SRCh. 3.2 - Prob. 3.2.3SRCh. 3.2 - When traveling through a translucent medium, such...Ch. 3.3 - Calculate the energy (in joules) of (a) a photon...Ch. 3.3 - Calculate the energy (in joules) of (a) a photon...Ch. 3.3 - (a) Calculate the wavelength (in nanometers) of...Ch. 3.3 - Calculate the energy per photon of light with...Ch. 3.3 - Calculate the wavelength (in centimeters) of light...Ch. 3.3 - Calculate the maximum kinetic energy of an...Ch. 3.3 - A clean metal surface is irradiated with light of...Ch. 3.3 - Prob. 3.3.5SRCh. 3.4 - Calculate the wavelength (in nanometers) of the...Ch. 3.4 - What is the wavelength (in nanometers) of a photon...Ch. 3.4 - What is the value of ni for an electron that emits...Ch. 3.4 - For each pair of transitions, determine which one...Ch. 3.4 - Calculate the energy of an electron in the n = 3...Ch. 3.4 - Calculate E of an electron that goes from n = 1 to...Ch. 3.4 - What is the wavelength (in meters) of light...Ch. 3.4 - What wavelength (in nanometers) corresponds to the...Ch. 3.5 - Calculate the de Broglie wavelength of the...Ch. 3.5 - Calculate the de Broglie wavelength (in...Ch. 3.5 - Use Equation 3.11 to calculate the momentum, p...Ch. 3.5 - Consider the impact of early electron diffraction...Ch. 3.5 - Calculate the de Broglie wavelength associated...Ch. 3.5 - At what speed must a helium-4 atom be traveling to...Ch. 3.5 - Determine the minimum speed required for a...Ch. 3.6 - An electron in a hydrogen atom is known to have a...Ch. 3.6 - Prob. 7PPACh. 3.6 - (a) Calculate the minimum uncertainty in the...Ch. 3.6 - Using Equation 3.13, we can calculate the minimum...Ch. 3.6 - What is the minimum uncertainty in the position of...Ch. 3.6 - What is the minimum uncertainty in the position of...Ch. 3.7 - What are the possible values for the magnetic...Ch. 3.7 - Prob. 8PPACh. 3.7 - Prob. 8PPBCh. 3.7 - Prob. 8PPCCh. 3.7 - Prob. 3.7.1SRCh. 3.7 - How many subshells are there in the shell...Ch. 3.7 - What is the total number of orbitals in the shell...Ch. 3.7 - What is the minimum value of the principal quantum...Ch. 3.8 - Prob. 3.9WECh. 3.8 - Prob. 9PPACh. 3.8 - Prob. 9PPBCh. 3.8 - Prob. 9PPCCh. 3.8 - Prob. 3.8.1SRCh. 3.8 - Prob. 3.8.2SRCh. 3.8 - In a hydrogen atom, which orbitals are higher in...Ch. 3.8 - Which of the following sets of quantum numbers, n,...Ch. 3.9 - Write the electron configuration and give the...Ch. 3.9 - Prob. 10PPACh. 3.9 - Write the electron configuration and give the...Ch. 3.9 - Prob. 10PPCCh. 3.9 - Which of the following electron configurations...Ch. 3.9 - Prob. 3.9.2SRCh. 3.9 - Which orbital diagram is collect for the...Ch. 3.10 - Without referring to Figure 3.26, write the...Ch. 3.10 - Prob. 11PPACh. 3.10 - Prob. 11PPBCh. 3.10 - Consider again the alternate universe and its...Ch. 3.10 - Which of the following electron configurations...Ch. 3.10 - Prob. 3.10.2SRCh. 3.10 - Prob. 3.10.3SRCh. 3.10 - Prob. 3.10.4SRCh. 3 - Prob. 3.1KSPCh. 3 - Which of the following electron configurations...Ch. 3 - Prob. 3.3KSPCh. 3 - Prob. 3.4KSPCh. 3 - Define these terms: potential energy, kinetic...Ch. 3 - What are the units for energy commonly employed in...Ch. 3 - A truck initially traveling at 60 km/h is brought...Ch. 3 - Describe the interconversions of forms of energy...Ch. 3 - Determine the kinetic energy of (a) a 1.25-kg mass...Ch. 3 - Determine the kinetic energy of (a) a 29-kg mass...Ch. 3 - Prob. 3.7QPCh. 3 - Determine (a) the velocity of an electron that has...Ch. 3 - Prob. 3.9QPCh. 3 - (a) How much greater is the electrostatic energy...Ch. 3 - Prob. 3.11QPCh. 3 - Prob. 3.12QPCh. 3 - List the types of electromagnetic radiation,...Ch. 3 - Prob. 3.14QPCh. 3 - Prob. 3.15QPCh. 3 - Prob. 3.16QPCh. 3 - The SI unit of time is the second, which is...Ch. 3 - Prob. 3.18QPCh. 3 - Prob. 3.19QPCh. 3 - Four waves represent light in four different...Ch. 3 - Prob. 3.21QPCh. 3 - Prob. 3.22QPCh. 3 - Prob. 3.23QPCh. 3 - What is a photon? What role did Einsteins...Ch. 3 - A photon has a wavelength of 705 nm. Calculate the...Ch. 3 - The blue color of the sky results from the...Ch. 3 - A photon has a frequency of 6.5 109 Hz. (a)...Ch. 3 - Prob. 3.28QPCh. 3 - Calculate the difference in energy (in joules)...Ch. 3 - How much more energy per photon is there in green...Ch. 3 - Prob. 3.31QPCh. 3 - A particular form of electromagnetic radiation has...Ch. 3 - Photosynthesis makes use of visible light to bring...Ch. 3 - The retina of a human eye can detect light when...Ch. 3 - Prob. 3.35QPCh. 3 - The binding energy of magnesium metal is 5.86 ...Ch. 3 - What is the kinetic energy of the ejected electron...Ch. 3 - A red light was shined onto a metal sample and the...Ch. 3 - A photoelectric experiment was performed by...Ch. 3 - Which of the following best explains why we see...Ch. 3 - One way to see the emission spectrum of hydrogen...Ch. 3 - How many lines would we see in the emission...Ch. 3 - For a hydrogen atom in which the electron has been...Ch. 3 - Prob. 3.40QPCh. 3 - Prob. 3.41QPCh. 3 - Briefly describe Bohrs theory of the hydrogen atom...Ch. 3 - Explain the meaning of the negative sign in...Ch. 3 - Consider the following energy levels of a...Ch. 3 - Prob. 3.45QPCh. 3 - Calculate the wavelength (in nanometers) of a...Ch. 3 - Calculate the frequency (hertz) and wavelength...Ch. 3 - What wavelength of light is needed to excite the...Ch. 3 - An electron in the hydrogen atom makes a...Ch. 3 - Explain why elements produce their own...Ch. 3 - Some copper-containing substances emit green light...Ch. 3 - Prob. 3.52QPCh. 3 - Prob. 3.53QPCh. 3 - Prob. 3.54QPCh. 3 - Why is Equation 3.11 meaningful only for...Ch. 3 - Prob. 3.56QPCh. 3 - Thermal neutrons are neutrons that move at speeds...Ch. 3 - Protons can be accelerated to speeds near that of...Ch. 3 - Prob. 3.59QPCh. 3 - What is the de Broglie wavelength (in nanometers)...Ch. 3 - Prob. 3.61QPCh. 3 - Prob. 3.62QPCh. 3 - What are the inadequacies of Bohrs theory?Ch. 3 - What is the Heisenberg uncertainty principle? What...Ch. 3 - Prob. 3.65QPCh. 3 - Prob. 3.66QPCh. 3 - Prob. 3.67QPCh. 3 - The speed of a thermal neutron (see Problem 3.57)...Ch. 3 - Alveoli are tiny sacs of air in the lungs. Their...Ch. 3 - In the beginning of the twentieth century, some...Ch. 3 - Suppose that photons of blue light (430 nm) are...Ch. 3 - Prob. 3.72QPCh. 3 - Prob. 3.73QPCh. 3 - Which of the four quantum numbers (n, , m, ms)...Ch. 3 - Prob. 3.75QPCh. 3 - Prob. 3.76QPCh. 3 - Indicate which of the following sets of three...Ch. 3 - Prob. 3.78QPCh. 3 - Describe the shapes of s, p, and d orbitals. How...Ch. 3 - Prob. 3.80QPCh. 3 - Describe the characteristics of an s orbital, p...Ch. 3 - Why is a boundary surface diagram useful in...Ch. 3 - Prob. 3.83QPCh. 3 - Give the values of the four quantum numbers of an...Ch. 3 - Describe how a 1s orbital and a 2s orbital are...Ch. 3 - Prob. 3.86QPCh. 3 - Prob. 3.87QPCh. 3 - Make a chart of all allowable orbitals in the...Ch. 3 - Prob. 3.89QPCh. 3 - Prob. 3.90QPCh. 3 - A 3s orbital is illustrated here. Using this as a...Ch. 3 - Prob. 3.92QPCh. 3 - Prob. 3.93QPCh. 3 - State the Aufbau principle, and explain the role...Ch. 3 - Indicate the total number of (a) p electrons in N...Ch. 3 - Calculate the total number of electrons that can...Ch. 3 - Determine the total number of electrons that can...Ch. 3 - Determine the maximum number of electrons that can...Ch. 3 - Prob. 3.99QPCh. 3 - The electron configuration of an atom in the...Ch. 3 - List the following atoms in order of increasing...Ch. 3 - Determine the number of unpaired electrons in each...Ch. 3 - Determine the number of impaired electrons in each...Ch. 3 - Determine the number of unpaired electrons in each...Ch. 3 - Prob. 3.105QPCh. 3 - Portions of orbital diagrams representing the...Ch. 3 - Prob. 3.107QPCh. 3 - Prob. 3.108QPCh. 3 - Prob. 3.109QPCh. 3 - Define the following terms and give an example of...Ch. 3 - Explain why the ground-state electron...Ch. 3 - Write the election configuration of a xenon core.Ch. 3 - Comment on the correctness of the following...Ch. 3 - Prob. 3.114QPCh. 3 - Prob. 3.115QPCh. 3 - Write the ground-state electron configurations for...Ch. 3 - Write the ground-state electron configurations for...Ch. 3 - What is the symbol of the element with the...Ch. 3 - Prob. 3.119QPCh. 3 - Prob. 3.120QPCh. 3 - Discuss the current view of the correctness of the...Ch. 3 - Distinguish carefully between the following terms:...Ch. 3 - What is the maximum number of electrons in an atom...Ch. 3 - Prob. 3.124QPCh. 3 - Prob. 3.125QPCh. 3 - A baseball pitchers fastball has been clocked at...Ch. 3 - A ruby laser produces radiation of wavelength 633...Ch. 3 - Four atomic energy levels of an atom are shown...Ch. 3 - Prob. 3.129QPCh. 3 - Spectral lines of the Lyman and Balmer series do...Ch. 3 - Only a fraction of the electric energy supplied to...Ch. 3 - The figure here illustrates a series of...Ch. 3 - When one of heliums electrons is removed, the...Ch. 3 - The retina of a human eye can detect light when...Ch. 3 - An electron in an excited state in a hydrogen atom...Ch. 3 - Prob. 3.136QPCh. 3 - The election configurations described in this...Ch. 3 - Draw the shapes (boundary surfaces) of the...Ch. 3 - Prob. 3.139QPCh. 3 - Consider the graph here. (a) Calculate the binding...Ch. 3 - Scientists have found interstellar hydrogen atoms...Ch. 3 - Ionization energy is the minimum energy required...Ch. 3 - Prob. 3.143QPCh. 3 - Prob. 3.144QPCh. 3 - The cone cells of the human eye are sensitive to...Ch. 3 - (a) An electron in the ground state of the...Ch. 3 - Prob. 3.147QPCh. 3 - Prob. 3.148QPCh. 3 - When an election makes a transition between energy...Ch. 3 - Blackbody radiation is the term used to describe...Ch. 3 - Suppose that photons of red light (675 nm) are...Ch. 3 - In an election microscope, electrons are...Ch. 3 - According to Einsteins special theory of...Ch. 3 - The mathematical equation for studying the...
Knowledge Booster
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
  • Chemistry: Principles and Practice
    Chemistry
    ISBN:9780534420123
    Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
    Publisher:Cengage Learning
    Chemistry: The Molecular Science
    Chemistry
    ISBN:9781285199047
    Author:John W. Moore, Conrad L. Stanitski
    Publisher:Cengage Learning
    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
  • Organic Chemistry
    Chemistry
    ISBN:9781305080485
    Author:John E. McMurry
    Publisher:Cengage Learning
    Principles of Instrumental Analysis
    Chemistry
    ISBN:9781305577213
    Author:Douglas A. Skoog, F. James Holler, Stanley R. Crouch
    Publisher:Cengage Learning
    Chemistry & Chemical Reactivity
    Chemistry
    ISBN:9781133949640
    Author:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
    Publisher:Cengage Learning
  • Chemistry: Principles and Practice
    Chemistry
    ISBN:9780534420123
    Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
    Publisher:Cengage Learning
    Chemistry: The Molecular Science
    Chemistry
    ISBN:9781285199047
    Author:John W. Moore, Conrad L. Stanitski
    Publisher:Cengage Learning
    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
    Organic Chemistry
    Chemistry
    ISBN:9781305080485
    Author:John E. McMurry
    Publisher:Cengage Learning
    Principles of Instrumental Analysis
    Chemistry
    ISBN:9781305577213
    Author:Douglas A. Skoog, F. James Holler, Stanley R. Crouch
    Publisher:Cengage Learning
    Chemistry & Chemical Reactivity
    Chemistry
    ISBN:9781133949640
    Author:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
    Publisher:Cengage Learning
    Quantum Mechanics - Part 1: Crash Course Physics #43; Author: CrashCourse;https://www.youtube.com/watch?v=7kb1VT0J3DE;License: Standard YouTube License, CC-BY